Tanda, Satoshi; Matsuyama, Toyoki; Oda, Migaku; Asano, Yasuhiro; Yakubo, Kousuke
2006-08-01
.]. Nanofibers of hydrogen storage alloy / I. Saita ... [et al.]. Synthesis of stable icosahedral quasicrystals in Zn-Sc based alloys and their magnetic properties / S. Kashimoto and T. Ishimasa. One-armed spiral wave excited by eam pressure in accretion disks in Be/X-Ray binaries / K. Hayasaki and A. T. Okazaki -- IV. Topological defects and excitations. Topological excitations in the ground state of charge density wave systems / P. Monceau. Soliton transport in nanoscale charge-density-wave systems / K. Inagaki, T. Toshima and S. Tanda. Topological defects in triplet superconductors UPt3, Sr[symbol]RuO[symbol], etc. / K. Maki ... [et al.]. Microscopic structure of vortices in type II superconductors / K. Machida ... [et al.]. Microscopic neutron investigation of the Abrikosov state of high-temperature superconductors / J. Mesot. Energy dissipation at nano-scale topological defects of high-Tc superconductors: microwave study / A. Maeda. Pressure induced topological phase transition in the heavy Fermion compound CeAl[symbol] / H. Miyagawa ... [et al.]. Explanation for the unusual orientation of LSCO square vortex lattice in terms of nodal superconductivity / M. Oda. Local electronic states in Bi[symbol]Sr[symbol]CaCu[symbol]O[symbol] / A. Hashimoto ... [et al.] -- V. Topology in quantum phenomena. Topological vortex formation in a Bose-Einstein condensate of alkali-metal atoms / M. Nakahara. Quantum phase transition of [symbol]He confined in nano-porous media / K. Shirahama, K. Yamamoto and Y. Shibayama. A new mean-field theory for Bose-Einstein condensates / T. Kita. Spin current in topological cristals / Y. Asano. Antiferromagnetic defects in non-magnetic hidden order of the heavy-electron system URu[symbol]Si[symbol] / H. Amitsuka, K. Tenya and M. Yokoyama. Magnetic-field dependences of thermodynamic quantities in the vortex state of Type-II superconductors / K. Watanabe, T. Kita and M. Arai. Three-magnon-mediated nuclear spin relaxation in quantum ferrimagnets of topological
Topology-driven magnetic quantum phase transition in topological insulators.
Zhang, Jinsong; Chang, Cui-Zu; Tang, Peizhe; Zhang, Zuocheng; Feng, Xiao; Li, Kang; Wang, Li-Li; Chen, Xi; Liu, Chaoxing; Duan, Wenhui; He, Ke; Xue, Qi-Kun; Ma, Xucun; Wang, Yayu
2013-03-29
The breaking of time reversal symmetry in topological insulators may create previously unknown quantum effects. We observed a magnetic quantum phase transition in Cr-doped Bi2(SexTe1-x)3 topological insulator films grown by means of molecular beam epitaxy. Across the critical point, a topological quantum phase transition is revealed through both angle-resolved photoemission measurements and density functional theory calculations. We present strong evidence that the bulk band topology is the fundamental driving force for the magnetic quantum phase transition. The tunable topological and magnetic properties in this system are well suited for realizing the exotic topological quantum phenomena in magnetic topological insulators.
Quantum gates with topological phases
Ionicioiu, R
2003-01-01
We investigate two models for performing topological quantum gates with the Aharonov-Bohm (AB) and Aharonov-Casher (AC) effects. Topological one- and two-qubit Abelian phases can be enacted with the AB effect using charge qubits, whereas the AC effect can be used to perform all single-qubit gates (Abelian and non-Abelian) for spin qubits. Possible experimental setups suitable for a solid state implementation are briefly discussed.
Robbins, J M
2010-01-01
Quantum eigenstates undergoing cyclic changes acquire a phase factor of geometric origin. This phase, known as the Berry phase, or the geometric phase, has found applications in a wide range of disciplines throughout physics, including atomic and molecular physics, condensed matter physics, optics, and classical dynamics. In this article, the basic theory of the geometric phase is presented along with a number of representative applications. The article begins with an account of the geometric phase for cyclic adiabatic evolutions. An elementary derivation is given along with a worked example for two-state systems. The implications of time-reversal are explained, as is the fundamental connection between the geometric phase and energy level degeneracies. We also discuss methods of experimental observation. A brief account is given of geometric magnetism; this is a Lorenz-like force of geometric origin which appears in the dynamics of slow systems coupled to fast ones. A number of theoretical developments of the...
Symmetric Topological Phases and Tensor Network States
Jiang, Shenghan
Classification and simulation of quantum phases are one of main themes in condensed matter physics. Quantum phases can be distinguished by their symmetrical and topological properties. The interplay between symmetry and topology in condensed matter physics often leads to exotic quantum phases and rich phase diagrams. Famous examples include quantum Hall phases, spin liquids and topological insulators. In this thesis, I present our works toward a more systematically understanding of symmetric topological quantum phases in bosonic systems. In the absence of global symmetries, gapped quantum phases are characterized by topological orders. Topological orders in 2+1D are well studied, while a systematically understanding of topological orders in 3+1D is still lacking. By studying a family of exact solvable models, we find at least some topological orders in 3+1D can be distinguished by braiding phases of loop excitations. In the presence of both global symmetries and topological orders, the interplay between them leads to new phases termed as symmetry enriched topological (SET) phases. We develop a framework to classify a large class of SET phases using tensor networks. For each tensor class, we can write down generic variational wavefunctions. We apply our method to study gapped spin liquids on the kagome lattice, which can be viewed as SET phases of on-site symmetries as well as lattice symmetries. In the absence of topological order, symmetry could protect different topological phases, which are often referred to as symmetry protected topological (SPT) phases. We present systematic constructions of tensor network wavefunctions for bosonic symmetry protected topological (SPT) phases respecting both onsite and spatial symmetries.
Fractional topological phase for entangled qudits
Oxman, L E
2010-01-01
We investigate the topological structure of entangled qudits under unitary local operations. Different sectors are identified in the evolution, and their geometrical and topological aspects are analyzed. The geometric phase is explicitly calculated in terms of the concurrence. As a main result, we predict a fractional topological phase for cyclic evolutions in the multiply connected space of maximally entangled states.
Topological phases: Wormholes in quantum matter
Schoutens, K.
2009-01-01
Proliferation of so-called anyonic defects in a topological phase of quantum matter leads to a critical state that can be visualized as a 'quantum foam', with topology-changing fluctuations on all length scales.
Dimensional Hierarchy of Fermionic Interacting Topological Phases
Queiroz, Raquel; Khalaf, Eslam; Stern, Ady
2016-11-01
We present a dimensional reduction argument to derive the classification reduction of fermionic symmetry protected topological phases in the presence of interactions. The dimensional reduction proceeds by relating the topological character of a d -dimensional system to the number of zero-energy bound states localized at zero-dimensional topological defects present at its surface. This correspondence leads to a general condition for symmetry preserving interactions that render the system topologically trivial, and allows us to explicitly write a quartic interaction to this end. Our reduction shows that all phases with topological invariant smaller than n are topologically distinct, thereby reducing the noninteracting Z classification to Zn.
Dimensional Hierarchy of Fermionic Interacting Topological Phases.
Queiroz, Raquel; Khalaf, Eslam; Stern, Ady
2016-11-11
We present a dimensional reduction argument to derive the classification reduction of fermionic symmetry protected topological phases in the presence of interactions. The dimensional reduction proceeds by relating the topological character of a d-dimensional system to the number of zero-energy bound states localized at zero-dimensional topological defects present at its surface. This correspondence leads to a general condition for symmetry preserving interactions that render the system topologically trivial, and allows us to explicitly write a quartic interaction to this end. Our reduction shows that all phases with topological invariant smaller than n are topologically distinct, thereby reducing the noninteracting Z classification to Z_{n}.
Signature of Topological Phases in Zitterbewegung
Ghosh, S.
2016-09-02
We have studied the Zitterbewegung effect on an infinite two-dimensional sheet with honeycomb lattice. By tuning the perpendicular electric field and the magnetization of the sheet, it can enter different topological phases. We have shown that the phase and magnitude of Zitterbewegung effect, i.e., the jittering motion of electron wavepackets, correlates with the various topological phases. The topological phase diagram can be reconstructed by analyzing these features. Our findings are applicable to materials like silicene, germanene, stanene, etc.
Topological phase transitions in superradiance lattices
Wang, Da-Wei; Yuan, Luqi; Liu, Ren-Bao; Zhu, Shi-Yao
2015-01-01
The discovery of the quantum Hall effect (QHE) reveals a new class of matter phases, topological insulators (TI's), which have been extensively studied in solid-state materials and recently in photonic structures, time-periodic systems and optical lattices of cold atoms. All these topological systems are lattices in real space. Our recent study shows that Scully's timed Dicke states (TDS) can form a superradiance lattice (SL) in momentum space. Here we report the discovery of topological phase transitions in a two-dimensional SL in electromagnetically induced transparency (EIT). By periodically modulating the three EIT coupling fields, we can create a Haldane model with in-situ tunable topological properties. The Chern numbers of the energy bands and hence the topological properties of the SL manifest themselves in the contrast between diffraction signals emitted by superradiant TDS. The topological superradiance lattices (TSL) provide a controllable platform for simulating exotic phenomena in condensed matte...
Fermion path integrals and topological phases
Witten, Edward
2016-07-01
Symmetry-protected topological (SPT) phases of matter have been interpreted in terms of anomalies, and it has been expected that a similar picture should hold for SPT phases with fermions. Here a description is given in detail of what this picture means for phases of quantum matter that can be understood via band theory and free fermions. The main examples considered are time-reversal invariant topological insulators and superconductors in two or three space dimensions. Along the way, the precise meaning of the statement that in the bulk of a 3D topological insulator, the electromagnetic θ angle is equal to π , is clarified.
Topological Phase Transitions and Thouless Pumping of Light in Photonic Lattices
Ke, Yongguan; Mei, Feng; Zhong, Honghua; Kivshar, Yuri S; Lee, Chaohong
2016-01-01
Photonic lattices provide an excellent platform for simulating conventional topological systems, and they can also be explored for the study of novel topological phases. However, a direct measurement of bulk topological invariants remains a great challenge. Here we study topological features of generalized commensurate Aubry-Andre-Harper (AAH) photonic lattices and construct a topological phase diagram by calculating all bulk Chern numbers, and then explore the bulk-edge correspondence by analyzing the topological edge states and their winding numbers. In contrast to incommensurate AAH models, we find that diagonal and off-diagonal commensurate AAH models are not topologically equivalent. In particular, nontrivial topological phases with large Chern numbers and topological phase transitions are possible. By implementing Thouless pumping of light in photonic lattices, we propose a simple scheme to measure the bulk Chern numbers.
Topological Phases of Sound and Light
Peano, V.; Brendel, C.; Schmidt, M.; Marquardt, F.
2015-07-01
Topological states of matter are particularly robust, since they exploit global features of a material's band structure. Topological states have already been observed for electrons, atoms, and photons. It is an outstanding challenge to create a Chern insulator of sound waves in the solid state. In this work, we propose an implementation based on cavity optomechanics in a photonic crystal. The topological properties of the sound waves can be wholly tuned in situ by adjusting the amplitude and frequency of a driving laser that controls the optomechanical interaction between light and sound. The resulting chiral, topologically protected phonon transport can be probed completely optically. Moreover, we identify a regime of strong mixing between photon and phonon excitations, which gives rise to a large set of different topological phases and offers an example of a Chern insulator produced from the interaction between two physically distinct particle species, photons and phonons.
Universalities of thermodynamic signatures in topological phases
Kempkes, S. N.; Quelle, A.; Smith, C. Morais
2016-12-01
Topological insulators (superconductors) are materials that host symmetry-protected metallic edge states in an insulating (superconducting) bulk. Although they are well understood, a thermodynamic description of these materials remained elusive, firstly because the edges yield a non-extensive contribution to the thermodynamic potential, and secondly because topological field theories involve non-local order parameters, and cannot be captured by the Ginzburg-Landau formalism. Recently, this challenge has been overcome: by using Hill thermodynamics to describe the Bernevig-Hughes-Zhang model in two dimensions, it was shown that at the topological phase transition the thermodynamic potential does not scale extensively due to boundary effects. Here, we extend this approach to different topological models in various dimensions (the Kitaev chain and Su-Schrieffer-Heeger model in one dimension, the Kane-Mele model in two dimensions and the Bernevig-Hughes-Zhang model in three dimensions) at zero temperature. Surprisingly, all models exhibit the same universal behavior in the order of the topological-phase transition, depending on the dimension. Moreover, we derive the topological phase diagram at finite temperature using this thermodynamic description, and show that it displays a good agreement with the one calculated from the Uhlmann phase. Our work reveals unexpected universalities and opens the path to a thermodynamic description of systems with a non-local order parameter.
Gauge interactions and topological phases of matter
Tachikawa, Yuji; Yonekura, Kazuya
2016-09-01
We study the effects of strongly coupled gauge interactions on the properties of the topological phases of matter. In particular, we discuss fermionic systems with three spatial dimensions, protected by time-reversal symmetry. We first derive a sufficient condition for the introduction of a dynamical Yang-Mills field to preserve the topological phase of matter, and then show how the massless pions capture in the infrared the topological properties of the fermions in the ultraviolet. Finally, we use the S-duality of calligraphy">N=2 supersymmetric SU(2) gauge theory with N=4 flavors to show that the ν=16 phase of Majorana fermions can be continuously connected to the trivial ν=0 phase.
Topological phase structure of entangled qudits
Khoury, A. Z.; Oxman, L. E.
2014-03-01
We discuss the appearance of fractional topological phases on cyclic evolutions of entangled qudits. The original result reported by Oxman and Khoury [Phys. Rev. Lett. 106, 240503 (2011), 10.1103/PhysRevLett.106.240503] is detailed and extended to qudits of different dimensions. The topological nature of the phase evolution and its restriction to fractional values are related to both the structure of the projective space of states and entanglement. For maximally entangled states of qudits with the same Hilbert-space dimension, the fractional geometric phases are the only ones attainable under local SU(d) operations, an effect that can be experimentally observed through conditional interference.
Phase Slips in Topological Superconductor Wire Devices
Goldberg, Samuel; Bergman, Doron; Pekker, David; Refael, Gil
2012-02-01
We make a detailed study of phase slips in topological superconducting wires and devices based on topological wires. We begin by investigating a device composed of a topological superconducting wire connected to a non-topological wire (T-S). In the T-segment only slips of the phase by multiples of 4π are allowed, while in the S-segment slips by 2π are also allowed. We show that near the interface, 2π phase slips are also allowed and we comment on the consequences of such phase slips for the Aharonov-Casher effect. We also consider an implementation of a q-bit consisting of a T-S-T device, where the quantum information is stored in the parity of the two topological segments via the four Majorana modes. We show that the central S-segment of this type of device can support 2π phase-slips which result in the decoherence of the q-bit.
Scaling theory of topological phase transitions
Chen, Wei
2016-02-01
Topologically ordered systems are characterized by topological invariants that are often calculated from the momentum space integration of a certain function that represents the curvature of the many-body state. The curvature function may be Berry curvature, Berry connection, or other quantities depending on the system. Akin to stretching a messy string to reveal the number of knots it contains, a scaling procedure is proposed for the curvature function in inversion symmetric systems, from which the topological phase transition can be identified from the flow of the driving energy parameters that control the topology (hopping, chemical potential, etc) under scaling. At an infinitesimal operation, one obtains the renormalization group (RG) equations for the driving energy parameters. A length scale defined from the curvature function near the gap-closing momentum is suggested to characterize the scale invariance at critical points and fixed points, and displays a universal critical behavior in a variety of systems examined.
Maxwell Duality, Lorentz Invariance, and Topological Phase
Dowling, J P; Franson, J D; Dowling, Jonathan P.; Williams, Colin P.
1999-01-01
We discuss the Maxwell electromagnetic duality relations between the Aharonov-Bohm, Aharonov-Casher, and He-McKellar-Wilkens topological phases, which allows a unified description of all three phenomena. We also elucidate Lorentz transformations that allow these effects to be understood in an intuitive fashion in the rest frame of the moving quantum particle. Finally, we propose a realistic set up for measuring and interpreting the He-McKellar-Wilkens phase directly in an experiment.
Detecting topological phases in cold atoms.
Liu, Xiong-Jun; Law, K T; Ng, T K; Lee, Patrick A
2013-09-20
Chern insulators are band insulators which exhibit a gap in the bulk and gapless excitations in the edge. Detection of Chern insulators is a serious challenge in cold atoms since the Hall transport measurements are technically unrealistic for neutral atoms. By establishing a natural correspondence between the time-reversal invariant topological insulator and the quantum anomalous Hall system, we show for a class of Chern insulators that the topology can be determined by only measuring Bloch eigenstates at highly symmetric points of the Brillouin zone. Furthermore, we introduce two experimental schemes, including the spin-resolved Bloch oscillation, to carry out the measurement. These schemes are highly feasible under realistic experimental conditions. Our results may provide a powerful tool to detect topological phases in cold atoms.
Phase rotation symmetry and the topology of oriented scattering networks
Delplace, Pierre; Fruchart, Michel; Tauber, Clément
2017-05-01
We investigate the topological properties of dynamical states evolving on periodic oriented graphs. This evolution, which encodes the scattering processes occurring at the nodes of the graph, is described by a single-step global operator, in the spirit of the Ho-Chalker model. When the successive scattering events follow a cyclic sequence, the corresponding scattering network can be equivalently described by a discrete time-periodic unitary evolution, in line with Floquet systems. Such systems may present anomalous topological phases where all the first Chern numbers are vanishing, but where protected edge states appear in a finite geometry. To investigate the origin of such anomalous phases, we introduce the phase rotation symmetry, a generalization of usual symmetries which only occurs in unitary systems (as opposed to Hamiltonian systems). Equipped with this new tool, we explore a possible explanation of the pervasiveness of anomalous phases in scattering network models, and we define bulk topological invariants suited to both equivalent descriptions of the network model, which fully capture the topology of the system. We finally show that the two invariants coincide, again through a phase rotation symmetry arising from the particular structure of the network model.
Experimental observation of fractional topological phases with photonic qudits
Matoso, A. A.; Sánchez-Lozano, X.; Pimenta, W. M.; Machado, P.; Marques, B.; Sciarrino, F.; Oxman, L. E.; Khoury, A. Z.; Pádua, S.
2016-11-01
Geometrical and topological phases play a fundamental role in quantum theory. Geometric phases have been proposed as a tool for implementing unitary gates for quantum computation. A fractional topological phase has been recently discovered for bipartite systems. The dimension of the Hilbert space determines the topological phase of entangled qudits under local unitary operations. Here we investigate fractional topological phases acquired by photonic entangled qudits. Photon pairs prepared as spatial qudits are operated inside a Sagnac interferometer and the two-photon interference pattern reveals the topological phase as fringes shifts when local operations are performed. Dimensions d =2 , 3, and 4 were tested, showing the expected theoretical values.
Topological and geometrical aspects of phase transitions
Santos, F. A. N.; Rehn, J. A.; Coutinho-Filho, M. D.
2014-03-01
In the first part of this review, we use a topological approach to describe the frustration- and field-induced phase transitions exhibited by the infinite-range XY model on the AB2 chain, including noncollinear spin structures. For this purpose, we have computed the Euler characteristic, χ, as well as other topological invariants, which are found to behave similarly as a function of the energy level in the context of Morse theory. Our findings and those available in the literature suggest that the cusp-like singularity exhibited by χ at the critical energy, Ec, put together with the divergence of the density of Jacobian's critical points emerge as necessary and sufficient conditions for the occurrence of finite-temperature topology-induced phase transitions. In the second part, we present an alternative solution of the Ising chain in a field under free and periodic boundary conditions, in the microcanonical, canonical, and grand canonical ensembles, from a unified combinatorial and topological perspective. In particular, the computation of the per-site entropy as a function of the energy unveils a residual value for critical values of the magnetic field, a phenomenon for which we provide a topological interpretation and a connection with the Fibonacci sequence. We also show that, in the thermodynamic limit, the per-site microcanonical entropy is equal to the logarithm of the per-site Euler characteristic. Finally, we emphasize that our combinatorial approach to the canonical ensemble allows exact computation of the thermally averaged value (T) of the Euler characteristic; our results show that the conjecture (Tc)= 0, where Tc is the critical temperature, is valid for the Ising chain.
Three lectures on topological phases of matter
Witten, E.
2016-07-01
These notes are based on lectures at the PSSCMP/PiTP summer school that was held at Princeton University and the Institute for Advanced Study in July, 2015. They are devoted largely to topological phases of matter that can be understood in terms of free fermions and band theory. They also contain an introduction to the fractional quantum Hall effect from the point of view of effective field theory.
Quantum Monte Carlo simulation of topological phase transitions
Yamamoto, Arata; Kimura, Taro
2016-12-01
We study the electron-electron interaction effects on topological phase transitions by the ab initio quantum Monte Carlo simulation. We analyze two-dimensional class A topological insulators and three-dimensional Weyl semimetals with the long-range Coulomb interaction. The direct computation of the Chern number shows the electron-electron interaction modifies or extinguishes topological phase transitions.
Quantum Monte Carlo simulation of topological phase transitions
Yamamoto, Arata
2016-01-01
We study the electron-electron interaction effects on topological phase transitions by the ab-initio quantum Monte Carlo simulation. We analyze two-dimensional class A topological insulators and three-dimensional Weyl semimetals with the long-range Coulomb interaction. The direct computation of the Chern number shows the electron-electron interaction modifies or extinguishes topological phase transitions.
Explorations in topology map coloring, surfaces and knots
Gay, David
2013-01-01
Explorations in Topology, Second Edition, provides students a rich experience with low-dimensional topology (map coloring, surfaces, and knots), enhances their geometrical and topological intuition, empowers them with new approaches to solving problems, and provides them with experiences that will help them make sense of future, more formal topology courses. The book's innovative story-line style models the problem-solving process, presents the development of concepts in a natural way, and engages students in meaningful encounters with the material. The updated end-of-chapter investigation
Strain-induced topological quantum phase transition in phosphorene oxide
Kang, Seoung-Hun; Park, Jejune; Woo, Sungjong; Kwon, Young-Kyun
Using ab initio density functional theory, we investigate the structural stability and electronic properties of phosphorene oxides (POx) with different oxygen compositions x. A variety of configurations are modeled and optimized geometrically to search for the equilibrium structure for each x value. Our electronic structure calculations on the equilibrium configuration obtained for each x reveal that the band gap tends to increase with the oxygen composition of x 0.5. We further explore the strain effect on the electronic structure of the fully oxidized phosphorene, PO, with x = 1. At a particular strain without spin-orbit coupling (SOC) is observed a band gap closure near the Γ point in the k space. We further find the strain in tandem with SOC induces an interesting band inversion with a reopened very small band gap (5 meV), and thus gives rise to a topological quantum phase transition from a normal insulator to a topological insulator. Such a topological phase transition is confirmed by the wave function analysis and the band topology identified by the Z2 invariant calculation.
Baruselli, Pier Paolo; Vojta, Matthias
2015-10-09
SmB_{6} was recently proposed to be both a strong topological insulator and a topological crystalline insulator. For this and related cubic topological Kondo insulators, we prove the existence of four different topological phases, distinguished by the sign of mirror Chern numbers. We characterize these phases in terms of simple observables, and we provide concrete tight-binding models for each phase. Based on theoretical and experimental results for SmB_{6} we conclude that it realizes the phase with C_{k_{z}=0}^{+}=+2, C_{k_{z}=π}^{+}=+1, C_{k_{x}=k_{y}}^{+}=-1, and we propose a corresponding minimal model.
Exploring topological edge states in photonic quasicrystals
Baboux, F; Lemaître, A; Gomez, C; Galopin, E; Gratiet, L Le; Sagnes, I; Amo, A; Bloch, J; Akkermans, E
2016-01-01
We experimentally investigate the topological properties of quasiperiodic chains using cavity polaritons confined in a potential following the Fibonacci sequence. Edge states forming in the gaps of a fractal energy spectrum are imaged both in real and momentum space. These edge states periodically traverse the gaps when varying a structural degree of freedom $\\phi$ of the Fibonacci sequence. The period and direction of the traverses are directly related to the Chern numbers assigned to each gap by the gap-labeling theorem. Additionally, we show that the Chern numbers determine the spatial symmetry properties of the edge states. These results highlight the potential of cavity polaritons to emulate nontrivial topological properties in a controlled environment.
Three-qubit topological phase on entangled photon pairs
Johansson, Markus; Singh, Kuldip; Sjöqvist, Erik
2013-01-01
We propose an experiment to observe the topological phases associated with cyclic evolutions, generated by local SU(2) operations, on three-qubit entangled states prepared on different degrees of freedom of entangled photon pairs. The topological phases reveal the nontrivial topological structure of the local SU(2) orbits. We describe how to prepare states showing different topological phases, and discuss their relation to entanglement. In particular, the presence of a $\\pi/2$ phase shift is a signature of genuine tripartite entanglement in the sense that it does not exist for two-qubit systems.
Floquet topological phases protected by time glide symmetry
Morimoto, Takahiro; Po, Hoi Chun; Vishwanath, Ashvin
2017-05-01
We study Floquet topological phases in periodically driven systems that are protected by "time glide symmetry", a combination of reflection and half time period translation. Time glide symmetry is an analog of glide symmetry with partial time translation replacing the partial space translation and, hence, is an intrinsically dynamical symmetry which may be engineered in periodically driven systems by exploiting the controllability of driving. We present lattice models of time glide symmetric Floquet topological insulators in two and three dimensions. The topological numbers characterizing those Floquet topological phases are derived from the half-period time-evolution operator along with time glide operator. Moreover, we classify Floquet topological phases protected by time glide symmetry in general dimensions using a Clifford algebra approach. The obtained classification table is similar to that for topological crystalline insulators protected by static reflection symmetry, but shows nontrivial entries in different combination of symmetries, which clarifies that time glide symmetric Floquet topological phases are a distinct set of topological phases from topological crystalline insulators. We also classify Floquet topological phases with "time screw symmetry", defined as a twofold spatial rotation accompanied by half-period time translation.
Exploring the topology of dynamical reconstructions
Garland, Joshua; Bradley, Elizabeth; Meiss, James D.
2016-11-01
Computing the state-space topology of a dynamical system from scalar data requires accurate reconstruction of those dynamics and construction of an appropriate simplicial complex from the results. The reconstruction process involves a number of free parameters and the computation of homology for a large number of simplices can be expensive. This paper is a study of how to compute the homology efficiently and effectively without a full (diffeomorphic) reconstruction. Using trajectories from the classic Lorenz system, we reconstruct the dynamics using the method of delays, then build a simplicial complex whose vertices are a small subset of the data: the "witness complex". Surprisingly, we find that the witness complex correctly resolves the homology of the underlying invariant set from noisy samples of that set even if the reconstruction dimension is well below the thresholds for assuring topological conjugacy between the true and reconstructed dynamics that are specified in the embedding theorems. We conjecture that this is because the requirements for reconstructing homology are less stringent: a homeomorphism is sufficient-as opposed to a diffeomorphism, as is necessary for the full dynamics. We provide preliminary evidence that a homeomorphism, in the form of a delay-coordinate reconstruction map, may exist at a lower dimension than that required to achieve an embedding.
Topological gapless phases in nonsymmorphic antiferromagnets
Brzezicki, Wojciech; Cuoco, Mario
2017-04-01
We investigate the nature of the electronic states in a variety of nonsymmorphic collinear antiferromagnets with glide reflection symmetry, a combination of mirror and half-lattice translation. In particular, the study refers to a class of systems with two-band itinerant electrons that are spin-orbit coupled and interacting with a magnetic background having a zigzag pattern. We describe the symmetry properties of the model system by focusing on the role of nonsymmorphic transformations arising from the antiferromagnetic structure of the spin ordering. Gapless phases with Dirac points having different types of symmetry-protection as well as electronic structures with triple and quadruple band-crossing points are obtained. A glide semimetal is shown to be converted into a gapless phase with Dirac points protected by inversion and time-inversion symmetry combination. Interestingly, we find a relation between the states in the glide sectors that provides a general mechanism to get multiple band touching points. The split of the multiple Fermi points drives the transition from a point node to a line node semimetal or to a metal with nontrivial winding around the Fermi pockets and an electronic structure that is tied to the presence of glide symmetric Dirac points. Besides a new perspective of ordered states in complex materials, our findings indicate relevant paths to topological gapless phases and edge states in a wide class of magnetic systems.
Sinai Diffusion at Quasi-1D Topological Phase Transitions
Bagrets, Dmitry; Altland, Alexander; Kamenev, Alex
2016-11-01
We consider critical quantum transport in disordered topological quantum wires at the transition between phases with different topological indices. Focusing on the example of thermal transport in class D ("Majorana") quantum wires, we identify a transport universality class distinguished for anomalous retardation in the propagation of excitations—a quantum generalization of Sinai diffusion. We discuss the expected manifestations of this transport mechanism for heat propagation in topological superconductors near criticality and provide a microscopic theory explaining the phenomenon.
Topological phases in the Neuberger-Dirac operator
Chiu, Ting-Wai
1999-12-01
The response of the Neuberger-Dirac fermion operator D=1+V in the topologically nontrivial background gauge field depends on the negative mass parameter m0 in the Wilson-Dirac fermion operator Dw, which enters D through the unitary operator V=Dw(D†wDw)-1/2. We classify the topological phases of D by comparing its index to the topological charge of the smooth background gauge field. An exact discrete symmetry in the topological phase diagram is proved for any gauge configurations. A formula for the index of D in each topological phase is derived by obtaining the total chiral charge of the zero modes in the exact solution of the free fermion propagator.
Wilson loops and topological phases in closed string theory
Cartas-Fuentevilla, R
2004-01-01
Using covariant phase space formulations for the natural topological invariants associated with the world-surface in closed string theory, we find that certain Wilson loops defined on the world-surface and that preserve topological invariance, correspond to wave functionals for the vacuum state with zero energy. The differences and similarities with the 2-dimensional QED proposed by Schwinger early are discussed.
Topological superconducting phase and Majorana bound states in Shiba chains
Pientka, Falko; Peng, Yang; Glazman, Leonid; von Oppen, Felix
2015-12-01
Chains of magnetic adatoms on a conventional superconducting substrate constitute a promising venue for realizing topological superconductivity and Majorana end states. Here, we give a brief overview over recent attempts to describe these systems theoretically, emphasizing how the topological phase emerges from the physics of individual magnetic impurities and their associated Shiba states.
Multifarious topological quantum phase transitions in two-dimensional topological superconductors
Liu, Xiao-Ping; Zhou, Yuan; Wang, Yi-Fei; Gong, Chang-De
2016-06-01
We study the two-dimensional topological superconductors of spinless fermions in a checkerboard-lattice Chern-insulator model. With the short-range p-wave superconducting pairing, multifarious topological quantum phase transitions have been found and several phases with high Chern numbers have been observed. We have established a rich phase diagram for these topological superconducting states. A finite-size checkerboard-lattice cylinder with a harmonic trap potential has been further investigated. Based upon the self-consistent numerical calculations of the Bogoliubov-de Gennes equations, various phase transitions have also been identified at different regions of the system. Multiple pairs of Majorana fermions are found to be well-separated and localized at the phase boundaries between the phases characterized by different Chern numbers.
Multifarious topological quantum phase transitions in two-dimensional topological superconductors
Liu, Xiao-Ping; Zhou, Yuan; Wang, Yi-Fei; Gong, Chang-De
2016-01-01
We study the two-dimensional topological superconductors of spinless fermions in a checkerboard-lattice Chern-insulator model. With the short-range p-wave superconducting pairing, multifarious topological quantum phase transitions have been found and several phases with high Chern numbers have been observed. We have established a rich phase diagram for these topological superconducting states. A finite-size checkerboard-lattice cylinder with a harmonic trap potential has been further investigated. Based upon the self-consistent numerical calculations of the Bogoliubov-de Gennes equations, various phase transitions have also been identified at different regions of the system. Multiple pairs of Majorana fermions are found to be well-separated and localized at the phase boundaries between the phases characterized by different Chern numbers. PMID:27329219
On topological phases in disordered p-wave superconducting wires
Rieder, Maria-Theresa
2015-07-10
Topological phases of matter have been the subject of intense experimental and theoretical research during the last years. Prominent examples are the Quantum Hall Effect, Topological Insulators or Topological Superconductors. The latter host special excitations, the Majorana states, at their boundaries, which can be thought of as the halves of an electron that can exist separately in this special case. These Majorana states have attracted great interest as they exhibit so-called non-Abelian braiding statistics, which could make them useful tools in the search for fault-tolerant quantum computation. In this context topologically superconducting wires are particularly useful as the Majorana states are located unambiguously at the wire's end, where they form localized end states. Topologically superconducting wires are not known to exist in nature but they can be engineered from commonly available ingredients: semiconductor or ferromagnet nano- wires and conventional superconductors. The nano-wires can inherit superconductivity by the proximity effect and can then exhibit a topologically nontrivial phase. By now, several experiments have been performed on such hybrid structures, reporting measurements that are consistent with the existence of a topologically superconducting phase in the nanowire. Most theoretical investigations on these systems, so far, have been restricted to a one-dimensional effective model: The one-dimensional p-wave superconductor, which is the prototype of a topologically superconducting wire. A nanowire, however, is in general in a quasi-one dimensional regime, with a continuous longitudinal but a quantized transverse degree of freedom. In this Thesis we study the multichannel generalization of a topologically superconducting wire by means of a two-dimensional p + ip-superconductor that is restricted to a narrow-strip geometry. Such systems can be in a topological phase, characterized by the existence of a zero-energy excitation at the
Fractional topological phase on spatially encoded photonic qudits
Khoury, A Z; Marques, B; Matoso, A; Pádua, S
2013-01-01
We discuss the appearance of fractional topological phases on cyclic evolutions of entangled qudits encoded on photonic degrees of freedom. We show how the spatial correlations between photons generated by spontaneous parametric down conversion can be used to evidence the multiple topological phases acquired by entangled qudits and the role played by the Hilbert space dimension. A realistic experimental proposal is presented with numerical predictions of the expected results.
Quantum phase transition induced by real-space topology
Li, C.; Zhang, G.; Lin, S.; Song, Z.
2016-12-01
A quantum phase transition (QPT), including both topological and symmetry breaking types, is usually induced by the change of global parameters, such as external fields or global coupling constants. In this work, we demonstrate the existence of QPT induced by the real-space topology of the system. We investigate the groundstate properties of the tight-binding model on a honeycomb lattice with the torus geometry based on exact results. It is shown that the ground state experiences a second-order QPT, exhibiting the scaling behavior, when the torus switches to a tube, which reveals the connection between quantum phase and the real-space topology of the system.
Quantum phase transition induced by real-space topology.
Li, C; Zhang, G; Lin, S; Song, Z
2016-12-22
A quantum phase transition (QPT), including both topological and symmetry breaking types, is usually induced by the change of global parameters, such as external fields or global coupling constants. In this work, we demonstrate the existence of QPT induced by the real-space topology of the system. We investigate the groundstate properties of the tight-binding model on a honeycomb lattice with the torus geometry based on exact results. It is shown that the ground state experiences a second-order QPT, exhibiting the scaling behavior, when the torus switches to a tube, which reveals the connection between quantum phase and the real-space topology of the system.
Topological phases and transport properties of screened interacting quantum wires
Xu, Hengyi; Xiong, Ye; Wang, Jun
2016-10-01
We study theoretically the effects of long-range and on-site Coulomb interactions on the topological phases and transport properties of spin-orbit-coupled quasi-one-dimensional quantum wires imposed on a s-wave superconductor. The distributions of the electrostatic potential and charge density are calculated self-consistently within the Hartree approximation. Due to the finite width of the wires and charge repulsion, the potential and density distribute inhomogeneously in the transverse direction and tend to accumulate along the lateral edges where the hard-wall confinement is assumed. This result has profound effects on the topological phases and the differential conductance of the interacting quantum wires and their hybrid junctions with superconductors. Coulomb interactions renormalize the gate voltage and alter the topological phases strongly by enhancing the topological regimes and producing jagged boundaries. Moreover, the multicritical points connecting different topological phases are modified remarkably in striking contrast to the predictions of the two-band model. We further suggest the possible non-magnetic topological phase transitions manipulated externally with the aid of long-range interactions. Finally, the transport properties of normal-superconductor junctions are further examined, in particular, the impacts of Coulomb interactions on the zero-bias peaks related to the Majorana fermions and near zero-energy peaks.
Topological Insulators and Nematic Phases from Spontaneous Symmetry Breaking in
Sun, K.
2010-05-26
We investigate the stability of a quadratic band-crossing point (QBCP) in 2D fermionic systems. At the non-interacting level, we show that a QBCP exists and is topologically stable for a Berry flux {-+}2{pi}, if the point symmetry group has either fourfold or sixfold rotational symmetries. This putative topologically stable free-fermion QBCP is marginally unstable to arbitrarily weak shortrange repulsive interactions. We consider both spinless and spin-1/2 fermions. Four possible ordered states result: a quantum anomalous Hall phase, a quantum spin Hall phase, a nematic phase, and a nematic-spin-nematic phase.
Multiple topological phase transitions in a gyromagnetic photonic crystal
Chen, Zeguo
2017-04-19
We present the design of a tunable two-dimensional photonic crystal that exhibits multiple topological phases, including a conventional insulator phase, a quantum spin Hall phase, and a quantum anomalous Hall phase under different combinations of geometric parameters and external magnetic fields. Our photonic crystal enables a platform to study the topology evolution attributed to the interplay between crystalline symmetry and time-reversal symmetry. A four-band tight-binding model unambiguously reveals that the topological property is associated with the pseudospin orientations and that it is characterized by the spin Chern number. The emerging quantum anomalous Hall phase features a single helical edge state that is locked by a specific pseudospin. Simulation results demonstrate that the propagation of such a single helical edge state is robust against magnetic impurities. Potential applications, such as spin splitters, are described.
Exotic quantum phase transitions of strongly interacting topological insulators
Slagle, Kevin; You, Yi-Zhuang; Xu, Cenke
2015-03-01
Using determinant quantum Monte Carlo simulations, we demonstrate that an extended Hubbard model on a bilayer honeycomb lattice has two novel quantum phase transitions. The first is a quantum phase transition between the weakly interacting gapless Dirac fermion phase and a strongly interacting fully gapped and symmetric trivial phase, which cannot be described by the standard Gross-Neveu model. The second is a quantum critical point between a quantum spin Hall insulator with spin Sz conservation and the previously mentioned strongly interacting fully gapped phase. At the latter quantum critical point the single-particle excitations remain gapped, while spin and charge gaps both close. We argue that the first quantum phase transition is related to the Z16 classification of the topological superconductor 3He-B phase with interactions, while the second quantum phase transition is a topological phase transition described by a bosonic O (4 ) nonlinear sigma model field theory with a Θ term.
Chen, M. N.; Su, W.; Deng, M. X.; Ruan, Jiawei; Luo, W.; Shao, D. X.; Sheng, L.; Xing, D. Y.
2016-11-01
A great deal of attention has been paid to the topological phases engineered by photonics over the past few years. Here, we propose a topological quantum phase transition to a quantum anomalous Hall (QAH) phase induced by off-resonant circularly polarized light in a two-dimensional system that is initially in a quantum spin Hall phase or a trivial insulator phase. This provides an alternative method to realize the QAH effect, other than magnetic doping. The circularly polarized light effectively creates a Zeeman exchange field and a renormalized Dirac mass, which are tunable by varying the intensity of the light and drive the quantum phase transition. Both the transverse and longitudinal Hall conductivities are studied, and the former is consistent with the topological phase transition when the Fermi level lies in the band gap. A highly controllable spin-polarized longitudinal electrical current can be generated when the Fermi level is in the conduction band, which may be useful for designing topological spintronics.
Topological Crystalline Insulator in a New Bi Semiconducting Phase
Munoz, F.; Vergniory, M. G.; Rauch, T.; Henk, J.; Chulkov, E. V.; Mertig, I.; Botti, S.; Marques, M. A. L.; Romero, A. H.
2016-02-01
Topological crystalline insulators are a type of topological insulators whose topological surface states are protected by a crystal symmetry, thus the surface gap can be tuned by applying strain or an electric field. In this paper we predict by means of ab initio calculations a new phase of Bi which is a topological crystalline insulator characterized by a mirror Chern number nM = -2, but not a strong topological insulator. This system presents an exceptional property: at the (001) surface its Dirac cones are pinned at the surface high-symmetry points. As a consequence they are also protected by time-reversal symmetry and can survive against weak disorder even if in-plane mirror symmetry is broken at the surface. Taking advantage of this dual protection, we present a strategy to tune the band-gap based on a topological phase transition unique to this system. Since the spin-texture of these topological surface states reduces the back-scattering in carrier transport, this effective band-engineering is expected to be suitable for electronic and optoelectronic devices with reduced dissipation.
Geometric quantum phase in the spacetime of topological defects
Bakke, K [Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford, OX1 3PU (United Kingdom); Furtado, C; Nascimento, J R [Departamento de Fisica, Universidade Federal da ParaIba, Caixa Postal 5008, 58051-970, Joao Pessoa, PB (Brazil)
2011-07-08
In this contribution, we study the quantum dynamics of a neutral particle in the presence of a topological defect. We investigate the appearance of a geometric phase in the relativistic quantum dynamics of a neutral particle which possesses permanent magnetic and electric dipole moments in the presence of an electromagnetic field in this curved background. We also study the influence of noninertial effects of a rotating frame and and obtain several contributions to the relativistic geometric phase due to the noninertial effects and the topology of spacetime. The analogous Aharonov-Casher and He-Mckellar-Wilkens effects are investigated in the nonrelativistic dynamics with the presence of a topological defect and under the influence of noninertial effects. We also obtain effects analogous to the Sagnac effect and Mashhoon effect due to the presence of the topological defect.
Geometric quantum phase in the spacetime of topological defects
Bakke, K.; Furtado, C.; Nascimento, J. R.
2011-07-01
In this contribution, we study the quantum dynamics of a neutral particle in the presence of a topological defect. We investigate the appearance of a geometric phase in the relativistic quantum dynamics of a neutral particle which possesses permanent magnetic and electric dipole moments in the presence of an electromagnetic field in this curved background. We also study the influence of noninertial effects of a rotating frame and and obtain several contributions to the relativistic geometric phase due to the noninertial effects and the topology of spacetime. The analogous Aharonov-Casher and He-Mckellar-Wilkens effects are investigated in the nonrelativistic dynamics with the presence of a topological defect and under the influence of noninertial effects. We also obtain effects analogous to the Sagnac effect and Mashhoon effect due to the presence of the topological defect.
Berry phase, topology, and degeneracies in quantum nanomagnets.
Bruno, Patrick
2006-03-24
A topological theory of the diabolical points (degeneracies) of quantum magnets is presented. Diabolical points are characterized by their diabolicity index, for which topological sum rules are derived. The paradox of the missing diabolical points for Fe8 molecular magnets is clarified. A new method is also developed to provide a simple interpretation, in terms of destructive interferences due to the Berry phase, of the complete set of diabolical points found in biaxial systems such as Fe8.
Topological phases of a three-dimensional topological insulator with structure inversion asymmetry
Guo, Xiaoyong; Wang, Zaijun; Zheng, Qiang; Peng, Jie
2015-11-01
We investigate the topological phases of a three-dimensional (3D) topological insulator (TI) without the top-bottom inversion symmetry. We calculate the momentum depended spin Chern number to extract the phase diagram. Various phases are found and we address the dependence of phase boundaries on the strength of inversion asymmetry. Opposite to the quasi-two-dimensional thin film TI, in our 3D system the TI state is stabilized by the structure inversion asymmetry (SIA). With a strong SIA the 3D TI phase can exist even under a large Zeeman field. In a tight-binding form, the surface modes are discussed to confirm with the phase diagram. Particularly we find that the SIA cannot destroy the surface states but open a gap on its spectrum.
Dai-Freed theorem and topological phases of matter
Yonekura, Kazuya
2016-09-01
We describe a physics derivation of theorems due to Dai and Freed about the Atiyah-Patodi-Singer eta-invariant which is important for anomalies and topological phases of matter. This is done by studying a massive fermion. The key role is played by the wave function of the ground state in the Hilbert space of the fermion in the large mass limit. The ground state takes values in the determinant line bundle and has nontrivial Berry phases which characterize the low energy topological phases.
Dai-Freed theorem and topological phases of matter
Yonekura, Kazuya
2016-01-01
We describe a physics derivation of theorems due to Dai and Freed about the Atiyah-Patodi-Singer eta-invariant which is important for anomalies and topological phases of matter. This is done by studying a massive fermion. The key role is played by the wave function of the ground state in the Hilbert space of the fermion in the large mass limit. The ground state takes values in the determinant line bundle and has nontrivial Berry phases which characterize the low energy topological phases.
Three-Phase Modulated Pole Machine Topologies Utilizing Mutual Flux Paths
Washington, Jamie G.; Atkinson, Glynn J.; Baker, Nick J.
2012-01-01
This paper discusses three-phase topologies for modulated pole machines (MPMs). The authors introduce a new threephase topology, which takes advantage of mutual flux paths; this is analyzed using 3-D finite-element methods and compared to a three-phase topology using three single-phase units...... both performance and constructional benefits over prior MPM topologies....
Parafermionic phases with symmetry breaking and topological order
Alexandradinata, A.; Regnault, N.; Fang, Chen; Gilbert, Matthew J.; Bernevig, B. Andrei
2016-09-01
Parafermions are the simplest generalizations of Majorana fermions that realize topological order. We propose a less restrictive notion of topological order in one-dimensional open chains, which generalizes the seminal work by Fendley [J. Stat. Mech. (2012) P11020, 10.1088/1742-5468/2012/11/P11020]. The first essential property is that the ground states are mutually indistinguishable by local, symmetric probes, and the second is a generalized notion of zero edge modes which cyclically permute the ground states. These two properties are shown to be topologically robust, and applicable to a wider family of topologically ordered Hamiltonians than has been previously considered. As an application of these edge modes, we formulate a notion of twisted boundary conditions on a closed chain, which guarantees that the closed-chain ground state is topological, i.e., it originates from the topological manifold of the open chain. Finally, we generalize these ideas to describe symmetry-breaking phases with a parafermionic order parameter. These exotic phases are condensates of parafermion multiplets, which generalize Cooper pairing in superconductors. The stability of these condensates is investigated on both open and closed chains.
Exploring complex networks via topological embedding on surfaces.
Aste, Tomaso; Gramatica, Ruggero; Di Matteo, T
2012-09-01
We demonstrate that graphs embedded on surfaces are a powerful and practical tool to generate, to characterize, and to simulate networks with a broad range of properties. Any network can be embedded on a surface with sufficiently high genus and therefore the study of topologically embedded graphs is non-restrictive. We show that the local properties of the network are affected by the surface genus which determines the average degree, which influences the degree distribution, and which controls the clustering coefficient. The global properties of the graph are also strongly affected by the surface genus which is constraining the degree of interwovenness, changing the scaling properties of the network from large-world kind (small genus) to small- and ultrasmall-world kind (large genus). Two elementary moves allow the exploration of all networks embeddable on a given surface and naturally introduce a tool to develop a statistical mechanics description for these networks. Within such a framework, we study the properties of topologically embedded graphs which dynamically tend to lower their energy towards a ground state with a given reference degree distribution. We show that the cooling dynamics between high and low "temperatures" is strongly affected by the surface genus with the manifestation of a glass-like transition occurring when the distance from the reference distribution is low. We prove, with examples, that topologically embedded graphs can be built in a way to contain arbitrary complex networks as subgraphs. This method opens a new avenue to build geometrically embedded networks on hyperbolic manifolds.
Interaction-induced topological and magnetic phases in the Hofstadter-Hubbard model
Kumar, Pramod; Mertz, Thomas; Hofstetter, Walter
2016-09-01
Interaction effects have been a subject of contemporary interest in topological phases of matter. But in the presence of interactions, the accurate determination of topological invariants in their general form is difficult due to their dependence on multiple integrals containing Green's functions and their derivatives. Here we employ the recently proposed "effective topological Hamiltonian" approach to explore interaction-induced topological phases in the time-reversal-invariant Hofstadter-Hubbard model. Within this approach, the zero-frequency part of the self-energy is sufficient to determine the correct topological invariant. We combine the topological Hamiltonian approach with the local self-energy approximation, both for the static and the full dynamical self-energy evaluated using dynamical mean field theory (DMFT), and present the resulting phase diagram in the presence of many-body interactions. We investigate the emergence of quantum spin Hall (QSH) states for different interaction strengths by calculating the Z2 invariant. The interplay of strong correlations and a staggered potential also induces magnetic long-range order with an associated first order transition. We present results for the staggered magnetization (ms), staggered occupancy (ns), and double occupancy across the transition.
He, Yuan-Yao; Wu, Han-Qing; You, Yi-Zhuang; Xu, Cenke; Meng, Zi Yang; Lu, Zhong-Yi
2016-03-01
It is expected that the interplay between nontrivial band topology and strong electron correlation will lead to very rich physics. Thus a controlled study of the competition between topology and correlation is of great interest. Here, employing large-scale quantum Monte Carlo simulations, we provide a concrete example of the Kane-Mele-Hubbard model on an AA-stacking bilayer honeycomb lattice with interlayer antiferromagnetic interaction. Our simulation identified several different phases: a quantum spin Hall insulator (QSH), an x y -plane antiferromagnetic Mott insulator, and an interlayer dimer-singlet insulator. Most importantly, a bona fide topological phase transition between the QSH and the dimer-singlet insulators, purely driven by the interlayer antiferromagnetic interaction, is found. At the transition, the spin and charge gap of the system close while the single-particle excitations remain gapped, which means that this transition has no mean-field analog and it can be viewed as a transition between bosonic symmetry-protected topological (SPT) states. At one special point, this transition is described by a (2 +1 )d O (4 ) nonlinear sigma model with exact S O (4 ) symmetry and a topological term at exactly Θ =π . The relevance of this work towards more general interacting SPT states is discussed.
Goswami, Pallab; Chakravarty, Sudip
2017-02-01
The quantum phase transition between two clean, noninteracting topologically distinct gapped states in three dimensions is governed by a massless Dirac fermion fixed point, irrespective of the underlying symmetry class, and this constitutes a remarkably simple example of superuniversality. For a sufficiently weak disorder strength, we show that the massless Dirac fixed point is at the heart of the robustness of superuniversality. We establish this by considering both perturbative and nonperturbative effects of disorder. The superuniversality breaks down at a critical strength of disorder, beyond which the topologically distinct localized phases become separated by a delocalized diffusive phase. In the global phase diagram, the disorder controlled fixed point where superuniversality is lost, serves as a multicritical point, where the delocalized diffusive and two topologically distinct localized phases meet and the nature of the localization-delocalization transition depends on the underlying symmetry class. Based on these features, we construct the global phase diagrams of noninteracting, dirty topological systems in three dimensions. We also establish a similar structure of the phase diagram and the superuniversality for weak disorder in higher spatial dimensions. By noting that 1 /r2 power-law correlated disorder acts as a marginal perturbation for massless Dirac fermions in any spatial dimension d , we have established a general renormalization group framework for addressing disorder driven critical phenomena for fixed spatial dimension d >2 .
Unconventional transformation of spin Dirac phase across a topological quantum phase transition.
Xu, Su-Yang; Neupane, Madhab; Belopolski, Ilya; Liu, Chang; Alidoust, Nasser; Bian, Guang; Jia, Shuang; Landolt, Gabriel; Slomski, Batosz; Dil, J Hugo; Shibayev, Pavel P; Basak, Susmita; Chang, Tay-Rong; Jeng, Horng-Tay; Cava, Robert J; Lin, Hsin; Bansil, Arun; Hasan, M Zahid
2015-04-17
The topology of a topological material can be encoded in its surface states. These surface states can only be removed by a bulk topological quantum phase transition into a trivial phase. Here we use photoemission spectroscopy to image the formation of protected surface states in a topological insulator as we chemically tune the system through a topological transition. Surprisingly, we discover an exotic spin-momentum locked, gapped surface state in the trivial phase that shares many important properties with the actual topological surface state in anticipation of the change of topology. Using a spin-resolved measurement, we show that apart from a surface bandgap these states develop spin textures similar to the topological surface states well before the transition. Our results offer a general paradigm for understanding how surface states in topological phases arise from a quantum phase transition and are suggestive for the future realization of Weyl arcs, condensed matter supersymmetry and other fascinating phenomena in the vicinity of a quantum criticality.
A symmetry-respecting topologically-ordered surface phase of 3d electron topological insulators
Metlitski, Max A.; Kane, C. L.; Fisher, Matthew P. A.
2013-01-01
A 3d electron topological insulator (ETI) is a phase of matter protected by particle-number conservation and time-reversal symmetry. It was previously believed that the surface of an ETI must be gapless unless one of these symmetries is broken. A well-known symmetry-preserving, gapless surface termination of an ETI supports an odd number of Dirac cones. In this paper we deduce a symmetry-respecting, gapped surface termination of an ETI, which carries an intrinsic 2d topological order, Moore-R...
Quantum charge pumps with topological phases in a Creutz ladder
Sun, Ning; Lim, Lih-King
2017-07-01
The quantum charge pumping phenomenon connects band topology through the dynamics of a one-dimensional quantum system. In terms of a microscopic model, the Su-Schrieffer-Heeger/Rice-Mele quantum pump continues to serve as a fruitful starting point for many considerations of topological physics. Here we present a generalized Creutz scheme as a distinct two-band quantum pump model. By noting that it undergoes two kinds of topological band transitions accompanying with a Zak-phase difference of π and 2 π , respectively, various charge pumping schemes are studied by applying an elaborate Peierls phase substitution. Translating into real space, the transportation of quantized charges is a result of cooperative quantum interference effect. In particular, an all-flux quantum pump emerges which operates with time-varying fluxes only and transports two charge units. This makes cold atoms with artificial gauge fields a unique system where this kind of phenomena can be realized.
Dynamical Scaling and Phase Coexistence in Topologically Constrained DNA Melting
Fosado, Y. A. G.; Michieletto, D.; Marenduzzo, D.
2017-09-01
There is a long-standing experimental observation that the melting of topologically constrained DNA, such as circular closed plasmids, is less abrupt than that of linear molecules. This finding points to an important role of topology in the physics of DNA denaturation, which is, however, poorly understood. Here, we shed light on this issue by combining large-scale Brownian dynamics simulations with an analytically solvable phenomenological Landau mean field theory. We find that the competition between melting and supercoiling leads to phase coexistence of denatured and intact phases at the single-molecule level. This coexistence occurs in a wide temperature range, thereby accounting for the broadening of the transition. Finally, our simulations show an intriguing topology-dependent scaling law governing the growth of denaturation bubbles in supercoiled plasmids, which can be understood within the proposed mean field theory.
Stehno, M. P.; Orlyanchik, V.; Nugroho, C. D.; Ghaemi, P.; Brahlek, M.; Koirala, N.; Oh, S.; Van Harlingen, D. J.
2016-01-01
Topological insulators (TIs) hold great promise for topological quantum computation in solid-state systems. Recently, several groups reported experimental data suggesting that signatures of Majorana modes have been observed in topological insulator Josephson junctions (TIJJs). A prerequisite for the exploration of Majorana physics is to obtain a good understanding of the properties of low-energy Andreev bound states (ABSs) in a material with a topologically nontrivial band structure. Here, we present experimental data and a theoretical analysis demonstrating that the band-structure inversion close to the surface of a TI has observable consequences for supercurrent transport in TIJJs prepared on surface-doped Bi2Se3 thin films. Electrostatic carrier depletion of the film surface leads to an abrupt drop in the critical current of such devices. The effect can be understood as a relocation of low-energy ABSs from a region deeper in the bulk of the material to the more strongly disordered surface, which is driven by the topology of the effective band structure in the presence of surface dopants.
Computational Power of Symmetry-Protected Topological Phases
Stephen, David T.; Wang, Dong-Sheng; Prakash, Abhishodh; Wei, Tzu-Chieh; Raussendorf, Robert
2017-07-01
We consider ground states of quantum spin chains with symmetry-protected topological (SPT) order as resources for measurement-based quantum computation (MBQC). We show that, for a wide range of SPT phases, the computational power of ground states is uniform throughout each phase. This computational power, defined as the Lie group of executable gates in MBQC, is determined by the same algebraic information that labels the SPT phase itself. We prove that these Lie groups always contain a full set of single-qubit gates, thereby affirming the long-standing conjecture that general SPT phases can serve as computationally useful phases of matter.
Birman-Wenzl-Murakami algebra, topological parameter and Berry phase
Zhou, Chengcheng; Xue, Kang; Gou, Lidan; Sun, Chunfang; Wang, Gangcheng; Hu, Taotao
2012-12-01
In this paper, a 3 × 3-matrix representation of Birman-Wenzl-Murakami (BWM) algebra has been presented. Based on which, unitary matrices A( θ, φ 1, φ 2) and B( θ, φ 1, φ 2) are generated via Yang-Baxterization approach. A Hamiltonian is constructed from the unitary B( θ, φ) matrix. Then we study Berry phase of the Yang-Baxter system, and obtain the relationship between topological parameter and Berry phase.
Evaluation of Three-Phase Transformerless Photovoltaic Inverter Topologies
Kerekes, Tamas; Liserre, Marco; Teodorescu, Remus
2009-01-01
This paper analyzes and compares three transformerless photovoltaic inverter topologies for three-phase grid connection with the main focus on the safety issues that result from the lack of galvanic isolation. A common-mode model, valid at frequencies lower than 50 kHz, is adopted to study...... the leakage current paths. The model is validated by both simulation and experimental results. These will be used to compare the selected topologies, and to explain the influence of system unbalance and the neutral conductor inductance on the leakage current. It will be demonstrated that the later has...
Exploration of New Principles in Spintronics Based on Topological Insulators (Option 1)
2012-05-14
Final Report Title: Exploration of New Principles in Spintronics Based on Topological Insulators (Option 1... Spintronics Based on Topological Insulators 5a. CONTRACT NUMBER FA23861014103 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) Yoichi Ando...quantum phenomena in topological insulators for conceiving devices with unprecedented functionalities. 15. SUBJECT TERMS Physics, Spintronics
Origin of time before inflation from a topological phase transition
Bellini, Mauricio
2017-09-01
We study the origin of the universe (or pre-inflation) by suggesting that the primordial space-time in the universe suffered a global topological phase transition, from a 4D Euclidean manifold to an asymptotic 4D hyperbolic one. We introduce a complex time, τ, such that its real part becomes dominant after started the topological phase transition. Before the big bang, τ is a space-like coordinate, so that can be considered as a reversal variable. After the phase transition is converted in a causal variable. The formalism solves in a natural manner the quantum to classical transition of the geometrical relativistic quantum fluctuations: σ, which has a geometric origin.
Detecting topological phases in silicene by anomalous Nernst effect
Xu, Yafang; Zhou, Xingfei; Jin, Guojun
2016-05-01
Silicene undergoes various topological phases under the interplay of intrinsic spin-orbit coupling, perpendicular electric field, and off-resonant light. We propose that the abundant topological phases can be distinguished by measuring the Nernst conductivity even at room temperature, and their phase boundaries can be determined by differentiating the charge and spin Nernst conductivities. By modulating the electric and light fields, pure spin polarized, valley polarized, and even spin-valley polarized Nernst currents can be generated. As Nernst conductivity is zero for linear polarized light, silicene can act as an optically controlled spin and valley field-effect transistor. Similar investigations can be extended from silicene to germanene and stanene, and a comparison is made for the anomalous thermomagnetic figure of merits between them. These results will facilitate potential applications in spin and valley caloritronics.
Emergence of topological and topological crystalline phases in TlBiS2 and TlSbS2
Zhang, Qingyun
2015-02-11
Using first-principles calculations, we investigate the band structure evolution and topological phase transitions in TlBiS2 and TlSbS2 under hydrostatic pressure as well as uniaxial and biaxial strain. The phase transitions are identified by parity analysis and by calculating the surface states. Zero, one, and four Dirac cones are found for the (111) surfaces of both TlBiS2 and TlSbS2 when the pressure grows, which confirms trivial-nontrivial-trivial phase transitions. The Dirac cones at the (M) over bar points are anisotropic with large out-of-plane component. TlBiS2 shows normal, topological, and topological crystalline insulator phases under hydrostatic pressure, thus being the first compound to exhibit a phase transition from a topological to a topological crystalline insulator.
Relativistic dipole interaction and the topological nature for induced HMW and AC phases
He, Xiao-Gang
2016-01-01
In this work we construct relativistic Lagrangian density for the AC and HMW topological phases by induced electric and magnetic dipoles and clarify some of the conditions for producing topological phases which have not been properly discussed in previous studies. We also found that in both cases, the topological phases are induced by the cross product of electric and magnetic fields in the form $\\bm{B} \\times \\bm{E}$ which reinforces the dual nature of these two topological phases.
Phase diagram and entanglement of two interacting topological Kitaev chains
Herviou, Loïc; Mora, Christophe; Le Hur, Karyn
2016-04-01
A superconducting wire described by a p -wave pairing and a Kitaev Hamiltonian exhibits Majorana fermions at its edges and is topologically protected by symmetry. We consider two Kitaev wires (chains) coupled by a Coulomb-type interaction and study the complete phase diagram using analytical and numerical techniques. A topological superconducting phase with four Majorana fermions occurs until moderate interactions between chains. For large interactions, both repulsive and attractive, by analogy with the Hubbard model, we identify Mott phases with Ising-type magnetic order. For repulsive interactions, the Ising antiferromagnetic order favors the occurrence of orbital currents spontaneously breaking time-reversal symmetry. By strongly varying the chemical potentials of the two chains, quantum phase transitions towards fully polarized (empty or full) fermionic chains occur. In the Kitaev model, the quantum critical point separating the topological superconducting phase and the polarized phase belongs to the universality class of the critical Ising model in two dimensions. When increasing the Coulomb interaction between chains, then we identify an additional phase corresponding to two critical Ising theories (or two chains of Majorana fermions). We confirm the existence of such a phase from exact mappings and from the concept of bipartite fluctuations. We show the existence of negative logarithmic corrections in the bipartite fluctuations, as a reminiscence of the quantum critical point in the Kitaev model. Other entanglement probes such as bipartite entropy and entanglement spectrum are also used to characterize the phase diagram. The limit of large interactions can be reached in an equivalent setup of ultracold atoms and Josephson junctions.
Optical phased array radiating optical vortex with manipulated topological charges.
Ma, Xiaoliang; Pu, Mingbo; Li, Xiong; Huang, Cheng; Pan, Wenbo; Zhao, Bo; Cui, Jianhua; Luo, Xiangang
2015-02-23
Optical antennas are key elements in quantum optics emitting and sensing, and behave wide range applications in optical domain. However, integration of optical antenna radiating orbital angular momentum is still a challenge in nano-scale. We theoretically demonstrate a sub-wavelength phased optical antenna array, which manipulates the distribution of the orbital angular momentum in the near field. Orbital angular momentum with topological charge of 4 can be obtained by controlling the phase distribution of the fundamental mode orbital angular momentum in each antenna element. Our results indicate this phased array may be utilized in high integrated optical communication systems.
Many-body topological invariants in fermionic symmetry protected topological phases
Shiozaki, Ken; Ryu, Shinsei
2016-01-01
We propose the definitions of many-body topological invariants to detect symmetry-protected topological phases protected by point group symmetry, using partial point group transformations on a given short-range entangled quantum ground state. Partial point group transformations $g_D$ are defined by point group transformations restricted to a spatial subregion $D$, which is closed under the point group transformations and sufficiently larger than the bulk correlation length $\\xi$. By analytical and numerical calculations,we find that the ground state expectation value of the partial point group transformations behaves generically as $\\langle GS | g_D | GS \\rangle \\sim \\exp \\Big[ i \\theta+ \\gamma - \\alpha \\frac{{\\rm Area}(\\partial D)}{\\xi^{d-1}} \\Big]$. Here, ${\\rm Area}(\\partial D)$ is the area of the boundary of the subregion $D$, and $\\alpha$ is a dimensionless constant. The complex phase of the expectation value $\\theta$ is quantized and serves as the topological invariant, and $\\gamma$ is a scale-independe...
Complex Nonlinearity Chaos, Phase Transitions, Topology Change and Path Integrals
Ivancevic, Vladimir G
2008-01-01
Complex Nonlinearity: Chaos, Phase Transitions, Topology Change and Path Integrals is a book about prediction & control of general nonlinear and chaotic dynamics of high-dimensional complex systems of various physical and non-physical nature and their underpinning geometro-topological change. The book starts with a textbook-like expose on nonlinear dynamics, attractors and chaos, both temporal and spatio-temporal, including modern techniques of chaos–control. Chapter 2 turns to the edge of chaos, in the form of phase transitions (equilibrium and non-equilibrium, oscillatory, fractal and noise-induced), as well as the related field of synergetics. While the natural stage for linear dynamics comprises of flat, Euclidean geometry (with the corresponding calculation tools from linear algebra and analysis), the natural stage for nonlinear dynamics is curved, Riemannian geometry (with the corresponding tools from nonlinear, tensor algebra and analysis). The extreme nonlinearity – chaos – corresponds to th...
Characterization of topological phases in models of interacting fermions
Motruk, Johannes
2016-05-25
The concept of topology in condensed matter physics has led to the discovery of rich and exotic physics in recent years. Especially when strong correlations are included, phenomenons such as fractionalization and anyonic particle statistics can arise. In this thesis, we study several systems hosting topological phases of interacting fermions. In the first part, we consider one-dimensional systems of parafermions, which are generalizations of Majorana fermions, in the presence of a Z{sub N} charge symmetry. We classify the symmetry-protected topological (SPT) phases that can occur in these systems using the projective representations of the symmetries and find a finite number of distinct phases depending on the prime factorization of N. The different phases exhibit characteristic degeneracies in their entanglement spectrum (ES). Apart from these SPT phases, we report the occurrence of parafermion condensate phases for certain values of N. When including an additional Z{sub N} symmetry, we find a non-Abelian group structure under the addition of phases. In the second part of the thesis, we focus on two-dimensional lattice models of spinless fermions. First, we demonstrate the detection of a fractional Chern insulator (FCI) phase in the Haldane honeycomb model on an infinite cylinder by means of the density-matrix renormalization group (DMRG). We report the calculation of several quantities characterizing the topological order of the state, i.e., (i) the Hall conductivity, (ii) the spectral flow and level counting in the ES, (iii) the topological entanglement entropy, and (iv) the charge and topological spin of the quasiparticles. Since we have access to sufficiently large system sizes without band projection with DMRG, we are in addition able to investigate the transition from a metal to the FCI at small interactions which we find to be of first order. In a further study, we consider a time-reversal symmetric model on the honeycomb lattice where a Chern insulator (CI
Floquet topological semimetal phases of an extended kicked Harper model
Bomantara, Raditya Weda; Raghava, Gudapati Naresh; Zhou, Longwen; Gong, Jiangbin
2016-02-01
Recent discoveries on topological characterization of gapless systems have attracted interest in both theoretical studies and experimental realizations. Examples of such gapless topological phases are Weyl semimetals, which exhibit three-dimensional (3D) Dirac cones (Weyl points), and nodal line semimetals, which are characterized by line nodes (two bands touching along a line). Inspired by our previous discoveries that the kicked Harper model exhibits many fascinating features of Floquet topological phases, in this paper we consider a generalization of the model, where two additional periodic system parameters are introduced into the Hamiltonian to serve as artificial dimensions, so as to simulate a 3 D periodically driven system. We observe that by increasing the hopping strength and the kicking strength of the system, many new Floquet band touching points at Floquet quasienergies 0 and π will start to appear. Some of them are Weyl points, while the others form line nodes in the parameter space. By taking open boundary conditions along the physical dimension, edge states analogous to Fermi arcs in static Weyl semimetal systems are observed. Finally, by designing an adiabatic pumping scheme, the chirality of the Floquet-band Weyl points and the π Berry phase around Floquet-band line nodes can be manifested.
A topological Dirac insulator in a quantum spin Hall phase
Hsieh, David; Qian, Dong; Wray, Lewis; Xia, Yuqi; San Hor, Yew; Cava, Robert; Hasan, Zahid
2009-03-01
When electrons are subject to a large external magnetic field, the conventional charge quantum Hall effect dictates that an electronic excitation gap is generated in the sample bulk, but metallic conduction is permitted at the boundary. Recent theoretical models suggest that certain bulk insulators with large spin orbit interactions may also naturally support conducting topological boundary states in the quantum limit, which opens up the possibility for studying unusual quantum Hall-like phenomena in zero external magnetic fields. Bulk Bi1-xSbx single crystals are predicted to be prime candidates for one such unusual Hall phase of matter known as the topological insulator. The hallmark of a topological insulator is the existence of metallic surface states that are higher-dimensional analogues of the edge states that characterize a quantum spin Hall insulator. Here, using incident-photon-energy-modulated angle-resolved photoemission spectroscopy, we report the direct observation of massive Dirac particles in the bulk of Bi0.9Sb0.1 and provide a comprehensive mapping of the Dirac insulators gapless surface electron bands. These findings taken together suggest that the observed surface state on the boundary of the bulk insulator is a realization of the topological metal.
Lapa, Matthew F.; Jian, Chao-Ming; Ye, Peng; Hughes, Taylor L.
2017-01-01
We calculate the topological part of the electromagnetic response of bosonic integer quantum Hall (BIQH) phases in odd (space-time) dimensions, and bosonic topological insulator (BTI) and bosonic chiral semimetal (BCSM) phases in even dimensions. To do this, we use the nonlinear sigma model (NLSM) description of bosonic symmetry-protected topological (SPT) phases, and the method of gauged Wess-Zumino (WZ) actions. We find the surprising result that for BIQH states in dimension 2 m -1 (m =1 ,2 ,⋯ ), the bulk response to an electromagnetic field Aμ is characterized by a Chern-Simons term for Aμ with a level quantized in integer multiples of m ! (factorial). We also show that BTI states (which have an extra Z2 symmetry) can exhibit a Z2-breaking quantum Hall effect on their boundaries, with this boundary quantum Hall effect described by a Chern-Simons term at level m/! 2 . We show that the factor of m ! can be understood by requiring gauge invariance of the exponential of the Chern-Simons term on a general Euclidean manifold, and we also use this argument to characterize the electromagnetic and gravitational responses of fermionic SPT phases with U(1 ) symmetry in all odd dimensions. We then use our gauged boundary actions for the BIQH and BTI states to (i) construct a bosonic analog of a chiral semimetal (BCSM) in even dimensions, (ii) show that the boundary of the BTI state exhibits a bosonic analog of the parity anomaly of Dirac fermions in odd dimensions, and (iii) study anomaly inflow at domain walls on the boundary of BTI states. In a series of Appendixes we derive important formulas and additional results. In particular, in Appendix A we use the connection between equivariant cohomology and gauged WZ actions to give a mathematical interpretation of the actions for the BIQH and BTI boundaries constructed in this paper.
He-McKellar-Wilkens Topological Phase in Atom Interferometry
Lepoutre, S.; Gauguet, A.; Trénec, G.; Büchner, M.; Vigué, J.
2012-09-01
We report an experimental test of the topological phase predicted by He and McKellar in 1993 and by Wilkens in 1994: this phase, which appears when an electric dipole propagates in a magnetic field, is connected to the Aharonov-Casher effect by electric-magnetic duality. The He-McKellar-Wilkens phase is quite small, at most 27 mrad in our experiment, and this experiment requires the high phase sensitivity of our atom interferometer with spatially separated arms as well as symmetry reversals such as the direction of the electric and magnetic fields. The measured value of the He-McKellar-Wilkens phase differs by 31% from its theoretical value, a difference possibly due to some as yet uncontrolled systematic errors.
He-McKellar-Wilkens topological phase in atom interferometry
Lepoutre, Steven; Büchner, Matthias; Vigué, Jacques; Gauguet, Alexandre
2012-01-01
We report the first experimental test of the topological phase predicted by He and McKellar and by Wilkens in 1993: this phase, which appears when an electric dipole propagates in a magnetic field, is connected to the Aharonov-Casher effect by electric-magnetic duality. The He-McKellar-Wilkens phase is quite small, at most 27 mrad in our experiment, and this experiment requires the high phase sensitivity of our atom interferometer with spatially separated arms as well as symmetry reversals such as the direction of the electric and magnetic fields. The measured value of the He-McKellar-Wilkens phase differs by 31% from its theoretical value, a difference possibly due to some as yet uncontrolled systematic errors.
Topological conditions for discrete symmetry breaking and phase transitions
Baroni, Fabrizio; Casetti, Lapo [Dipartimento di Fisica, Universita di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino (Finland) (Italy)
2006-01-20
In the framework of a recently proposed topological approach to phase transitions, some sufficient conditions ensuring the presence of the spontaneous breaking of a Z{sub 2} symmetry and of a symmetry-breaking phase transition are introduced and discussed. A very simple model, which we refer to as the hypercubic model, is introduced and solved. The main purpose of this model is that of illustrating the content of the sufficient conditions, but it is interesting also in itself due to its simplicity. Then some mean-field models already known in the literature are discussed in the light of the sufficient conditions introduced here.
Ye, Peng; Hughes, Taylor L.; Maciejko, Joseph; Fradkin, Eduardo
2016-09-01
Topological phases of matter are usually realized in deconfined phases of gauge theories. In this context, confined phases with strongly fluctuating gauge fields seem to be irrelevant to the physics of topological phases. For example, the low-energy theory of the two-dimensional (2D) toric code model (i.e., the deconfined phase of Z2 gauge theory) is a U(1 )×U(1 ) Chern-Simons theory in which gauge charges (i.e., e and m particles) are deconfined and the gauge fields are gapped, while the confined phase is topologically trivial. In this paper, we point out a route to constructing exotic three-dimensional (3D) gapped fermionic phases in a confining phase of a gauge theory. Starting from a parton construction with strongly fluctuating compact U(1 )×U(1 ) gauge fields, we construct gapped phases of interacting fermions by condensing two linearly independent bosonic composite particles consisting of partons and U(1 )×U(1 ) magnetic monopoles. This can be regarded as a 3D generalization of the 2D Bais-Slingerland condensation mechanism. Charge fractionalization results from a Debye-Hückel-type screening cloud formed by the condensed composite particles. Within our general framework, we explore two aspects of symmetry-enriched 3D Abelian topological phases. First, we construct a new fermionic state of matter with time-reversal symmetry and Θ ≠π , the fractional topological insulator. Second, we generalize the notion of anyonic symmetry of 2D Abelian topological phases to the charge-loop excitation symmetry (Charles ) of 3D Abelian topological phases. We show that line twist defects, which realize Charles transformations, exhibit non-Abelian fusion properties.
Qin, Wei; Zhang, Zhenyu
2014-12-31
At the interface of an s-wave superconductor and a three-dimensional topological insulator, Majorana zero modes and Majorana helical states have been proposed to exist respectively around magnetic vortices and geometrical edges. Here we first show that randomly distributed magnetic impurities at such an interface will induce bound states that broaden into impurity bands inside (but near the edges of) the superconducting gap, which remains open unless the impurity concentration is too high. Next we find that an increase in the superconducting gap suppresses both the oscillation magnitude and the period of the Ruderman-Kittel-Kasuya-Yosida interaction between two magnetic impurities. Within a mean-field approximation, the ferromagnetic Curie temperature is found to be essentially independent of the superconducting gap, an intriguing phenomenon due to a compensation effect between the short-range ferromagnetic and long-range antiferromagnetic interactions. The existence of robust superconductivity and persistent ferromagnetism at the interface allows realization of a novel topological phase transition from a nonchiral to a chiral superconducting state at sufficiently low temperatures, providing a new platform for topological quantum computation.
Topological Phase Transition in Metallic Single-Wall Carbon Nanotube
Okuyama, Rin; Izumida, Wataru; Eto, Mikio
2017-01-01
The topological phase transition is theoretically studied in a metallic single-wall carbon nanotube (SWNT) by applying a magnetic field B parallel to the tube. The Z topological invariant, winding number, is changed discontinuously when a small band gap is closed at a critical value of B, which can be observed as a change in the number of edge states owing to the bulk-edge correspondence. This is confirmed by numerical calculations for finite SWNTs of ˜1 µm length, using a one-dimensional lattice model to effectively describe the mixing between σ and π orbitals and spin-orbit interaction, which are relevant to the formation of the band gap in metallic SWNTs.
Controlled Topological Phases and Bulk-edge Correspondence
Kubota, Yosuke
2017-01-01
In this paper, we introduce a variation of the notion of topological phase reflecting metric structure of the position space. This framework contains not only periodic and non-periodic systems with symmetries in Kitaev's periodic table but also topological crystalline insulators. We also define the bulk and edge indices as invariants taking values in the twisted equivariant K-groups of Roe algebras as generalizations of existing invariants such as the Hall conductance or the Kane-Mele Z_2-invariant. As a consequence, we obtain a new mathematical proof of the bulk-edge correspondence by using the coarse Mayer-Vietoris exact sequence. As a new example, we study the index of reflection-invariant systems.
Phase transitions and topology in 2+k XY mean-field models.
Angelani, L; Ruocco, G
2007-11-01
The thermodynamics and topology of mean-field models with 2+k body interaction terms (generalizing XY model) are derived. Focusing on two particular cases (2+4 and 2+6 body interaction terms), a comparison between thermodynamic (phase transition energy, thermodynamically forbidden energy regions) and topological (singularity and curvature of saddle entropy) properties is performed. We find that (i) a topological change is present at the phase transition energy; however, (ii) only one topological change occurs, also for those models exhibiting two phase transitions; (iii) the order of a phase transition is not completely signaled by the curvature of topological quantities.
Valley polarized quantum Hall effect and topological insulator phase transitions in silicene
Tahir, M.
2013-01-25
The electronic properties of silicene are distinct from both the conventional two dimensional electron gas and the famous graphene due to strong spin orbit interaction and the buckled structure. Silicene has the potential to overcome limitations encountered for graphene, in particular the zero band gap and weak spin orbit interaction. We demonstrate a valley polarized quantum Hall effect and topological insulator phase transitions. We use the Kubo formalism to discuss the Hall conductivity and address the longitudinal conductivity for elastic impurity scattering in the first Born approximation. We show that the combination of an electric field with intrinsic spin orbit interaction leads to quantum phase transitions at the charge neutrality point, providing a tool to experimentally tune the topological state. Silicene constitutes a model system for exploring the spin and valley physics not accessible in graphene due to the small spin orbit interaction.
Majorana modes in InSb nanowires (II): resolving the topological phase diagram
Zhang, Hao; Gül, Önder; de Moor, Michiel; de Vries, Fokko; van Veen, Jasper; van Woerkom, David; Zuo, Kun; Mourik, Vincent; Cassidy, Maja; Geresdi, Attila; Car, Diana; Bakkers, Erik; Goswami, Srijit; Watanabe, Kenji; Taniguchi, Takashi; Kouwenhoven, Leo
Majorana modes in hybrid superconductor-semiconductor nanowire devices can be probed via tunnelling spectroscopy which shows a zero bias peak (ZBP) in differential conductance (1). Majoranas are formed when the Zeeman energy EZ and the chemical potential μ satisfy the condition EZ >√{Δ2 +μ2 } , with Δ the superconducting gap. This Majorana condition outlines the topologically non-trivial phase and predicts a particular dependence of ZBPs on the gate voltage and the external magnetic field. In this talk we show that the magnetic field range of ZBPs can be tuned by gate voltage and vice versa, consistent with these Majorana predictions. Supported by measurements in different external magnetic field orientations, these observations pave the way for exploring the topological phase diagram of spin-orbit coupled semiconductor nanowires with induced superconductivity.
Lefschetz, Solomon
1930-01-01
Lefschetz's Topology was written in the period in between the beginning of topology, by PoincarÃ©, and the establishment of algebraic topology as a well-formed subject, separate from point-set or geometric topology. At this time, Lefschetz had already proved his first fixed-point theorems. In some sense, the present book is a description of the broad subject of topology into which Lefschetz's theory of fixed points fits. Lefschetz takes the opportunity to describe some of the important applications of his theory, particularly in algebraic geometry, to problems such as counting intersections of
Hocking, John G
1988-01-01
""As textbook and reference work, this is a valuable addition to the topological literature."" - Mathematical ReviewsDesigned as a text for a one-year first course in topology, this authoritative volume offers an excellent general treatment of the main ideas of topology. It includes a large number and variety of topics from classical topology as well as newer areas of research activity.There are four set-theoretic chapters, followed by four primarily algebraic chapters. Chapter I covers the fundamentals of topological and metrical spaces, mappings, compactness, product spaces, the Tychonoff t
Zhang, Qianfan
2012-03-27
Topological insulator is a new state of matter attracting tremendous interest due to its gapless linear dispersion and spin momentum locking topological states located near the surface. Heterostructures, which have traditionally been powerful in controlling the electronic properties of semiconductor devices, are interesting for topological insulators. Here, we studied the spatial distribution of the topological state in Sb 2Se 3-Bi 2Se 3 heterostructures by first-principle simulation and discovered that an exotic topological state exists. Surprisingly, the state migrates from the nontrivial Bi 2Se 3 into the trivial Sb 2Se 3 region and spreads across the entire Sb 2Se 3 slab, extending beyond the concept of "surface" state while preserving all of the topological surface state characteristics. This unusual topological state arises from the coupling between different materials and the modification of electronic structure near Fermi energy. Our study demonstrates that heterostructures can open up opportunities for controlling the real-space distribution of the topological state and inducing quantum phase transitions between topologically trivial and nontrivial states. © 2012 American Chemical Society.
Structural phase transitions and topological defects in ion Coulomb crystals
Partner, Heather L. [Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig (Germany); Nigmatullin, Ramil [Institute of Quantum Physics, Albert-Einstein Allee-11, Ulm University, 89069 Ulm (Germany); Burgermeister, Tobias; Keller, Jonas; Pyka, Karsten [Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig (Germany); Plenio, Martin B. [Center for Integrated Quantum Science and Technology, Albert-Einstein-Allee 11, Ulm University, 89069 Ulm (Germany); Institute for Theoretical Physics, Albert-Einstein-Allee 11, Ulm University, 89069 Ulm (Germany); Retzker, Alex [Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Givat Ram (Israel); Zurek, Wojciech H. [Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87544 (United States); Campo, Adolfo del [Department of Physics, University of Massachusetts Boston, Boston, MA 02125 (United States); Mehlstäubler, Tanja E., E-mail: tanja.mehlstaeubler@ptb.de [Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig (Germany)
2015-03-01
We use laser-cooled ion Coulomb crystals in the well-controlled environment of a harmonic radiofrequency ion trap to investigate phase transitions and defect formation. Topological defects in ion Coulomb crystals (kinks) have been recently proposed for studies of nonlinear physics with solitons and as carriers of quantum information. Defects form when a symmetry breaking phase transition is crossed nonadiabatically. For a second order phase transition, the Kibble–Zurek mechanism predicts that the formation of these defects follows a power law scaling in the rate of the transition. We demonstrate a scaling of defect density and describe kink dynamics and stability. We further discuss the implementation of mass defects and electric fields as first steps toward controlled kink preparation and manipulation.
Structural phase transitions and topological defects in ion Coulomb crystals
Partner, Heather L. [Physikalisch-Technische Bundesanstalt, Braunschweig (Germany); Nigmatullin, Ramil [Institute of Quantum Physics, Ulm Univ., Ulm (Germany); Burgermeister, Tobias [Physikalisch-Technische Bundesanstalt, Braunschweig (Germany); Keller, Jonas [Physikalisch-Technische Bundesanstalt, Braunschweig (Germany); Pyka, Karsten [Physikalisch-Technische Bundesanstalt, Braunschweig (Germany); Plenio, Martin B. [Center for Integrated Quantum Science and Technology, Ulm Univ., Ulm, (Germany):Institute for Theoretical Physics, Ulm Univ.,Ulm, (Germany); Retzker, Alex [Racah Institute of Physics, The Hebrew University of Jerusalem, Givat Ram (Israel); Zurek, Wojciech Hubert [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); del Campo, Adolfo [Univ. of Massachusetts, Amherst, MA (United States). Dept. of Physics; Mehlstaubler, Tanja E. [Physikalisch-Technische Bundesanstalt, Braunschweig (Germany)
2014-11-19
We use laser-cooled ion Coulomb crystals in the well-controlled environment of a harmonic radiofrequency ion trap to investigate phase transitions and defect formation. Topological defects in ion Coulomb crystals (kinks) have been recently proposed for studies of nonlinear physics with solitons and as carriers of quantum information. Defects form when a symmetry breaking phase transition is crossed non-adiabatically. For a second order phase transition, the Kibble-Zurek mechanism predicts that the formation of these defects follows a power law scaling in the rate of the transition. We demonstrate a scaling of defect density and describe kink dynamics and stability. We further discuss the implementation of mass defects and electric fields as first steps toward controlled kink preparation and manipulation.
Nucleation of vacuum phase transitions by topological defects
Hiscock, W A
1995-01-01
The Euclidean action is calculated in the thin-wall approximation for a first-order vacuum phase transition in which the bubble appears symmetrically around either a global monopole or a gauge cosmic string. The bubble is assumed to be much larger than the core size of the monopole or string. In both cases the value of the Euclidean action is shown to be reduced below the O(4) symmetric action value, indicating that the topological defects act as effective nucleation sites for vacuum decay.
Transpose symmetry of the Jones matrix and topological phases.
Bhandari, Rajendra
2008-04-15
The transmission Jones matrix of an arbitrary stack of reciprocal plane-parallel plates that has been turned through 180 degrees about an axis in the plane of the stack is, in an appropriate basis, the transpose of the transmission matrix of the unturned slab with a change in the sign of the off-diagonal elements. We prove this convention-free result for the case where reflection at the interfaces can be ignored and use it to devise an experimental scheme to separate isotropic and topological phase changes in a reciprocal optical medium.
Topological Effects on Quantum Phase Slips in Superfluid Spin Transport
Kim, Se Kwon; Tserkovnyak, Yaroslav
2016-03-01
We theoretically investigate effects of quantum fluctuations on superfluid spin transport through easy-plane quantum antiferromagnetic spin chains in the large-spin limit. Quantum fluctuations result in the decaying spin supercurrent by unwinding the magnetic order parameter within the easy plane, which is referred to as phase slips. We show that the topological term in the nonlinear sigma model for the spin chains qualitatively differentiates the decaying rate of the spin supercurrent between the integer versus half-odd-integer spin chains. An experimental setup for a magnetoelectric circuit is proposed, in which the dependence of the decaying rate on constituent spins can be verified by measuring the nonlocal magnetoresistance.
Topological Phase Diagrams of Bulk and Monolayer TiS2−xTex
Zhu, Zhiyong
2013-02-12
With the use of ab initio calculations, the topological phase diagrams of bulk and monolayer TiS2−xTex are established. Whereas bulk TiS2−xTex shows two strong topological phases [1;(000)] and [1;(001)] for 0.44
Topological phase diagrams of bulk and monolayer TiS2-x Tex.
Zhu, Zhiyong; Cheng, Yingchun; Schwingenschlögl, Udo
2013-02-15
With the use of ab initio calculations, the topological phase diagrams of bulk and monolayer TiS(2-x) Te(x) are established. Whereas bulk TiS(2-x) Te(x) shows two strong topological phases [1;(000)] and [1;(001)] for 0.44
The topology of evolving rift fault networks: Single-phase vs multi-phase rifts
Duffy, Oliver B.; Nixon, Casey W.; Bell, Rebecca E.; Jackson, Christopher A.-L.; Gawthorpe, Rob L.; Sanderson, David J.; Whipp, Paul S.
2017-03-01
Rift fault networks can be complex, particularly those developed by multiple periods of non-coaxial extension, comprising non-colinear faults with many interactions. Thus, topology, rather than simple geometry, is required to characterise such networks, as it provides a way to describe the arrangement of individual faults in the network. Topology is analysed here in terms of nodes (isolated I nodes or connected Y or X nodes) and branches (I-I, I-C, C-C branches). In map view, the relative proportions of these parameters vary in natural single- and multi-phase rift fault networks and in scaled physical models at different stages of development and strain. Interactions in single-phase rifting are limited to fault splays and along-strike fault linkage (I node and I-I or I-C branch dominated networks), whereas in multi-phase rifting the topology evolves towards Y node and C-C branch dominated networks, with the degree of connectivity increasing with greater strain. The changes in topology and network connectivity have significant implications for fluid flow and reservoir compartmentalisation studies. Furthermore, topology helps to distinguish single and multiple phase extension (i.e. tectonic histories), and thus provide constraints on the geodynamic context of sedimentary basins.
Geometric phase mediated topological transport of sound vortices
Wang, Shubo; Chan, C T
2016-01-01
When a physical system undergoes a cyclic evolution, a non-integrable phase can arise in addition to the normal dynamical phase. This phase, depending only on the geometry of the path traversed in the parameter space and hence named geometric phase, has profound impact in both classical and quantum physics, leading to exotic phenomena such as electron weak anti-localization and light spin-Hall effect. Experimental observations of the geometric phase effect in classical system are typically realized using vector waves such as light characterized by a polarization. We show here that such an effect can also be realized in scalar wave systems such as sound wave. Using a helical hollow waveguide, we show that the geometric phase effect associated with the transportation of sound vortices, i.e. sound wave carrying intrinsic orbital angular momentum, can serve as a potential mechanism to control the flow of sound vortices with different topological charges, resulting in geometric phase-based sound vortex filters.
Topological Methods for Visualization
Berres, Anne Sabine [Los Alamos National Lab. (LANL), Los Alamos, NM (United Stat
2016-04-07
This slide presentation describes basic topological concepts, including topological spaces, homeomorphisms, homotopy, betti numbers. Scalar field topology explores finding topological features and scalar field visualization, and vector field topology explores finding topological features and vector field visualization.
Topological phases reviewed: The Aharonov Bohm, Aharonov Casher, and He McKellar Wilkens phases
McKellar, B. H. J. [ARC Centre of Excellence for Particle Physics at the Terrascale, School of Physics, University of Melbourne (Australia); He, X-G. [Department of Physics, National Taiwan University, Taipei, Taiwan (China); Klein, A. G. [School of Physics, University of Melbourne (Australia)
2014-03-05
There are three topological phases related to electromagnetic interactions in quantum mechanics: 1. The Aharonov Bohm phase acquired when a charged particle encircles a magnetic field but travels through a field free region. 2. The Aharonov Casher phase acquired when a magnetic dipole encircles electric charges but travels through a charge free region. 3. The He McKellar Wilkens phase acquired when an electric dipole encircles magnetic charges but travels through a charge free region. We review the conditions under which these phases are indeed topological and their experimental realisation. Because the He McKellar Wilkens phase has been recently observed we pay particular attention to how the basic concept of 'an electric dipole encircles magnetic charges' was realised experimentally, and discuss possible future experimental realisations.
Topological phase and edge states dependence of the RKKY interaction in zigzag silicene nanoribbon
Zare, Moslem; Parhizgar, Fariborz; Asgari, Reza
2016-07-01
We propose versatile materials based on the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in a zigzag silicene nanoribbon (ZSNR) on half filling in the presence of an out-of-plane electric field. We show that the topological phase transition in the band dispersion of ZSNR can be probed by using the RKKY interaction. We find that, due to the zero-energy edge states of the ZSNR, the exchange coupling is significantly enhanced when the impurities are located on the zigzag edges, and also explore that the strength of the interaction in the topological insulator phase is much greater than that when the system is in the band insulator region. We present a model to investigate the phase of a system of two magnetic impurities located on the edge of the ZSNR and find that three different magnetic phases, spiral, ferromagnetic, and antiferromagnetic, are possible for different values of the electric field. This electrical tunability of the magnetic phases in silicene can be explored by using current experimental techniques and can be of interest in the field of spintronics.
Shiozaki, Ken
2016-01-01
Matrix Product States (MPSs) provide a powerful framework to study and classify gapped quantum phases --symmetry-protected topological (SPT) phases in particular--defined in one dimensional lattices. On the other hand, it is natural to expect that gapped quantum phases in the limit of zero correlation length are described by topological quantum field theories (TFTs or TQFTs). In this paper, for (1+1)-dimensional bosonic SPT phases protected by symmetry $G$, we bridge their descriptions in terms of MPSs, and those in terms of $G$-equivariant TFTs. In particular, for various topological invariants (SPT invariants) constructed previously using MPSs, we provide derivations from the point of view of (1+1) TFTs. We also discuss the connection between boundary degrees of freedom, which appear when one introduces a physical boundary in SPT phases, and "open" TFTs, which are TFTs defined on spacetimes with boundaries.
Kuratowski, Kazimierz
1966-01-01
Topology, Volume I deals with topology and covers topics ranging from operations in logic and set theory to Cartesian products, mappings, and orderings. Cardinal and ordinal numbers are also discussed, along with topological, metric, and complete spaces. Great use is made of closure algebra. Comprised of three chapters, this volume begins with a discussion on general topological spaces as well as their specialized aspects, including regular, completely regular, and normal spaces. Fundamental notions such as base, subbase, cover, and continuous mapping, are considered, together with operations
Kuratowski, Kazimierz
1968-01-01
Topology, Volume II deals with topology and covers topics ranging from compact spaces and connected spaces to locally connected spaces, retracts, and neighborhood retracts. Group theory and some cutting problems are also discussed, along with the topology of the plane. Comprised of seven chapters, this volume begins with a discussion on the compactness of a topological space, paying particular attention to Borel, Lebesgue, Riesz, Cantor, and Bolzano-Weierstrass conditions. Semi-continuity and topics in dimension theory are also considered. The reader is then introduced to the connecte
Exploring Alternative Topologies for Network-on-Chip Architectures
Shafi Patel
2011-01-01
Full Text Available With increase in integration density and complexity of the system-on-Chip (SOC, the conventional interconnects are not suitable to fulfill the demands. The application of traditional network technologies in the form of Network-on-Chip is a potential solution. NoC design space has many variables. Selection of a better topology results in lesser complexities and better power-efficiency. In the proposed work, key research area in Network-on-chip design targeting communication infrastructure specially focusing on optimized topology design is worked upon. The simulation is modeled using a conventional network simulator tool packet tracer 5.3, in which by selecting proposed Topology 35.7 % reduction in traversing the longest path is observed.
UNIVERSALITY OF PHASE TRANSITION DYNAMICS: TOPOLOGICAL DEFECTS FROM SYMMETRY BREAKING
Zurek, Wojciech H. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Del Campo, Adolfo [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2014-02-13
In the course of a non-equilibrium continuous phase transition, the dynamics ceases to be adiabatic in the vicinity of the critical point as a result of the critical slowing down (the divergence of the relaxation time in the neighborhood of the critical point). This enforces a local choice of the broken symmetry and can lead to the formation of topological defects. The Kibble-Zurek mechanism (KZM) was developed to describe the associated nonequilibrium dynamics and to estimate the density of defects as a function of the quench rate through the transition. During recent years, several new experiments investigating formation of defects in phase transitions induced by a quench both in classical and quantum mechanical systems were carried out. At the same time, some established results were called into question. We review and analyze the Kibble-Zurek mechanism focusing in particular on this surge of activity, and suggest possible directions for further progress.
Topological String in Quantum-Chromodynamical Chiral Phase Transitions
LI Yun-De
2005-01-01
@@ It is pointed out that if in heavy ion collision processes, the quark-gluon plasma SU(2) chiral phase transition really takes place and the phase transition is a second order. Then the topological string, i.e., the π string, will be formed. The main effect of this phenomenon is that there will be a number of pions produced by decay of the π string in the final state. The pions from the decay of the π string lead to the same effect of decreasing the Hanbury-Brown-Twiss peak in two-pion spectra which is just as that of the long-lived hadronic resonances.At relativistic heavy-ion collision and large hadron collision energies, it is expected that the factors are about α～ 0.7 - 0.9 and α～ 0.6 - 0.85, respectively.
Exploring the stability of dimers through protein structure topology.
Di Paola, Luisa; Mei, Giampiero; Di Venere, Almerinda; Giuliani, Alessandro
2016-01-01
Protein homodimers pose some intriguing questions about the relation between structure and stability. We approached the problem by means of a topological methodology based on protein contact networks. We correlated local interface descriptors with structure and energy global properties of the systems under analysis. We demonstrated that the graph energy, formerly applied to the analysis of unconjugated hydrocarbons structures, is the bridge between the topological and energetic description of protein complexes. This is a first step for the generation of a "protein structural formula", analogous to the molecular graphs in organic chemistry.
Observation of topological nodal fermion semimetal phase in ZrSiS
Neupane, Madhab; Belopolski, Ilya; Hosen, M. Mofazzel; Sanchez, Daniel S.; Sankar, Raman; Szlawska, Maria; Xu, Su-Yang; Dimitri, Klauss; Dhakal, Nagendra; Maldonado, Pablo; Oppeneer, Peter M.; Kaczorowski, Dariusz; Chou, Fangcheng; Hasan, M. Zahid; Durakiewicz, Tomasz
2016-05-01
Unveiling new topological phases of matter is one of the current objectives in condensed matter physics. Recent experimental discoveries of Dirac and Weyl semimetals prompt the search for other exotic phases of matter. Here we present a systematic angle-resolved photoemission spectroscopy study of ZrSiS, a prime topological nodal semimetal candidate. Our wider Brillouin zone (BZ) mapping shows multiple Fermi surface pockets such as the diamond-shaped Fermi surface, elliptical-shaped Fermi surface, and a small electron pocket encircling at the zone center (Γ ) point, the M point, and the X point of the BZ, respectively. We experimentally establish the spinless nodal fermion semimetal phase in ZrSiS, which is supported by our first-principles calculations. Our findings evidence that the ZrSiS-type of material family is a new platform on which to explore exotic states of quantum matter; these materials are expected to provide an avenue for engineering two-dimensional topological insulator systems.
Topological phase in two flavor neutrino oscillations and imprint of the CP phase
Mehta, Poonam [Raman Research Institute, C. V. Raman Avenue, Bangalore 560 080 (India)
2012-08-15
We show that the coherent phase involved in the neutrino oscillation formalism can be decomposed into two parts, one corresponding to the usual energy-dependent dynamical phase and the other part being the achromatic geometric phase. This study was carried out specifically for (a) CP conserving two flavor case [P. Mehta. Topological phase in two flavor neutrino oscillations. Phys. Rev. D, 79:096013, 2009.] and (b) CP violating two flavor case [P. Mehta. Geometric imprint of cp violation in two flavor neutrino oscillations. (arXiv:0907.0562 [hep-ph]).]. We noted that the geometric phase is actually topological for case (a) irrespective of details of evolution while it can become geometric in case (b).
Exact result on topology and phase transitions at any finite N.
Casetti, Lapo; Cohen, E G D; Pettini, Marco
2002-03-01
We study analytically the topology of a family of submanifolds of the configuration space of the mean-field XY model, computing also a topological invariant (the Euler characteristic). We prove that a particular topological change of these submanifolds is connected to the phase transition of this system, and exists also at finite N. The present result is the first analytic proof that a phase transition has a topological origin and provides a key to a possible better understanding of the origin of phase transitions at their deepest level, as well as to a possible definition of phase transitions at finite N.
Xu, Zhihao; Zhang, Yunbo; Chen, Shu
2017-07-01
Experimental realizations of topological quantum systems and detections of topological invariants in ultracold atomic systems have been a greatly attractive topic. In this work, we propose a scheme to realize topologically different phases in a bichromatic optical lattice subjected to a periodically driven tilt harmonic oscillation, which can be effectively described by a superlattice model with tunable long-range hopping processes. By tuning the ratio of nearest-neighbor (NN) and next-nearest-neighbor (NNN) hopping amplitudes, the system undergoes a topological phase transition accompanied by the change of topological numbers of the lowest band from -1 to 2. Using a slowly time-periodic modulation, the system emerges distinct quantized topological pumped charges (TPCs) of atoms in the filled band for different topological phases. Our scheme is realizable in current cold atomic technique.
Pitfalls and feedback when constructing topological pressure-temperature phase diagrams
Ceolin, R.; Toscani, S.; Rietveld, Ivo B.; Barrio, M.; Tamarit, J. Ll.
2017-04-01
The stability hierarchy between different phases of a chemical compound can be accurately reproduced in a topological phase diagram. This type of phase diagrams may appear to be the result of simple extrapolations, however, experimental complications quickly increase in the case of crystalline trimorphism (and higher order polymorphism). To ensure the accurate positioning of stable phase domains, a topological phase diagram needs to be consistent. This paper gives an example of how thermodynamic feedback can be used in the topological construction of phase diagrams to ensure overall consistency in a phase diagram based on the case of piracetam crystalline trimorphism.
Weinberg, David H.; Gott, J. Richard, III; Melott, Adrian L.
1987-01-01
Many models for the formation of galaxies and large-scale structure assume a spectrum of random phase (Gaussian), small-amplitude density fluctuations as initial conditions. In such scenarios, the topology of the galaxy distribution on large scales relates directly to the topology of the initial density fluctuations. Here a quantitative measure of topology - the genus of contours in a smoothed density distribution - is described and applied to numerical simulations of galaxy clustering, to a variety of three-dimensional toy models, and to a volume-limited sample of the CfA redshift survey. For random phase distributions the genus of density contours exhibits a universal dependence on threshold density. The clustering simulations show that a smoothing length of 2-3 times the mass correlation length is sufficient to recover the topology of the initial fluctuations from the evolved galaxy distribution. Cold dark matter and white noise models retain a random phase topology at shorter smoothing lengths, but massive neutrino models develop a cellular topology.
Haaker, S.M.
2014-01-01
The research described in this thesis focuses on topological phases in condensed matter systems. It can be roughly divided into two parts. In the first part noninteracting systems are studied. The symmetry algebra of a charged spin-1/2 particle coupled to a non-Abelian magnetic field is determined,
Computer Based Porosity Design by Multi Phase Topology Optimization
Burblies, Andreas; Busse, Matthias
2008-02-01
A numerical simulation technique called Multi Phase Topology Optimization (MPTO) based on finite element method has been developed and refined by Fraunhofer IFAM during the last five years. MPTO is able to determine the optimum distribution of two or more different materials in components under thermal and mechanical loads. The objective of optimization is to minimize the component's elastic energy. Conventional topology optimization methods which simulate adaptive bone mineralization have got the disadvantage that there is a continuous change of mass by growth processes. MPTO keeps all initial material concentrations and uses methods adapted from molecular dynamics to find energy minimum. Applying MPTO to mechanically loaded components with a high number of different material densities, the optimization results show graded and sometimes anisotropic porosity distributions which are very similar to natural bone structures. Now it is possible to design the macro- and microstructure of a mechanical component in one step. Computer based porosity design structures can be manufactured by new Rapid Prototyping technologies. Fraunhofer IFAM has applied successfully 3D-Printing and Selective Laser Sintering methods in order to produce very stiff light weight components with graded porosities calculated by MPTO.
Zeeman-Field-Tuned Topological Phase Transitions in a Two-Dimensional Class-DIII Superconductor.
Deng, W Y; Geng, H; Luo, W; Sheng, L; Xing, D Y
2016-01-01
We investigate the topological phase transitions in a two-dimensional time-reversal invariant topological superconductor in the presence of a Zeeman field. Based on the spin Chern number theory, we find that the system exhibits a number of topologically distinct phases with changing the out-of-plane component of the Zeeman field, including a quantum spin Hall-like phase, quantum anomalous Hall-like phases with total Chern number C = -2, -1, 1 and 2, and a topologically trivial superconductor phase. The BdG band gap closes at each boundary of the phase transitions. Furthermore, we demonstrate that the zero bias conductance provides clear transport signatures of the different topological phases, which are robust against symmetry-breaking perturbations.
Vortex driven phase transition in Topologically Massive QED
Hoshino, Yuichi
2016-01-01
There is chiral like symmetry for 4-component massless fermion in (2+1)-dimensional gauge theory.Since QED$_{3}$ with Chern-Simons term contains vortex solution for vector potential,one may expect vortex driven phase transition as Kosterlitz-Thouless type where chiral condensate is washed away at zero temperature.To study this possibility,we evaluate the fermion propagator by Dyson-Schwinger equation numerically and spectral function analytically in the Landau gauge.For quenched case we adopt Ball-Chiu vertex to keep gauge invariance of the results.The critical value of topological mass,above which chiral condensate washed away, turned out to be $O(10^{-2})e^{2}$ at least for weak coupling in both cases.
The topological Anderson insulator phase in the Kane-Mele model.
Orth, Christoph P; Sekera, Tibor; Bruder, Christoph; Schmidt, Thomas L
2016-04-05
It has been proposed that adding disorder to a topologically trivial mercury telluride/cadmium telluride (HgTe/CdTe) quantum well can induce a transition to a topologically nontrivial state. The resulting state was termed topological Anderson insulator and was found in computer simulations of the Bernevig-Hughes-Zhang model. Here, we show that the topological Anderson insulator is a more universal phenomenon and also appears in the Kane-Mele model of topological insulators on a honeycomb lattice. We numerically investigate the interplay of the relevant parameters, and establish the parameter range in which the topological Anderson insulator exists. A staggered sublattice potential turns out to be a necessary condition for the transition to the topological Anderson insulator. For weak enough disorder, a calculation based on the lowest-order Born approximation reproduces quantitatively the numerical data. Our results thus considerably increase the number of candidate materials for the topological Anderson insulator phase.
Design of materials with extreme thermal expansion using a three-phase topology optimization method
Sigmund, Ole; Torquato, S.
1997-01-01
Composites with extremal or unusual thermal expansion coefficients are designed using a three-phase topology optimization method. The composites are made of two different material phases and a void phase. The topology optimization method consists in finding the distribution of material phases...... materials having maximum directional thermal expansion (thermal actuators), zero isotropic thermal expansion, and negative isotropic thermal expansion. It is shown that materials with effective negative thermal expansion coefficients can be obtained by mixing two phases with positive thermal expansion...
Manetti, Marco
2015-01-01
This is an introductory textbook on general and algebraic topology, aimed at anyone with a basic knowledge of calculus and linear algebra. It provides full proofs and includes many examples and exercises. The covered topics include: set theory and cardinal arithmetic; axiom of choice and Zorn's lemma; topological spaces and continuous functions; connectedness and compactness; Alexandrov compactification; quotient topologies; countability and separation axioms; prebasis and Alexander's theorem; the Tychonoff theorem and paracompactness; complete metric spaces and function spaces; Baire spaces; homotopy of maps; the fundamental group; the van Kampen theorem; covering spaces; Brouwer and Borsuk's theorems; free groups and free product of groups; and basic category theory. While it is very concrete at the beginning, abstract concepts are gradually introduced. It is suitable for anyone needing a basic, comprehensive introduction to general and algebraic topology and its applications.
Phase Field Models for Thin Elastic Structures with Topological Constraint
Dondl, Patrick W.; Lemenant, Antoine; Wojtowytsch, Stephan
2017-02-01
This article is concerned with the problem of minimising the Willmore energy in the class of connected surfaces with prescribed area which are confined to a small container. We propose a phase field approximation based on De Giorgi's diffuse Willmore functional to this variational problem. Our main contribution is a penalisation term which ensures connectedness in the sharp interface limit. The penalisation of disconnectedness is based on a geodesic distance chosen to be small between two points that lie on the same connected component of the transition layer of the phase field. We prove that in two dimensions, sequences of phase fields with uniformly bounded diffuse Willmore energy and diffuse area converge uniformly to the zeros of a double-well potential away from the support of a limiting measure. In three dimensions, we show that they converge H^1-almost everywhere on curves. This enables us to show {Γ}-convergence to a sharp interface problem that only allows for connected structures. The results also imply Hausdorff convergence of the level sets in two dimensions and a similar result in three dimensions. Furthermore, we present numerical evidence of the effectiveness of our model. The implementation relies on a coupling of Dijkstra's algorithm in order to compute the topological penalty to a finite element approach for the Willmore term.
Lokman Tsui
2017-06-01
Full Text Available The study of continuous phase transitions triggered by spontaneous symmetry breaking has brought revolutionary ideas to physics. Recently, through the discovery of symmetry protected topological phases, it is realized that continuous quantum phase transition can also occur between states with the same symmetry but different topology. Here we study a specific class of such phase transitions in 1+1 dimensions – the phase transition between bosonic topological phases protected by Zn×Zn. We find in all cases the critical point possesses two gap opening relevant operators: one leads to a Landau-forbidden symmetry breaking phase transition and the other to the topological phase transition. We also obtained a constraint on the central charge for general phase transitions between symmetry protected bosonic topological phases in 1+1D.
Symmetry enrichment in three-dimensional topological phases
Ning, Shang-Qiang; Liu, Zheng-Xin; Ye, Peng
2016-12-01
While two-dimensional symmetry-enriched topological phases (SETs ) have been studied intensively and systematically, three-dimensional ones are still open issues. We propose an algorithmic approach of imposing global symmetry Gs on gauge theories (denoted by GT) with gauge group Gg. The resulting symmetric gauge theories are dubbed "symmetry-enriched gauge theories" (SEG), which may be served as low-energy effective theories of three-dimensional symmetric topological quantum spin liquids. We focus on SEGs with gauge group Gg=ZN1×ZN2×⋯ and onsite unitary symmetry group Gs=ZK1×ZK2×⋯ or Gs=U (1 ) ×ZK 1×⋯ . Each SEG(Gg,Gs) is described in the path-integral formalism associated with certain symmetry assignment. From the path-integral expression, we propose how to physically diagnose the ground-state properties (i.e., SET orders) of SEGs in experiments of charge-loop braidings (patterns of symmetry fractionalization) and the mixed multiloop braidings among deconfined loop excitations and confined symmetry fluxes. From these symmetry-enriched properties, one can obtain the map from SEGs to SETs . By giving full dynamics to background gauge fields, SEGs may be eventually promoted to a set of new gauge theories (denoted by GT*). Based on their gauge groups, GT*s may be further regrouped into different classes, each of which is labeled by a gauge group Gg*. Finally, a web of gauge theories involving GT,SEG,SET, and GT* is achieved. We demonstrate the above symmetry-enrichment physics and the web of gauge theories through many concrete examples.
Topological Origin of the Phase Transition in a Mean-Field Model
Casetti, L. [Istituto Nazionale per la Fisica della Materia (INFM), Unita di Ricerca del Politecnico di Torino, Dipartimento di Fisica, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino (Italy); Cohen, E.G. [The Rockefeller University, 1230 York Avenue, New York, New York 10021-6399 (United States); Pettini, M.; Pettini, M. [Istituto Nazionale per la Fisica della Materia (INFM), Unita di Ricerca di Firenze, Firenze, Italy] [RAMAN SPECTRA, MICROSCOPY, IMAGES, BIOPHYSICS, MULTI-PHOTON PROCESSES, FLUORESCENCE, BACTERIA, VIBRATIONAL STATES
1999-05-01
We argue that the phase transition in the mean-field XY model is related to a particular change in the topology of its configuration space. The nature of this topological change can be discussed on the basis of elementary Morse theory using the potential energy per particle V as a Morse function. The value of V where such a topological change occurs equals the thermodynamic value of V at the phase transition and the number of (Morse) critical points grows very fast with the number of particles N . Furthermore, as in statistical mechanics, the way the thermodynamic limit is taken is crucial in topology. {copyright} {ital 1999} {ital The American Physical Society}
Topological phase transition in a ladder of the dimerized Kitaev superconductor chains
Zhou, Bo-Zhen; Zhou, Bin
2016-10-01
We investigate the topological properties of a ladder model of the dimerized Kitaev superconductor chains. The topological class of the system is determined by the relative phase θ between the inter- and intra-chain superconducting pairing. One topological class is the class BDI characterized by the ℤ index, and the other is the class D characterized by the ℤ2 index. For the two different topological classes, the topological phase diagrams of the system are presented by calculating two different topological numbers, i.e., the ℤ index winding number W and the ℤ2 index Majorana number ℳ, respectively. In the case of θ =0, the topological class belongs to the class BDI, multiple topological phase transitions accompanying the variation of the number of Majorana zero modes are observed. In the case of θ =π/2 it belongs to the class D. Our results show that for the given value of dimerization, the topologically nontrivial and trivial phases alternate with the variation of chemical potential. Project supported by the National Natural Science Foundation of China (Grant No. 11274102), the Program for New Century Excellent Talents in University of Ministry of Education of China (Grant No. NCET-11-0960), and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20134208110001).
Fermi points and topological quantum phase transitions in a multi-band superconductor.
Puel, T O; Sacramento, P D; Continentino, M A
2015-10-28
The importance of models with an exact solution for the study of materials with non-trivial topological properties has been extensively demonstrated. The Kitaev model plays a guiding role in the search for Majorana modes in condensed matter systems. Also, the sp-chain with an anti-symmetric mixing among the s and p bands is a paradigmatic example of a topological insulator with well understood properties. Interestingly, these models share the same universality class for their topological quantum phase transitions. In this work we study a two-band model of spinless fermions with attractive inter-band interactions. We obtain its zero temperature phase diagram, which presents a rich variety of phases including a Weyl superconductor and a topological insulator. The transition from the topological to the trivial superconducting phase has critical exponents different from those of Kitaev's model.
Stability of Topological Quantum Phases at Zero Temperature
Michalakis, Spyridon; Pytel, Justyna
2012-02-01
We prove stability of the spectral gap for gapped, frustration-free Hamiltonians under general, quasi-local perturbations. We present a necessary and sufficient condition for stability, which we call Local Topological Quantum Order and show that this condition implies an area law for the entanglement entropy of the groundstate subspace. This result extends previous work by Bravyi et al, on the stability of topological quantum order for the groundstate subspace of Hamiltonians composed of commuting projections with a common zero-energy subspace. Moreover, our result implies that zero-temperature topological order is robust against quasi-local perturbations, for all topologically ordered subspaces that correspond to the groundstate space of a gapped, frustration-free Hamiltonian. Finally, even in the absence of topological order, we show that symmetry-protected sectors are also stable against perturbations respecting the same symmetries.
The ω-SQUIPT as a tool to phase-engineer Josephson topological materials
Strambini, E.; D'Ambrosio, S.; Vischi, F.; Bergeret, F. S.; Nazarov, Yu. V.; Giazotto, F.
2016-12-01
Multi-terminal superconducting Josephson junctions based on the proximity effect offer the opportunity to tailor non-trivial quantum states in nanoscale weak links. These structures can realize exotic topologies in several dimensions, for example, artificial topological superconductors that are able to support Majorana bound states, and pave the way to emerging quantum technologies and future quantum information schemes. Here we report the realization of a three-terminal Josephson interferometer based on a proximized nanosized weak link. Our tunnelling spectroscopy measurements reveal transitions between gapped (that is, insulating) and gapless (conducting) states that are controlled by the phase configuration of the three superconducting leads connected to the junction. We demonstrate the topological nature of these transitions: a gapless state necessarily occurs between two gapped states of different topological indices, in much the same way that the interface between two insulators of different topologies is necessarily conducting. The topological numbers that characterize such gapped states are given by superconducting phase windings over the two loops that form the Josephson interferometer. As these gapped states cannot be transformed to one another continuously without passing through a gapless condition, they are topologically protected. The same behaviour is found for all of the points of the weak link, confirming that this topology is a non-local property. Our observation of the gapless state is pivotal for enabling phase engineering of different and more sophisticated artificial topological materials.
Chiral Aromaticities. A Topological Exploration of Möbius Homoaromaticity.
Allan, Charlotte S M; Rzepa, Henry S
2008-11-11
A series of C2-symmetric homoderivatives of the cyclo C9H9(+) cation first identified by Schleyer as Möbius aromatic are shown to themselves sustain Möbius 4n-π-electron homoaromaticity. Analogous double-twist Möbius bis-homoaromatics follow a 4n+2 electron rule. AIM (atoms-in-molecules) and ELF (electron localization function) analysis of the electron topology in the region of the homobond of these systems reveals that the presence of a AIM bond-critical point in this region is not mandatory, it being unstable to subtle variations in the local electron density induced by local or remote substituents, and which can in turn induce self-annihilation or creation of a pair of bond and ring critical points. The same substituent-induced annihilation/creation of such a BCP/RCP pair can also be observed in the nonclassical norbornyl cation. We suggest that the ELF and ELFπ thresholds for any basin found in the homoregion are better indicators of the delocalized nature of the homoaromatic interaction and the aromaticity of the system.
Topological Phases in InAs1 -xSbx: From Novel Topological Semimetal to Majorana Wire
Winkler, Georg W.; Wu, QuanSheng; Troyer, Matthias; Krogstrup, Peter; Soluyanov, Alexey A.
2016-08-01
Superconductor proximitized one-dimensional semiconductor nanowires with strong spin-orbit interaction (SOI) are, at this time, the most promising candidates for the realization of topological quantum information processing. In current experiments the SOI originates predominantly from extrinsic fields, induced by finite size effects and applied gate voltages. The dependence of the topological transition in these devices on microscopic details makes scaling to a large number of devices difficult unless a material with dominant intrinsic bulk SOI is used. Here, we show that wires made of certain ordered alloys InAs1 -xSbx have spin splittings up to 20 times larger than those reached in pristine InSb wires. In particular, we show this for a stable ordered CuPt structure at x =0.5 , which has an inverted band ordering and realizes a novel type of a topological semimetal with triple degeneracy points in the bulk spectrum that produce topological surface Fermi arcs. Experimentally achievable strains can either drive this compound into a topological insulator phase or restore the normal band ordering, making the CuPt-ordered InAs0.5Sb0.5 a semiconductor with a large intrinsic linear in k bulk spin splitting.
The modular S-matrix as order parameter for topological phase transition
Bais, F.A.; Romers, J.C.
2012-01-01
Part of Focus on Topological Quantum Computation We study topological phase transitions in discrete gauge theories in two spatial dimensions induced by the formation of a Bose condensate. We analyse a general class of euclidean lattice actions for these theories which contain one coupling constant f
A Generic Topology Derivation Method for Single-phase Converters with Active Capacitive DC-links
Wang, Haoran; Wang, Huai; Zhu, Guorong;
2016-01-01
capacitive DCDC- link solutions, but important aspects of the topology assess-ment, such as the total energy storage, overall capacitive energy buffer ratio, cost, and reliability are still not available. This paper proposes a generic topology derivation method of single-phase power converters...... with capacitive DC-links, which derives all existing topologies to our best knowledge, and identify a few new topologies. A reliability-oriented design process is applied to compare the cost of different solutions with the lifetime target of 10 years and 35 years, respectively. It reveals that the most cost...
T Santosh Kumar; Dr. K. B. Madhu Sahu
2014-01-01
This paper presents the detailed model, control and simulation of H-Bridge VSI topology based DSTATCOM. It also describes the control of multilevel inverter supplied by Photovoltaic system and a battery bank which is connected to the supply system. It is well known that the Power Quality of the Multililevel Inverter signals depends upon the number of levels. Basic structure and operating principle of the Cascaded H-Bridge Multilevel Inverter are explored. The phase shifted SPW...
Quantum entanglement in topological phases on a torus
Luo, Zhu-Xi; Hu, Yu-Ting; Wu, Yong-Shi
2016-08-01
In this paper, we study the effect of nontrivial spatial topology on quantum entanglement by examining the degenerate ground states of a topologically ordered system on a torus. Using the string-net (fixed-point) wave function, we propose a general formula of the reduced density matrix when the system is partitioned into two cylinders. The cylindrical topology of the subsystems makes a significant difference in regard to entanglement: a global quantum number for the many-body states comes into play, together with a decomposition matrix M which describes how topological charges of the ground states decompose into boundary degrees of freedom. We obtain a general formula for entanglement entropy and generalize the concept of minimally entangled states to minimally entangled sectors. Concrete examples are demonstrated with data from both finite groups and modular tensor categories (i.e., Fibonacci, Ising, etc.), supported by numerical verification.
Topological Phases in Graphene Nanoribbons: Junction States, Spin Centers, and Quantum Spin Chains
Cao, Ting; Zhao, Fangzhou; Louie, Steven G.
2017-08-01
We show that semiconducting graphene nanoribbons (GNRs) of different width, edge, and end termination (synthesizable from molecular precursors with atomic precision) belong to different electronic topological classes. The topological phase of GNRs is protected by spatial symmetries and dictated by the terminating unit cell. We have derived explicit formulas for their topological invariants and shown that localized junction states developed between two GNRs of distinct topology may be tuned by lateral junction geometry. The topology of a GNR can be further modified by dopants, such as a periodic array of boron atoms. In a superlattice consisting of segments of doped and pristine GNRs, the junction states are stable spin centers, forming a Heisenberg antiferromagnetic spin 1 /2 chain with tunable exchange interaction. The discoveries here not only are of scientific interest for studies of quasi-one-dimensional systems, but also open a new path for design principles of future GNR-based devices through their topological characters.
Using maximum topology matching to explore differences in species distribution models
Poco, Jorge; Doraiswamy, Harish; Talbert, Marian K.; Morisette, Jeffrey; Silva, Claudio
2015-01-01
Species distribution models (SDM) are used to help understand what drives the distribution of various plant and animal species. These models are typically high dimensional scalar functions, where the dimensions of the domain correspond to predictor variables of the model algorithm. Understanding and exploring the differences between models help ecologists understand areas where their data or understanding of the system is incomplete and will help guide further investigation in these regions. These differences can also indicate an important source of model to model uncertainty. However, it is cumbersome and often impractical to perform this analysis using existing tools, which allows for manual exploration of the models usually as 1-dimensional curves. In this paper, we propose a topology-based framework to help ecologists explore the differences in various SDMs directly in the high dimensional domain. In order to accomplish this, we introduce the concept of maximum topology matching that computes a locality-aware correspondence between similar extrema of two scalar functions. The matching is then used to compute the similarity between two functions. We also design a visualization interface that allows ecologists to explore SDMs using their topological features and to study the differences between pairs of models found using maximum topological matching. We demonstrate the utility of the proposed framework through several use cases using different data sets and report the feedback obtained from ecologists.
Chen, Wei; Legner, Markus; Rüegg, Andreas; Sigrist, Manfred
2017-02-01
The correlation functions related to topological phase transitions in inversion-symmetric lattice models described by 2 ×2 Dirac Hamiltonians are discussed. In one dimension, the correlation function measures the charge-polarization correlation between Wannier states at different positions, while in two dimensions it measures the itinerant-circulation correlation between Wannier states. The correlation function is nonzero in both the topologically trivial and nontrivial states, and allows us to extract a correlation length that diverges at topological phase transitions. The correlation length and the curvature function that defines the topological invariants are shown to have universal critical exponents, allowing the notion of universality classes to be introduced. Particularly in two dimensions, the universality class is determined by the orbital symmetry of the Dirac model. The scaling laws that constrain the critical exponents are revealed, and are predicted to be satisfied even in interacting systems, as demonstrated in an interacting topological Kondo insulator.
Fingerprint of topological Andreev bound states in phase-dependent heat transport
Sothmann, Björn; Hankiewicz, Ewelina M.
2016-08-01
We demonstrate that phase-dependent heat currents through superconductor-topological insulator Josephson junctions provide a useful tool to probe the existence of topological Andreev bound states, even for multichannel surface states. We predict that in the tunneling regime topological Andreev bound states lead to a minimum of the thermal conductance for a phase difference ϕ =π , in clear contrast to a maximum of the thermal conductance at ϕ =π that occurs for trivial Andreev bound states in superconductor-normal-metal tunnel junctions. This opens up the possibility that phase-dependent heat transport can distinguish between topologically trivial and nontrivial 4 π modes. Furthermore, we propose a superconducting quantum interference device geometry where phase-dependent heat currents can be measured using available experimental technology.
Experiments on Quantum Hall Topological Phases in Ultra Low Temperatures
Du, Rui-Rui [Rice Univ., Houston, TX (United States). Dept. of Physics and Astronomy
2015-02-14
This project is to cool electrons in semiconductors to extremely low temperatures and to study new states of matter formed by low-dimensional electrons (or holes). At such low temperatures (and with an intense magnetic field), electronic behavior differs completely from ordinary ones observed at room temperatures or regular low temperature. Studies of electrons at such low temperatures would open the door for fundamental discoveries in condensed matter physics. Present studies have been focus on topological phases in the fractional quantum Hall effect in GaAs/AlGaAs semiconductor heterostructures, and the newly discovered (by this group) quantum spin Hall effect in InAs/GaSb materials. This project consists of the following components: 1) Development of efficient sample cooling techniques and electron thermometry: Our goal is to reach 1 mK electron temperature and reasonable determination of electron temperature; 2) Experiments at ultra-low temperatures: Our goal is to understand the energy scale of competing quantum phases, by measuring the temperature-dependence of transport features. Focus will be placed on such issues as the energy gap of the 5/2 state, and those of 12/5 (and possible 13/5); resistive signature of instability near 1/2 at ultra-low temperatures; 3) Measurement of the 5/2 gaps in the limit of small or large Zeeman energies: Our goal is to gain physics insight of 5/2 state at limiting experimental parameters, especially those properties concerning the spin polarization; 4) Experiments on tuning the electron-electron interaction in a screened quantum Hall system: Our goal is to gain understanding of the formation of paired fractional quantum Hall state as the interaction pseudo-potential is being modified by a nearby screening electron layer; 5) Experiments on the quantized helical edge states under a strong magnetic field and ultralow temperatures: our goal is to investigate both the bulk and edge states in a quantum spin Hall insulator under time
Time reversal symmetry broken fractional topological phases at zero magnetic field
Meng, Tobias; Sela, Eran
2014-12-01
We extend the coupled-wire construction of quantum Hall phases, and search for fractional topological insulating states in models of weakly coupled wires at zero external magnetic field. Focusing on systems beyond double copies of fractional quantum Hall states at opposite fields, we find that spin-spin interactions can stabilize a large family of fractional topological phases with broken time reversal invariance. The latter is manifested by spontaneous spin polarization, by a finite Hall conductivity, or by both. This suggests the possibility that fractional topological insulators may be unstable to spontaneous symmetry breaking.
Quantum spin/valley Hall effect and topological insulator phase transitions in silicene
Tahir, M.
2013-04-26
We present a theoretical realization of quantum spin and quantum valley Hall effects in silicene. We show that combination of an electric field and intrinsic spin-orbit interaction leads to quantum phase transitions at the charge neutrality point. This phase transition from a two dimensional topological insulator to a trivial insulating state is accompanied by a quenching of the quantum spin Hall effect and the onset of a quantum valley Hall effect, providing a tool to experimentally tune the topological state of silicene. In contrast to graphene and other conventional topological insulators, the proposed effects in silicene are accessible to experiments.
Floquet Topological Phases Driven by $\\mathcal{PT}$ Symmetric Nonunitary Time Evolution
Kim, Dakyeong; Kawakami, Norio; Obuse, Hideaki
2016-01-01
We study Floquet topological phases driven by $\\mathcal{PT}$ symmetric nonunitary time evolution in one dimension, based on an experimental setup of discrete-time quantum walks. We develop, for nonunitary time-evolution operators, a procedure to calculate topological invariants for Floquet topological phases and find that the bulk-edge correspondence gives correct predictions of the emergent edge states. These edge states make exponential growth of wavefunction amplitudes at specific positions with time controllable. Hereby, we propose that these phenomena inherent in open quantum systems are feasibly observed by present experiments of quantum walks in both classical and quantum regimes.
Lapa, Matthew F; Ye, Peng; Hughes, Taylor L
2016-01-01
We calculate the topological part of the electromagnetic response of Bosonic Integer Quantum Hall (BIQH) phases in odd (spacetime) dimensions, and Bosonic Topological Insulator (BTI) and Bosonic chiral semi-metal (BCSM) phases in even dimensions. To do this we use the Nonlinear Sigma Model (NLSM) description of bosonic symmetry-protected topological (SPT) phases, and the method of gauged Wess-Zumino (WZ) actions. We find the surprising result that for BIQH states in dimension $2m-1$ ($m=1,2,\\dots$), the bulk response to an electromagnetic field $A_{\\mu}$ is characterized by a Chern-Simons term for $A_{\\mu}$ with a level quantized in integer multiples of $m!$ (factorial). We also show that BTI states (which have an extra $\\mathbb{Z}_2$ symmetry) can exhibit a $\\mathbb{Z}_2$ breaking Quantum Hall effect on their boundaries, with this boundary Quantum Hall effect described by a Chern-Simons term at level $\\frac{m!}{2}$. We show that the factor of $m!$ can be understood by requiring gauge invariance of the expone...
Topological phase transition in hexagonal boron-nitride bilayers modulated by gate voltage
Jin, Guojun; Zhai, Xuechao
2013-03-01
We study the gate-voltage modulated electronic properties of hexagonal boron-nitride bilayers with two different stacking structures in the presence of intrinsic and Rashba spin-orbit interactions. Our analytical results show that there are striking cooperation effects arising from the spin-orbit interactions and the interlayer bias voltage. For realizing topological phase transition, in contrast to a gated graphene bilayer for increasing its energy gap, the energy gap of a boron-nitride bilayer is significantly reduced by an applied gate voltage. For the AA stacking-bilayer which has the inversion symmetry, a strong topological phase is found, and there is an interesting reentrant behavior from a normal phase to a topological phase and then to a normal phase again, characterized by the topological index. Therefore, the gate voltage modulated AA-boron nitride bilayer can be taken as a newcomer of the topological insulator family. For the AB stacking-bilayer which is lack of the inversion symmetry, it is always topologically trivial, but exhibits an unusual quantum Hall phase with four degenerate low-energy states localized at a single edge. It is suggested that these theoretical findings could be verified experimentally in the transport properties of boron-nitride bylayers. This research was supported by the NSFC (Nos. 60876065, 11074108), PAPD, and NBRPC (Nos. 2009CB929504, 2011CB922102).
Edge Quantum Criticality and Emergent Supersymmetry in Topological Phases
Li, Zi-Xiang; Jiang, Yi-Fan; Yao, Hong
2017-09-01
Proposed as a fundamental symmetry describing our Universe, spacetime supersymmetry (SUSY) has not been discovered yet in nature. Nonetheless, it has been predicted that SUSY may emerge in low-energy physics of quantum materials such as topological superconductors and Weyl semimetals. Here, by performing state-of-the-art sign-problem-free quantum Monte Carlo simulations of an interacting two-dimensional topological superconductor, we show convincing evidence that the N =1 SUSY emerges at its edge quantum critical point (EQCP) while its bulk remains gapped and topologically nontrivial. Remarkably, near the EQCP, we find that the edge Majorana fermion acquires a mass that is identical with that of its bosonic superpartner. To the best of our knowledge, this is the first observation that fermions and bosons have equal dynamically generated masses, a hallmark of emergent SUSY. We further discuss experimental signatures of such EQCP and associated SUSY.
You, Yi-Zhuang; Bi, Zhen; Mao, Dan; Xu, Cenke
2016-03-01
We propose a series of simple two-dimensional (2D) lattice interacting fermion models that we demonstrate at low energy describe bosonic symmetry-protected topological (SPT) states and quantum phase transitions between them. This is because due to interaction, the fermions are gapped both at the boundary of the SPT states and at the bulk quantum phase transition, thus these models at low energy can be described completely by bosonic degrees of freedom. We show that the bulk of these models is described by a Sp (N ) principal chiral model with a topological Θ term, whose boundary is described by a Sp (N ) principal chiral model with a Wess-Zumino-Witten term at level 1. The quantum phase transition between SPT states in the bulk is tuned by a particular interaction term, which corresponds to tuning Θ in the field theory, and the phase transition occurs at Θ =π . The simplest version of these models with N =1 is equivalent to the familiar O(4) nonlinear sigma model (NLSM) with a topological term, whose boundary is a (1 +1 )D conformal field theory with central charge c =1 . After breaking the O(4) symmetry to its subgroups, this model can be viewed as bosonic SPT states with U(1), or Z2 symmetries, etc. All of these fermion models, including the bulk quantum phase transitions, can be simulated with the determinant quantum Monte Carlo method without the sign problem. Recent numerical results strongly suggest that the quantum disordered phase of the O(4) NLSM with precisely Θ =π is a stable (2 +1 )D conformal field theory with gapless bosonic modes.
Importance of charge fluctuations for the topological phase in SmB(6).
Min, Chul-Hee; Lutz, P; Fiedler, S; Kang, B Y; Cho, B K; Kim, H-D; Bentmann, H; Reinert, F
2014-06-06
Typical Kondo insulators (KIs) can have a nontrivial Z_{2} topology because the energy gap opens at the Fermi energy (E_{F}) by a hybridization between odd- and even-parity bands. SmB_{6} deviates from such KI behavior, and it has been unclear how the insulating phase occurs. Here, we demonstrate that charge fluctuations are the origin of the topological insulating phase in SmB_{6}. Our angle-resolved photoemission spectroscopy results reveal that with decreasing temperature the bottom of the d-f hybridized band at the X[over ¯] point, which is predicted to have odd parity and is required for a topological phase, gradually shifts from below to above E_{F}. We conclude that SmB_{6} is a charge-fluctuating topological insulator.
Two-dimensional topological crystalline insulator phase in quantum wells of trivial insulators
Niu, Chengwang; Buhl, Patrick M.; Bihlmayer, Gustav; Wortmann, Daniel; Blügel, Stefan; Mokrousov, Yuriy
2016-06-01
The realization of two-dimensional (2D) topological insulators (TIs) in HgTe/CdTe quantum wells (QWs) has generated an explosion of research on TIs and novel topologically nontrivial phases. Here we predict, based on first-principles calculations, that the newly discovered 2D topological crystalline insulators (TCIs) phase exists even in the QWs of trivial insulators, e.g. (Sn/Pb)Te and Na(Cl/Br), with mirror Chern number {n}{{M}}=-2. Tunable nontrivial energy gaps ranging from 4 to 238 meV are obtained, guaranteeing further room-temperature observations and applications. The combined effect of strain and electrostatic interaction that can be engineered by the cladding layers leads to a band inversion, resulting in the phase transition from trivial insulator to 2D TCIs. Our work provides a new strategy for engineering topological states in 2D materials.
Topological states and phase transitions in Sb2Te3-GeTe multilayers
Nguyen, Thuy-Anh; Backes, Dirk; Singh, Angadjit; Mansell, Rhodri; Barnes, Crispin; Ritchie, David A.; Mussler, Gregor; Lanius, Martin; Grützmacher, Detlev; Narayan, Vijay
2016-06-01
Topological insulators (TIs) are bulk insulators with exotic ‘topologically protected’ surface conducting modes. It has recently been pointed out that when stacked together, interactions between surface modes can induce diverse phases including the TI, Dirac semimetal, and Weyl semimetal. However, currently a full experimental understanding of the conditions under which topological modes interact is lacking. Here, working with multilayers of the TI Sb2Te3 and the band insulator GeTe, we provide experimental evidence of multiple topological modes in a single Sb2Te3-GeTe-Sb2Te3 structure. Furthermore, we show that reducing the thickness of the GeTe layer induces a phase transition from a Dirac-like phase to a gapped phase. By comparing different multilayer structures we demonstrate that this transition occurs due to the hybridisation of states associated with different TI films. Our results demonstrate that the Sb2Te3-GeTe system offers strong potential towards manipulating topological states as well as towards controlledly inducing various topological phases.
Wire constructions of Abelian topological phases in three or more dimensions
Iadecola, Thomas; Neupert, Titus; Chamon, Claudio; Mudry, Christopher
2016-05-01
Coupled-wire constructions have proven to be useful tools to characterize Abelian and non-Abelian topological states of matter in two spatial dimensions. In many cases, their success has been complemented by the vast arsenal of other theoretical tools available to study such systems. In three dimensions, however, much less is known about topological phases. Since the theoretical arsenal in this case is smaller, it stands to reason that wire constructions, which are based on one-dimensional physics, could play a useful role in developing a greater microscopic understanding of three-dimensional topological phases. In this paper, we provide a comprehensive strategy, based on the geometric arrangement of commuting projectors in the toric code, to generate and characterize coupled-wire realizations of strongly interacting three-dimensional topological phases. We show how this method can be used to construct pointlike and linelike excitations, and to determine the topological degeneracy. We also point out how, with minor modifications, the machinery already developed in two dimensions can be naturally applied to study the surface states of these systems, a fact that has implications for the study of surface topological order. Finally, we show that the strategy developed for the construction of three-dimensional topological phases generalizes readily to arbitrary dimensions, vastly expanding the existing landscape of coupled-wire theories. Throughout the paper, we discuss Zm topological order in three and four dimensions as a concrete example of this approach, but the approach itself is not limited to this type of topological order.
Supersymmetry protected topological phases of isostatic lattices and kagome antiferromagnets
Lawler, Michael J.
2016-10-01
I generalize the theory of phonon topological band structures of isostatic lattices to frustrated antiferromagnets. I achieve this with a discovery of a many-body supersymmetry (SUSY) in the phonon problem of balls and springs and its connection to local constraints satisfied by ground states. The Witten index of the SUSY model demands the Maxwell-Calladine index of mechanical structures. "Spontaneous supersymmetry breaking" is identified as the need to gap all modes in the bulk to create the topological isostatic lattice state. Since ground states of magnetic systems also satisfy local constraint conditions (such as the vanishing of the total spin on a triangle), I identify a similar SUSY structure for many common models of antiferromagnets including the square, triangluar, kagome, pyrochlore nearest-neighbor antiferromagnets, and the J2=J1/2 square-lattice antiferromagnet. Remarkably, the kagome family of antiferromagnets is the analog of topological isostatic lattices among this collection of models. Thus, a solid-state realization of the theory of phonon topological band structure may be found in frustrated magnetic materials.
Cho, Gil Young; Shiozaki, Ken; Ryu, Shinsei; Ludwig, Andreas W. W.
2017-07-01
Quantum phase transitions out of a symmetry-protected topological (SPT) phase in (1 + 1) dimensions into an adjacent, topologically distinct SPT phase protected by the same symmetry or a trivial gapped phase, are typically described by a conformal field theory (CFT). At the same time, the low-lying entanglement spectrum of a gapped phase close to such a quantum critical point is known (Cho et al arXiv:1603.04016), very generally, to be universal and described by (gapless) boundary conformal field theory. Using this connection we show that symmetry properties of the boundary conditions in boundary CFT can be used to characterize the symmetry-protected degeneracies of the entanglement spectrum, a hallmark of non-trivial symmetry-protected topological phases. Specifically, we show that the relevant boundary CFT is the orbifold of the quantum critical point with respect to the symmetry group defining the SPT, and that the boundary states of this orbifold carry a quantum anomaly that determines the topological class of the SPT. We illustrate this connection using various characteristic examples such as the time-reversal breaking ‘Kitaev chain’ superconductor (symmetry class D), the Haldane phase, and the {Z}8 classification of interacting topological superconductors in symmetry class BDI in (1 + 1) dimensions.
Using Pareto optimality to explore the topology and dynamics of the human connectome.
Avena-Koenigsberger, Andrea; Goñi, Joaquín; Betzel, Richard F; van den Heuvel, Martijn P; Griffa, Alessandra; Hagmann, Patric; Thiran, Jean-Philippe; Sporns, Olaf
2014-10-05
Graph theory has provided a key mathematical framework to analyse the architecture of human brain networks. This architecture embodies an inherently complex relationship between connection topology, the spatial arrangement of network elements, and the resulting network cost and functional performance. An exploration of these interacting factors and driving forces may reveal salient network features that are critically important for shaping and constraining the brain's topological organization and its evolvability. Several studies have pointed to an economic balance between network cost and network efficiency with networks organized in an 'economical' small-world favouring high communication efficiency at a low wiring cost. In this study, we define and explore a network morphospace in order to characterize different aspects of communication efficiency in human brain networks. Using a multi-objective evolutionary approach that approximates a Pareto-optimal set within the morphospace, we investigate the capacity of anatomical brain networks to evolve towards topologies that exhibit optimal information processing features while preserving network cost. This approach allows us to investigate network topologies that emerge under specific selection pressures, thus providing some insight into the selectional forces that may have shaped the network architecture of existing human brains.
Sun, Fadi; Ye, Jinwu
2017-07-01
It is well established that physical quantities satisfy scaling functions across a quantum phase transition with an order parameter. It remains an open problem if there are scaling functions across a topological quantum phase transition (TQPT) with extended Fermi surfaces (FSs). Here, we study a simple system of fermions hopping in a cubic lattice subject to Weyl-type spin-orbit coupling (SOC). As one tunes the SOC parameter at half filling, the system displays both type-I and type-II Weyl fermions and also various TQPTs driven by the collision of particle-particle or hole-hole Weyl FSs. At zero temperature, the TQPT is found to be third order, and its critical exponents are determined. Then we investigate if the physical quantities such as specific heat, compressibility, and magnetic susceptibilities satisfy any sort of scaling across the TQPT. In contrast to all the previous cases in quantum or topological transitions, we find that although the leading terms are nonuniversal and cutoff dependent, the subleading terms are nonanalytic and satisfy universal scaling relations. The subleading scaling leads to topological depletions which show non-Fermi-liquid corrections and √{T } quantum cusps. One can also form a topological Wilson ratio from the subleading scalings of two conserved quantities such as the specific heat and the compressibility. One may also interpret the type-I and type-II Weyl fermions as a TQPT driven by the collision of particle-hole Weyl FSs. Experimental realizations and detections in cold-atom systems and materials with SOC are discussed.
Towards laboratory detection of topological vortices in superfluid phases of QCD
Das, Arpan; De, Somnath; Srivastava, Ajit M
2016-01-01
Topological defects arise in a variety of systems, e.g. vortices in superfluid helium to cosmic strings in the early universe. There is an indirect evidence of neutron superfluid vortices from glitches in pulsars. One also expects that topological defects may arise in various high baryon density phases of quantum chromodynamics (QCD), e.g. superfluid topological vortices in the color flavor locked (CFL) phase. We investigate the possibility of detecting these topological superfluid vortices in laboratory experiments, namely heavy-ion collisions. Using hydrodynamic simulations, we show that vortices can qualitatively affect the power spectrum of flow fluctuations. This can give unambiguous signal for superfluid transition resulting in vortices, allowing for check of defect formation theories in a relativistic quantum field theory system.
Dynamical Quantum Phase Transitions: Role of Topological Nodes in Wave Function Overlaps
Huang, Zhoushen; Balatsky, Alexander V.
2016-08-01
A sudden quantum quench of a Bloch band from one topological phase toward another has been shown to exhibit an intimate connection with the notion of a dynamical quantum phase transition (DQPT), where the returning probability of the quenched state to the initial state—i.e., the Loschmidt echo—vanishes at critical times {t*}. Analytical results to date are limited to two-band models, leaving the exact relation between topology and DQPT unclear. In this Letter, we show that, for a general multiband system, a robust DQPT relies on the existence of nodes (i.e., zeros) in the wave function overlap between the initial band and the postquench energy eigenstates. These nodes are topologically protected if the two participating wave functions have distinctive topological indices. We demonstrate these ideas in detail for both one and two spatial dimensions using a three-band generalized Hofstadter model. We also discuss possible experimental observations.
Huang, Ching-Yu; Wei, Tzu-Chieh
2016-04-01
Symmetry-protected topological (SPT) phases exhibit nontrivial order if symmetry is respected but are adiabatically connected to the trivial product phase if symmetry is not respected. However, unlike the symmetry-breaking phase, there is no local order parameter for SPT phases. Here we employ a tensor-network method to compute the topological invariants characterized by the simulated modular S and T matrices to study transitions in a few families of two-dimensional (2D) wave functions which are ZN (N =2 and3 ) symmetric. We find that in addition to the topologically ordered phases, the modular matrices can be used to identify nontrivial SPT phases and detect transitions between different SPT phases as well as between symmetric and symmetry-breaking phases. Therefore modular matrices can be used to characterize various types of gapped phases in a unifying way.
Termination-dependent topological surface states of the natural superlattice phase Bi4Se3
Gibson, Q. D.; Schoop, L. M.; Weber, A. P.; Ji, Huiwen; Nadj-Perge, S.; Drozdov, I. K.; Beidenkopf, H.; Sadowski, J. T.; Fedorov, A.; Yazdani, A.; Valla, T.; Cava, R. J.
2013-08-01
We describe the topological surface states of Bi4Se3, a compound in the infinitely adaptive Bi2-Bi2Se3 natural superlattice phase series, determined by a combination of experimental and theoretical methods. Two observable cleavage surfaces, terminating at Bi or Se, are characterized by angle-resolved photoelectron spectroscopy and scanning tunneling microscopy, and modeled by ab initio density functional theory calculations. Topological surface states are observed on both surfaces, but with markedly different dispersions and Kramers point energies. Bi4Se3 therefore represents the only known compound with different topological states on differently terminated, easily distinguished and stable surfaces.
Isogeometric Analysis for Topology Optimization with a Phase Field Model
2011-09-01
been successfully considered. For example, this is the case for applications in fluid dynamics [1], heat conduction [45], vibration [58], multiphysics...Laboratories SAND2006–2649 (2006). [45] A. Gersborg–Hansen, M.P. Bendsøe and O. Sigmund, Topology optimization of heat conduction problems using the...novel stent platform with drug reservoirs, Med. Eng. Phys. 30 (2008), 1177–1185. [111] Y.M. Xie and G.P. Steven, Evolutionary Structural Optimization
Topological phase transition and interface states in hybrid plasmonic-photonic systems
Ge, Lixin; Liu, Liang; Xiao, Meng; Du, Guiqiang; Shi, Lei; Han, Dezhuan; Chan, C. T.; Zi, Jian
2017-06-01
The geometric phase and topological property for one-dimensional hybrid plasmonic-photonic crystals consisting of a simple lattice of graphene sheets are investigated systematically. For transverse magnetic waves, both plasmonic and photonic modes exist in the momentum space. The accidental degeneracy point of these two kinds of modes is identified to be a diabolic point accompanied with a topological phase transition. For a closed loop around this degeneracy point, the Berry phase is π as a consequence of the discontinuous jump of the geometric Zak phase. The wave impedance is calculated analytically for the semi-infinite system, and the corresponding topological interface states either start from or terminate at the degeneracy point. This type of localized interface state may find potential applications in manipulation of photon emission of quantum dots, optical sensing and enhancement of nonlinear effects, etc.
A quantum phase transition between a topological and a trivial semi-metal in holography
Landsteiner, Karl; Sun, Ya-Wen
2015-01-01
We present a holographic model of a topological Weyl semi-metal state. Key ingredient is a time-reversal breaking parameter and a mass deformation. Upon varying the ratio of mass to time reversal breaking parameter the model undergoes a quantum phase transition from a topologically non-trivial state to a trivial one. The order parameter for this phase transition is the anomalous Hall effect (AHE). The results can be interpreted in terms of the holographic RG flow leading to restoration of time reversal at the end point of the RG flow in the trivial phase.
Disorder-driven topological phase transition in B i2S e3 films
Brahlek, Matthew; Koirala, Nikesh; Salehi, Maryam; Moon, Jisoo; Zhang, Wenhan; Li, Haoxiang; Zhou, Xiaoqing; Han, Myung-Geun; Wu, Liang; Emge, Thomas; Lee, Hang-Dong; Xu, Can; Rhee, Seuk Joo; Gustafsson, Torgny; Armitage, N. Peter; Zhu, Yimei; Dessau, Daniel S.; Wu, Weida; Oh, Seongshik
2016-10-01
Topological insulators (TI) are a phase of matter that host unusual metallic surface states. Unlike the states that exist on the surface of conventional materials, these so-called topological surfaces states (TSS) are protected against disorder-related localization effects by time reversal symmetry through strong spin-orbit coupling. By combining transport measurements, angle-resolved photoemission spectroscopy, and scanning tunneling microscopy, we show that there exists a critical level of disorder beyond which the TI B i2S e3 loses its ability to protect the metallic TSS and transitions to a fully insulating state. The absence of the metallic surface channels dictates that there is a change in the material's topological character, implying that disorder can lead to a topological phase transition even without breaking the time reversal symmetry. This observation challenges the conventional notion of topologically protected surface states and should prompt new studies as to the fundamental nature of topological phase of matter in the presence of disorder.
Cheng, Meng; Zaletel, Michael; Barkeshli, Maissam; Vishwanath, Ashvin; Bonderson, Parsa
2016-10-01
The Lieb-Schultz-Mattis theorem and its higher-dimensional generalizations by Oshikawa and Hastings require that translationally invariant 2D spin systems with a half-integer spin per unit cell must either have a continuum of low energy excitations, spontaneously break some symmetries, or exhibit topological order with anyonic excitations. We establish a connection between these constraints and a remarkably similar set of constraints at the surface of a 3D interacting topological insulator. This, combined with recent work on symmetry-enriched topological phases with on-site unitary symmetries, enables us to develop a framework for understanding the structure of symmetry-enriched topological phases with both translational and on-site unitary symmetries, including the effective theory of symmetry defects. This framework places stringent constraints on the possible types of symmetry fractionalization that can occur in 2D systems whose unit cell contains fractional spin, fractional charge, or a projective representation of the symmetry group. As a concrete application, we determine when a topological phase must possess a "spinon" excitation, even in cases when spin rotational invariance is broken down to a discrete subgroup by the crystal structure. We also describe the phenomena of "anyonic spin-orbit coupling," which may arise from the interplay of translational and on-site symmetries. These include the possibility of on-site symmetry defect branch lines carrying topological charge per unit length and lattice dislocations inducing degeneracies protected by on-site symmetry.
Chakravarty, Sudip; Goswami, Pallab
In the absence of spin rotational invariance, time reversal symmetric topological superconducting states (belonging to the class DIII) can be realized in all three spatial dimensions. We construct the global phase diagrams of disordered, class DIII superconductors in two and three dimensions. In both spatial dimensions the Bogoliubov de Gennes quasiparticles can exhibit two topologically distinct localized (gapped) phases, in addition to a diffusive (gapless) phase that possesses metallic thermal conductivity. We also obtain exact localization length exponents and approximate crossover scaling functions for the relevant topological quantum phase transitions. For sufficiently weak disorder, we show that the direct topological transition between two gapped states is described by a four component, massless Dirac fermion with a dynamical exponent z = 1 and a correlation/localization length exponent νM = 1 . For stronger disorder, we demonstrate how two topologically distinct localized states and the delocalized diffusive phase meet at a line of disorder controlled fixed points, which governs the nature of the localization-delocalization transitions. We show the existence of a universal localization length exponent νM = 2 / d and a nonuniversal dynamical exponent for the localizati
Topological phases and circulating states of Bose-Einstein condensates
Petrosyan, K G
1999-01-01
We show that the quantum topological effect predicted by Aharonov and Casher (AC effect) [Phys. Rev. Lett. 53, 319 (1984)] may be used to create circulating states of magnetically trapped atomic Bose-Einstein condensates (BEC). A simple experimental setup is suggested based on a multiply connected geometry such as a toroidal trap or a magnetic trap pinched by a blue-detuned laser. We give numerical estimates of such effects within the current atomic BEC experiments, and point out some interesting properties of the associated quantized circulating states.
Gana, Ines [EAD Physico-chimie Industrielle du Medicament (EA 4066), Faculte de Pharmacie, Universite Paris Descartes, 4 Avenue de l' Observatoire, 75006 Paris (France) and Etablissement pharmaceutique de l' Assistance Publique - Hopitaux de Paris, Agence Generale des Equipements et Produits de Sante, 7 Rue du Fer a moulin, 75005 Paris (France); Ceolin, Rene [EAD Physico-chimie Industrielle du Medicament (EA 4066), Faculte de Pharmacie, Universite Paris Descartes, 4 Avenue de l' Observatoire, 75006 Paris (France); Rietveld, Ivo B., E-mail: ivo.rietveld@parisdescartes.fr [EAD Physico-chimie Industrielle du Medicament (EA 4066), Faculte de Pharmacie, Universite Paris Descartes, 4 Avenue de l' Observatoire, 75006 Paris (France)
2012-10-20
Highlights: Black-Right-Pointing-Pointer The topological pressure-temperature phase diagram for the dimorphism of finasteride. Black-Right-Pointing-Pointer Pressure affects phase equilibria: an enantiotropic phase relationship turning monotropic at high pressure. Black-Right-Pointing-Pointer The influence of pressure on phase behavior inferred from data obtained under ordinary conditions. - Abstract: Knowledge of the phase behavior in the solid state of active pharmaceutical ingredients is important for the development of stable drug formulations. The topological method for the construction of pressure-temperature phase diagrams has been applied to study the phase behavior of finasteride. It is demonstrated that with basic calorimetric measurements and X-ray diffraction sufficient data can be obtained to construct a complete topological pressure-temperature phase diagram. The dimorphism observed for finasteride gives rise to a phase diagram similar to the paradigmatic diagram of sulfur. The solid-solid phase relationship is enantiotropic at ordinary pressure and becomes monotropic at elevated pressure, where solid I is the only stable phase.
Strong correlation effects on topological quantum phase transitions in three dimensions
Amaricci, A.; Budich, J. C.; Capone, M.; Trauzettel, B.; Sangiovanni, G.
2016-06-01
We investigate the role of short-ranged electron-electron interactions in a paradigmatic model of three-dimensional topological insulators, using dynamical mean-field theory and focusing on nonmagnetically ordered solutions. The noninteracting band structure is controlled by a mass term M , whose value discriminates between three different insulating phases, a trivial band insulator and two distinct topologically nontrivial phases. We characterize the evolution of the transitions between the different phases as a function of the local Coulomb repulsion U and find a remarkable dependence of the U -M phase diagram on the value of the local Hund's exchange coupling J . However, regardless of the value of J , following the evolution of the topological transition line between a trivial band insulator and a topological insulator, we find a critical value of U separating a continuous transition from a first-order one. When the Hund's coupling is significant, a Mott insulator is stabilized at large U . In proximity of the Mott transition we observe the emergence of an anomalous "Mott-like" strong topological insulator state.
Flux-driven quantum phase transitions in two-leg Kitaev ladder topological superconductor systems
Wang, H. Q.; Shao, L. B.; Pan, Y. M.; Shen, R.; Sheng, L.; Xing, D. Y.
2016-12-01
We investigate a two-leg ladder topological superconductor system consisting of two parallel Kitaev chains with interchain coupling. It is found that either uniform or staggered fluxes threading through the ladder holes may change the ladder system from the BDI class in the Altland-Zirnbauer (AZ) classification to the D class. After explicitly calculating the topological Z and/or Z2 indices and from the evolution of Majorana zero energy states (MZES), we obtain the flux-dependent phase diagrams, and find that quantum phase transitions between topologically distinct phases characterized by different number of MZES may happen by simply tuning the flux, which could be realized experimentally in ultracold systems.
Topological Dirac semimetal phase in Pd and Pt oxides
Li, Gang; Yan, Binghai; Wang, Zhijun; Held, Karsten
2017-01-01
Topological Dirac semimetals (DSMs) exhibit nodal points through which energy bands disperse linearly in three-dimensional (3D) momentum space, a 3D analog of graphene. The first experimentally confirmed DSMs with a pair of Dirac points (DPs), Na3Bi and Cd3As2 , show topological surface Fermi arc states and exotic magnetotransport properties, boosting the interest in the search for stable and nontoxic DSM materials. Based on density-functional theory and dynamical mean-field theory calculations, we predict a family of palladium and platinum oxides to be robust 3D DSMs with three pairs of Dirac points that are well separated from bulk bands. The Fermi arcs at the surface display a Lifshitz transition upon a continuous change of the chemical potential. Corresponding oxides are already available as high-quality single crystals, an excellent precondition for the verification of our predictions by photoemission and magnetotransport experiments, extending DSMs to the versatile family of transition-metal oxides.
Lattice quantum codes and exotic topological phases of matter
Haah, Jeongwan
2014-03-01
Is it possible to build a ``hard disk drive'' for quantum information? The quantum coherence time in a usual thermal system is fundamentally limited by the inverse Boltzmann factor exp [ Δ / kT ] , where Δ is the energy scale of the system. This limitation is not enhanced even with a conventional topologically ordered system in three or lower dimensions. Here, a new three-dimensional spin model is presented that shows a qualitatively different behavior. It can be viewed as a quantum error correcting code, and is thus exactly solvable. The ground states are locally indistinguishable, for which it may be called topologically ordered. However, the model only admits immobile pointlike excitations, and the immobility is not affected by small perturbations of the Hamiltonian. The degeneracy of the ground state, though also insensitive to perturbations, is a complicated number-theoretic function of the system size. Under real-space renormalization group transformations, the system bifurcates into multiple noninteracting copies of itself. Similarities and differences of the model in comparison to Wegner's Ising gauge theory will be explained. When quantum information is encoded into a ground state of this model and subjected to thermal errors, the errors remain easily correctable for a long time without any active intervention, because a macroscopic energy barrier due to the immobility of excitations keeps the errors well localized. As a result, stored quantum information can be retrieved faithfully for a memory time exp [(Δ / kT) 2 ] .
Jahromi, Saeed S.; Langari, Abdollah
2017-04-01
We use the topological entanglement entropy (TEE) as an efficient tool to fully characterize the Abelian phase of a {{{Z}}2}× {{{Z}}2} spin liquid emerging as the ground state of topological color code (TCC), which is a class of stabilizer states on the honeycomb lattice. We provide the fusion rules of the quasiparticle (QP) excitations of the model by introducing single- or two-body operators on physical spins for each fusion process which justify the corresponding fusion outcome. Besides this, we extract the TEE from Renyi entanglement entropy (EE) of the TCC, analytically and numerically by finite size exact diagonalization on the disk shape regions with contractible boundaries. We obtain that the EE has a local contribution, which scales linearly with the boundary length in addition to a topological term, i.e. the TEE, arising from the condensation of closed strings in the ground state. We further investigate the ground state dependence of the TEE on regions with non-contractible boundaries, i.e. by cutting the torus to half cylinders, from which we further identify multiple independent minimum entropy states (MES) of the TCC and then extract the U and S modular matrices of the system, which contain the self and mutual statistics of the anyonic QPs and fully characterize the topological phase of the TCC. Eventually, we show that, in spite of the lack of a local order parameter, TEE and other physical quantities obtained from the ground state wave function such as the entanglement spectrum (ES) and ground state fidelity are sensitive probes to study the robustness of a topological phase. We find that the topological order in the presence of a magnetic field persists until the vicinity of the transition point, where the TEE and fidelity drops to zero and the ES splits severely, signaling breakdown of the topological phase of the TCC.
The topological AC effect on noncommutative phase space
Li, K; Li, Kang; Wang, Jianhua
2006-01-01
The Aharonov-Casher (AC) effect in non-commutative(NC) quantum mechanics is studied. Instead of using the star product method, we use a generalization of Bopp's shift method. After solving the Dirac equations both on noncommutative space and noncommutative phase space by the new method, we obtain the corrections to AC phase on NC space and NC phase space respectively.
Parity-symmetry breaking and topological phases in a superfluid ring
Zhang, Xiurong; Piazza, Francesco; Li, WeiDong; Smerzi, Augusto
2016-12-01
We study analytically the superfluid flow of a Bose-Einstein condensate in a ring geometry in the presence of a rotating barrier. We show that a phase transition breaking a parity symmetry among two topological phases occurs at a critical value of the height of the barrier. Furthermore, a discontinuous (accompanied by hysteresis) phase transition is observed in the ordered phase when changing the angular velocity of the barrier. At the critical point where the hysteresis area vanishes, the chemical potential of the ground state develops a cusp (a discontinuity in the first derivative). Along this path, the jump between the two corresponding states having a different winding number shows analogies with a topological phase transition. We finally study the current-phase relation of the system and compare some of our calculations with published experimental results.
Sushko, Gennady B; Verkhovtsev, Alexey V; Volkov, Sergey N; Solov'yov, Andrey V
2015-01-01
The concept of molecular mechanics force field has nowadays been widely accepted for studying various processes in biomolecular systems. In this paper we suggest a modification for the standard CHARMM force field, that permits simulations of systems with dynamically changing molecular topologies. The implementation of the modified force field was carried out in the popular program MBN Explorer, and, to support the development, in this paper we provide several case studies where dynamical topology is necessary. In particular, it is shown, that the modified molecular mechanics force field can be applied for studying processes where rupture of chemical bonds plays an essential role, e.g., in irradiation or collision induced damage, transformation and fragmentation processes involving biomolecular systems.
Topological phase transition of a fractal spin system: The relevance of the network complexity
Torres, Felipe; Rogan, José; Kiwi, Miguel; Valdivia, Juan Alejandro
2016-05-01
A new type of collective excitations, due to the topology of a complex random network that can be characterized by a fractal dimension DF, is investigated. We show analytically that these excitations generate phase transitions due to the non-periodic topology of the DF > 1 complex network. An Ising system, with long range interactions, is studied in detail to support the claim. The analytic treatment is possible because the evaluation of the partition function can be decomposed into closed factor loops, in spite of the architectural complexity. The removal of the infrared divergences leads to an unconventional phase transition, with spin correlations that are robust against thermal fluctuations.
Topological phase transition of a fractal spin system: The relevance of the network complexity
Felipe Torres
2016-05-01
Full Text Available A new type of collective excitations, due to the topology of a complex random network that can be characterized by a fractal dimension DF, is investigated. We show analytically that these excitations generate phase transitions due to the non-periodic topology of the DF > 1 complex network. An Ising system, with long range interactions, is studied in detail to support the claim. The analytic treatment is possible because the evaluation of the partition function can be decomposed into closed factor loops, in spite of the architectural complexity. The removal of the infrared divergences leads to an unconventional phase transition, with spin correlations that are robust against thermal fluctuations.
Sato, T.; Segawa, Kouji; Kosaka, K.; Souma, S.; Nakayama, K.; Eto, K.; Minami, T.; Ando, Yoichi; Takahashi, T.
2011-11-01
The three-dimensional (3D) topological insulator is a novel quantum state of matter where an insulating bulk hosts a linearly dispersing surface state, which can be viewed as a sea of massless Dirac fermions protected by the time-reversal symmetry (TRS). Breaking the TRS by a magnetic order leads to the opening of a gap in the surface state, and consequently the Dirac fermions become massive. It has been proposed theoretically that such a mass acquisition is necessary to realize novel topological phenomena, but achieving a sufficiently large mass is an experimental challenge. Here we report an unexpected discovery that the surface Dirac fermions in a solid-solution system TlBi(S1-xSex)2 acquire a mass without explicitly breaking the TRS. We found that this system goes through a quantum phase transition from the topological to the non-topological phase, and, by tracing the evolution of the electronic states using the angle-resolved photoemission, we observed that the massless Dirac state in TlBiSe2 switches to a massive state before it disappears in the non-topological phase. This result suggests the existence of a condensed-matter version of the `Higgs mechanism' where particles acquire a mass through spontaneous symmetry breaking.
The topological AC effect on non-commutative phase space
Li, Kang [Hangzhou Teachers College, Department of Physics, Hangzhou (China); The Abdus Salam International Center for Theoretical Physics, Trieste (Italy); Wang, Jianhua [Shaanxi University of Technology, Department of Physics, Hanzhong (China); The Abdus Salam International Center for Theoretical Physics, Trieste (Italy)
2007-05-15
The Aharonov-Casher (AC) effect in non-commutative (NC) quantum mechanics is studied. Instead of using the star product method, we use a generalization of Bopp's shift method. After solving the Dirac equations both on non-commutative space and non-commutative phase space by the new method, we obtain corrections to the AC phase on NC space and NC phase space, respectively. (orig.)
Kharitonov, Maxim; Juergens, Stefan; Trauzettel, Björn
2016-07-01
We consider a class of quantum Hall topological insulators: topologically nontrivial states with zero Chern number at finite magnetic field, in which the counterpropagating edge states are protected by a symmetry (spatial or spin) other than time-reversal. HgTe-type heterostructures and graphene are among the relevant systems. We study the effect of electron interactions on the topological properties of the system. We particularly focus on the vicinity of the topological phase transition, marked by the crossing of two Landau levels, where the system is a strongly interacting quantum Hall ferromagnet. We analyze the edge properties using the formalism of the nonlinear σ -model. We establish the symmetry requirement for the topological protection in this interacting system: effective continuous U(1) symmetry with respect to uniaxial isospin rotations must be preserved. If U(1) symmetry is preserved, the topologically nontrivial phase persists; its edge is a helical Luttinger liquid with highly tunable effective interactions. We obtain explicit analytical expressions for the parameters of the Luttinger liquid in the quantum-Hall-ferromagnet regime. However, U(1) symmetry may be broken, either spontaneously or by U(1)-asymmetric interactions. In either case, interaction-induced transitions occur to the respective topologically trivial phases with gapped edge charge excitations.
Kagome Chiral Spin Liquid as a Gauged U(1) Symmetry Protected Topological Phase.
He, Yin-Chen; Bhattacharjee, Subhro; Pollmann, Frank; Moessner, R
2015-12-31
While the existence of a chiral spin liquid (CSL) on a class of spin-1/2 kagome antiferromagnets is by now well established numerically, a controlled theoretical path from the lattice model leading to a low-energy topological field theory is still lacking. This we provide via an explicit construction starting from reformulating a microscopic model for a CSL as a lattice gauge theory and deriving the low-energy form of its continuum limit. A crucial ingredient is the realization that the bosonic spinons of the gauge theory exhibit a U(1) symmetry protected topological (SPT) phase, which upon promoting its U(1) global symmetry to a local gauge structure ("gauging"), yields the CSL. We suggest that such an explicit lattice-based construction involving gauging of a SPT phase can be applied more generally to understand topological spin liquids.
Kagome Chiral Spin Liquid as a Gauged U (1 ) Symmetry Protected Topological Phase
He, Yin-Chen; Bhattacharjee, Subhro; Pollmann, Frank; Moessner, R.
2015-12-01
While the existence of a chiral spin liquid (CSL) on a class of spin-1 /2 kagome antiferromagnets is by now well established numerically, a controlled theoretical path from the lattice model leading to a low-energy topological field theory is still lacking. This we provide via an explicit construction starting from reformulating a microscopic model for a CSL as a lattice gauge theory and deriving the low-energy form of its continuum limit. A crucial ingredient is the realization that the bosonic spinons of the gauge theory exhibit a U (1 ) symmetry protected topological (SPT) phase, which upon promoting its U (1 ) global symmetry to a local gauge structure ("gauging"), yields the CSL. We suggest that such an explicit lattice-based construction involving gauging of a SPT phase can be applied more generally to understand topological spin liquids.
He, Huan; von Keyserlingk, Curt
2016-01-01
Dijkgraaf-Witten (DW) theories are of recent interest to the condensed matter community, in part because they represent topological phases of matter, but also because they characterize the response theory of certain symmetry protected topological (SPT) phases. However, as yet there has not been a comprehensive treatment of the spectra of these models in the field theoretic setting -- the goal of this work is to fill the gap in the literature, at least for a selection of DW models with abelian gauge groups but non-abelian topological order. As applications, various correlation functions and fusion rules of line operators are calculated. We discuss for example the appearance of non-abelian statistics in DW theories with abelian gauge groups.
Spin Chern number and topological phase transition on the Lieb lattice with spin-orbit coupling
Chen, Rui; Zhou, Bin
2017-03-01
We propose that quantum anomalous Hall effect may occur in the Lieb lattice, when Rashba spin-orbit coupling, spin-independent and spin-dependent staggered potentials are introduced into the lattice. It is found that spin Chern numbers of two degenerate flat bands change from 0 to ±2 due to Rashba spin-orbit coupling effect. The inclusion of Rashba spin-orbit coupling and two kinds of staggered potentials opens a gap between the two flat bands. The topological property of the gap is determined by the amplitudes of Rashba spin-orbit coupling and staggered potentials, and thus the topological phase transition from quantum anomalous Hall effect to normal insulator can occur. Finally, the topological phase transition from quantum spin Hall state to normal insulator is discussed when Rashba spin-orbit coupling and intrinsic spin-orbit coupling coexist in the Lieb lattice.
Topological phase transitions and universality in the Haldane-Hubbard model
Giuliani, Alessandro; Jauslin, Ian; Mastropietro, Vieri; Porta, Marcello
2016-11-01
We study the Haldane-Hubbard model by exact renormalization group techniques. We analytically construct the topological phase diagram, for weak interactions. We predict that many-body interactions induce a shift of the transition line: in particular, repulsive interactions enlarge the topologically nontrivial region. The presence of new intermediate phases, absent in the noninteracting case, is rigorously excluded at weak coupling. Despite the nontrivial renormalization of the wave function and of the Fermi velocity, the conductivity is universal: at the renormalized critical line, both the discontinuity of the transverse conductivity and the longitudinal conductivity are independent of the interaction, thanks to remarkable cancellations due to lattice Ward identities. In contrast to the quantization of the transverse conductivity, the universality of the longitudinal conductivity cannot be explained via topological arguments.
Euler Characteristic and Topological Phase Transition of NUT-Kerr-Newman Black Hole
FAN Hong-Yi; YUE Jing-Hua; YANG Guo-Hong; TIAN Li-Jun; ZHU Shu
2008-01-01
From the Causs-Bonnet-Chern theorem, the Euler characteristic of NUT-Kerr-Newman black hole is calculated to be some discrete numbers from 0 to 2. We find that the Bekenstein-Hawking entropy is the largest entropy in topology by taking into account of the relationship between the entropy and the Euler characteristic. The NUT-Kerr-Newman black hole evolves from the torus-like topological structure to the spherical structure with the changes of mass, angular momentum, electric and NUT charges. In this process, the Euler characteristic and the entropy are changed discontinuously, which give the topological aspect of the first-order phase transition of NUT-Kerr-Newman black hole. The corresponding latent heat of the topologicaJ phase transition is also obtained. The estimated latent heat of the black hole evolving from the star just lies in the range of the energy of gamma ray bursts.
Higashikawa, Sho
2016-01-01
A symmetry broken phase of a system with internal degrees of freedom often features a complex order parameter, which generates a rich variety of topological excitations and topological influence between them, yet the very complexity of the order parameter makes it difficult to treat topological excitations and topological influence in a unified manner. To overcome this problem, we develop a general method to calculate homotopy groups and derive decomposition formulas which express homotopy groups of a quotient space $G/H$ in terms of those of the symmetry $G$ of the system and those of the remaining symmetry $H$ of the state. We apply these formulas to analyze a general monopole and a general three-dimensional skyrmion, and show that their textures are obtained through substitution of the corresponding $\\mathfrak{su}(2)$-subalgebra for the $\\mathfrak{su}(2)$-spin. We also show that a discrete symmetry of $H$ is necessary for the presence of topological influence and find the topological influence on a skyrmio...
Topology in the S U (Nf) chiral symmetry restored phase of unquenched QCD and axion cosmology
Azcoiti, Vicente
2016-11-01
We investigate the topological properties of unquenched QCD on the basis of numerical results of simulations at fixed topological charge, recently reported by Borsanyi et al. We demonstrate that their results for the mean value of the chiral condensate at fixed topological charge are inconsistent with the analytical prediction of the large-volume expansion around the saddle point, and argue that the most plausible explanation for the failure of the saddle-point expansion is a vacuum energy density that is θ -independent at high temperatures, but surprisingly not too high (T ˜2 Tc), a result which would imply a vanishing topological susceptibility and the absence of all physical effects of the U (1 ) axial anomaly at these temperatures. We also show that under a general assumption concerning the high-temperature phase of QCD, where the S U (Nf)A symmetry is restored, the analytical prediction for the chiral condensate at fixed topological charge is in very good agreement with the numerical results of Borsanyi et al., all effects of the axial anomaly should disappear, the topological susceptibility and all the θ derivatives of the vacuum energy density vanish, and the theory becomes θ independent at any T >Tc in the infinite-volume limit.
The induced nontrivial Z 2 topological phase in graphene sandwiched by pnictogen bilayers.
Shu, Cheng; Qu, Jinfeng; Peng, Xiangyang; Yang, Hong; Liu, Wenliang; Wei, Xiaolin; Zhang, Kaiwang; Zhong, Jianxin
2016-06-15
By performing first-principles calculations, we find that graphene with nearly zero spin orbit coupling can be turned into a topological insulator after being sandwiched between pnictogen bilayers. It is found that a dipole field is induced between graphene and pnictogen bilayers, which will significantly pull down the Dirac point of graphene. Depending on the initial position of the Dirac point of graphene with respect to the energy gap of the pnictogen bilayers, Bi/graphene/Bi is found to be a metallic system while Sb/graphene/Sb a topological insulator. In Sb/graphene/Sb, a sizable gap is opened at the Dirac point of graphene. The strong spin-orbit coupling in Sb bilayers leads to a band inversion in the gapped Dirac cones of graphene via the proximity effect and the calculated Z 2 topological index further confirms that a nontrivial topological phase is induced in graphene. By applying longitudinal or lateral strains to Sb/graphene/Sb, topological phase transition occurs based on the change of the thickness of the Sb bilayer instead of the change of the separation between graphene and Sb bilayers.
Temperature-driven topological quantum phase transitions in a phase-change material Ge2Sb2Te5
Eremeev, S. V.; Rusinov, I. P.; Echenique, P. M.; Chulkov, E. V.
2016-12-01
The Ge2Sb2Te5 is a phase-change material widely used in optical memory devices and is a leading candidate for next generation non-volatile random access memory devices which are key elements of various electronics and portable systems. Despite the compound is under intense investigation its electronic structure is currently not fully understood. The present work sheds new light on the electronic structure of the Ge2Sb2Te5 crystalline phases. We demonstrate by predicting from first-principles calculations that stable crystal structures of Ge2Sb2Te5 possess different topological quantum phases: a topological insulator phase is realized in low-temperature structure and Weyl semimetal phase is a characteristic of the high-temperature structure. Since the structural phase transitions are caused by the temperature the switching between different topologically non-trivial phases can be driven by variation of the temperature. The obtained results reveal the rich physics of the Ge2Sb2Te5 compound and open previously unexplored possibility for spintronics applications of this material, substantially expanding its application potential.
Topological phase transition and quantum spin Hall edge states of antimony few layers
Kim, Sung Hwan; Jin, Kyung-Hwan; Park, Joonbum; Kim, Jun Sung; Jhi, Seung-Hoon; Yeom, Han Woong
2016-09-01
While two-dimensional (2D) topological insulators (TI’s) initiated the field of topological materials, only very few materials were discovered to date and the direct access to their quantum spin Hall edge states has been challenging due to material issues. Here, we introduce a new 2D TI material, Sb few layer films. Electronic structures of ultrathin Sb islands grown on Bi2Te2Se are investigated by scanning tunneling microscopy. The maps of local density of states clearly identify robust edge electronic states over the thickness of three bilayers in clear contrast to thinner islands. This indicates that topological edge states emerge through a 2D topological phase transition predicted between three and four bilayer films in recent theory. The non-trivial phase transition and edge states are confirmed for epitaxial films by extensive density-functional-theory calculations. This work provides an important material platform to exploit microscopic aspects of the quantum spin Hall phase and its quantum phase transition.
Symmetry-protected topological phases with uniform computational power in one dimension
Raussendorf, Robert; Wang, Dong-Sheng; Prakash, Abhishodh; Wei, Tzu-Chieh; Stephen, David T.
2017-07-01
We investigate the usefulness of ground states of quantum spin chains with symmetry-protected topological order (SPTO) for measurement-based quantum computation. We show that, in spatial dimension 1, if an SPTO phase protects the identity gate, then, subject to an additional symmetry condition that is satisfied in all cases so far investigated, it can also be used for quantum computation.
The modular S-matrix as order parameter for topological phase transitions
Bais, F.A.; Romers, J.C.
2012-01-01
We study topological phase transitions in discrete gauge theories in two spatial dimensions induced by the formation of a Bose condensate. We analyse a general class of euclidean lattice actions for these theories which contain one coupling constant for each conjugacy class of the gauge group. To pr
Effect of disorders on topological phases in one-dimensional optical superlattices
Zhizhou, Wang; Yidong, Wu; Huijing, Du; Xili, Jing
2016-07-01
In a recent paper, Lang et al. proposed that edge states and topological phases can be observed in one-dimensional optical superlattices. They showed that the topological phases can be revealed by observing the density profile of a trapped fermion system, which displays plateaus with their positions. However, disorders are not considered in their model. To study the effect of disorders on the topological phases, we introduce random potentials to the model for optical superlattcies. Our calculations show that edge states are robust against the disorders. We find the edge states are very sensitive to the number of the sites in the optical superlattice and we propose a simple rule to describe the relationship between the edge states and the number of sites. The density plateaus are also robust against weak disorders provided that the average density is calculated over a long interval. The widths of the plateaus are proportional to the widths of the bulk energy gaps when there are disorders. The disorders can diminish the bulk energy gaps. So the widths of the plateaus decrease with the increase of disorders and the density plateaus disappear when disorders are too strong. The results in our paper can be used to guide the experimental detection of topological phases in one-dimensional systems. Project supported by the National Natural Science Foundation of China (Grant No. 41174116), the Graduate Student Education Teaching Reform Project, China (Grant No. JG201512), and the Young Teachers’ Research Project of Yanshan University, China (Grant No. 13LGB028).
Borisevich, A Y; Morozovska, A N; Kim, Young-Min; Leonard, D; Oxley, M P; Biegalski, M D; Eliseev, E A; Kalinin, S V
2012-08-10
Vacancy-ordered transition metal oxides have multiple similarities to classical ferroic systems including ferroelectrics and ferroelastics. The expansion coefficients for corresponding Ginzburg-Landau-type free energies are readily accessible from bulk phase diagrams. Here, we demonstrate that the gradient and interfacial terms can quantitatively be determined from the atomically resolved scanning transmission electron microscopy data of the topological defects and interfaces in model lanthanum-strontium cobaltite. With this knowledge, the interplay between ordering, chemical composition, and mechanical effects at domain walls, interfaces and structural defects can be analyzed.
Topological Phase and Half-Integer Orbital Angular Momenta in Circular Quantum Dots
Kuleshov, V. M.; Mur, V. D.; Narozhny, N. B.; Lozovik, Yu. E.
2016-12-01
We show that there exists a non-trivial topological phase in circular two-dimensional quantum dots with an odd number of electrons. The possible non-zero value of this phase is explained by axial symmetry of two-dimensional quantum systems. The particular value of this phase (π ) is fixed by T-invariance and the Pauli exclusion principle and leads to half-integer values of the angular orbital momentum for ground states of such systems. This conclusion agrees with the experimental data for ground-state energies of few-electron circular quantum dots in perpendicular magnetic field (Schmidt et al. in Phys Rev B 51:5570, 1995). Hence, these data may be considered as the first experimental evidence for the existence of topological phase leading to half-integer quantization of the orbital angular momentum in circular quantum dots with an odd number of electrons.
Phase-tunable Majorana bound states in a topological N-SNS junction
Hansen, Esben Bork; Danon, Jeroen; Flensberg, Karsten
2016-03-01
We theoretically study the differential conductance of a one-dimensional normal-superconductor-normal-superconductor (N-SNS) junction with a phase bias applied between the two superconductors. We consider specifically a junction formed by a spin-orbit coupled semiconducting nanowire with regions of the nanowire having superconducting pairing induced by a bulk s -wave superconductor. When the nanowire is tuned into a topologically nontrivial phase by a Zeeman field, it hosts zero-energy Majorana modes at its ends as well as at the interface between the two superconductors. The phase-dependent splitting of the Majorana modes gives rise to features in the differential conductance that offer a clear distinction between the topologically trivial and nontrivial phases. We calculate the transport properties of the junction numerically and also present a simple analytical model that captures the main properties of the predicted tunneling spectroscopy.
Detection of Zak phases and topological invariants in a chiral photonic quantum walk
Cardano, F; Dauphin, A; Maffei, M; Piccirillo, B; de Lisio, C; De Filippis, G; Cataudella, V; Santamato, E; Marrucci, L; Lewenstein, M; Massignan, P
2016-01-01
Topological insulators are fascinating states of matter exhibiting protected edge states and robust quantized features in their bulk. Here, we propose and validate experimentally a method to detect topological properties in the bulk of one-dimensional chiral systems. We first introduce the mean chiral displacement, and we show that it rapidly approaches a multiple of the Zak phase in the long time limit. Then we measure the Zak phase in a photonic quantum walk, by direct observation of the mean chiral displacement in its bulk. Next, we measure the Zak phase in an alternative, inequivalent timeframe, and combine the two windings to characterize the full phase diagram of this Floquet system. Finally, we prove the robustness of the measure by introducing dynamical disorder in the system. This detection method is extremely general, as it can be applied to all one-dimensional platforms simulating static or Floquet chiral systems.
Lu, Yuan-Ming; Vishwanath, Ashvin
2016-04-01
We study (2+1)-dimensional phases with topological order, such as fractional quantum Hall states and gapped spin liquids, in the presence of global symmetries. Phases that share the same topological order can then differ depending on the action of symmetry, leading to symmetry-enriched topological (SET) phases. Here, we present a K -matrix Chern-Simons approach to identify distinct phases with Abelian topological order, in the presence of unitary or antiunitary global symmetries. A key step is the identification of a smooth edge sewing condition that is used to check if two putative phases are indeed distinct. We illustrate this method by classifying Z2 topological order (Z2 spin liquids) in the presence of an internal Z2 global symmetry for which we find six distinct phases. These include two phases with an unconventional action of symmetry that permutes anyons leading to symmetry-protected Majorana edge modes. Other routes to realizing protected edge states in SET phases are identified. Symmetry-enriched Laughlin states and double-semion theories are also discussed. Somewhat surprisingly, we observe that (i) gauging the global symmetry of distinct SET phases leads to topological orders with the same total quantum dimension, and (ii) a pair of distinct SET phases can yield the same topological order on gauging the symmetry.
P. A. Deymier
2016-12-01
Full Text Available We illustrate the concept of geometric phase in the case of two prototypical elastic systems, namely the one-dimensional harmonic oscillator and a one-dimensional binary superlattice. We demonstrate formally the relationship between the variation of the geometric phase in the spectral and wave number domains and the parallel transport of a vector field along paths on curved manifolds possessing helicoidal twists which exhibit non-conventional topology.
Fessel, Adrian; Oettmeier, Christina; Bernitt, Erik; Gauthier, Nils C.; Döbereiner, Hans-Günther
2012-08-01
We study the formation of transportation networks of the true slime mold Physarum polycephalum after fragmentation by shear. Small fragments, called microplasmodia, fuse to form macroplasmodia in a percolation transition. At this topological phase transition, one single giant component forms, connecting most of the previously isolated microplasmodia. Employing the configuration model of graph theory for small link degree, we have found analytically an exact solution for the phase transition. It is generally applicable to percolation as seen, e.g., in vascular networks.
Deymier, P. A.; Runge, K.; Vasseur, J. O.
2016-12-01
We illustrate the concept of geometric phase in the case of two prototypical elastic systems, namely the one-dimensional harmonic oscillator and a one-dimensional binary superlattice. We demonstrate formally the relationship between the variation of the geometric phase in the spectral and wave number domains and the parallel transport of a vector field along paths on curved manifolds possessing helicoidal twists which exhibit non-conventional topology.
Design of materials with extreme thermal expansion using a three-phase topology optimization method
Sigmund, Ole; Torquato, S.
1997-01-01
We show how composites with extremal or unusual thermal expansion coefficients can be designed using a numerical topology optimization method. The composites are composed of two different material phases and void. The optimization method is illustrated by designing materials having maximum thermal...... expansion, zero thermal expansion, and negative thermal expansion. Assuming linear elasticity, it is shown that materials with effective negative thermal expansion coefficients can be obtained by mixing two phases with positive thermal expansion coefficients and void. We also show...
Topological phase transitions in thin films by tuning multivalley boundary-state couplings
Li, Xiao; Niu, Qian
2017-06-01
Dirac boundary states on opposite boundaries can overlap and interact owing to finite size effect. We propose that in a thin film system with symmetry-unrelated valleys, valley-contrasting couplings between Dirac boundary states can be exploited to design various two-dimensional topological quantum phases. Our first-principles calculations demonstrate the mechanism in tin telluride slab and nanoribbon array, respectively, by top-down and bottom-up material designs. Both two-dimensional topological crystalline insulator and quantum spin Hall insulator emerge in the same material system, which offers highly tunable quantum transport of edge channels with a set of quantized conductances.
Tunable spin-charge conversion through topological phase transitions in zigzag nanoribbons
Li, Hang
2016-06-29
We study spin-orbit torques and charge pumping in magnetic quasi-one-dimensional zigzag nanoribbons with a hexagonal lattice, in the presence of large intrinsic spin-orbit coupling. Such a system experiences a topological phase transition from a trivial band insulator to a quantum spin Hall insulator by tuning of either the magnetization direction or the intrinsic spin-orbit coupling. We find that the spin-charge conversion efficiency (i.e., spin-orbit torque and charge pumping) is dramatically enhanced at the topological transition, displaying a substantial angular anisotropy.
Series of topological phase transitions in TiTe2 under strain
Zhang, Qingyun
2013-10-21
First-principles calculations are performed to investigate the topological properties of TiTe2 under hydrostatic pressure, uniaxial strain, and biaxial strain. It is found that the system is unusually accessible to strain effects and the first compound that under hydrostatic pressure (up to experimentally reasonable 30 GPa) is subject to a series of four topological phase transitions, which are related to band inversions at different points of the Brillouin zone. Therefore, TiTe2 enables experimental access to all these transitions in a single compound.
Offroy, Marc; Duponchel, Ludovic
2016-03-03
An important feature of experimental science is that data of various kinds is being produced at an unprecedented rate. This is mainly due to the development of new instrumental concepts and experimental methodologies. It is also clear that the nature of acquired data is significantly different. Indeed in every areas of science, data take the form of always bigger tables, where all but a few of the columns (i.e. variables) turn out to be irrelevant to the questions of interest, and further that we do not necessary know which coordinates are the interesting ones. Big data in our lab of biology, analytical chemistry or physical chemistry is a future that might be closer than any of us suppose. It is in this sense that new tools have to be developed in order to explore and valorize such data sets. Topological data analysis (TDA) is one of these. It was developed recently by topologists who discovered that topological concept could be useful for data analysis. The main objective of this paper is to answer the question why topology is well suited for the analysis of big data set in many areas and even more efficient than conventional data analysis methods. Raman analysis of single bacteria should be providing a good opportunity to demonstrate the potential of TDA for the exploration of various spectroscopic data sets considering different experimental conditions (with high noise level, with/without spectral preprocessing, with wavelength shift, with different spectral resolution, with missing data). Copyright © 2016 Elsevier B.V. All rights reserved.
Wang, Rui; Qiao, Qian; Wang, Bin; Ding, Xiu-Huan; Zhang, Yi-Fu
2016-09-01
The quantum spin Hall (QSH) effect and the quantum anomalous Hall (QAH) effect in Lieb lattice are investigated in the presence of both Rashba spin-orbit coupling (SOC) and uniform exchange field. The Lieb lattice has a simple cubic symmetry, which is characterized by the single Dirac-cone per Brillouin zone and the middle flat band in the band structure. The intrinsic SOC is essentially needed to open the full energy gap in the bulk. The QSH effect could survive even in the presence of the exchange field. In terms of the first Chern number and the spin Chern number, we study the topological nature and the topological phase transition from the time-reversal symmetry broken QSH effect to the QAH effect. For Lieb lattice ribbons, the energy spectrum and the wave-function distributions are obtained numerically, where the helical edge states and the chiral edge states reveal the non-trivial topological QSH and QAH properties, respectively.
Topological phases of the kicked Harper-Kitaev model with ultracold atoms
Chen, M. N.; Mei, Feng; Su, W.; Wang, Huai-Qiang; Zhu, Shi-Liang; Sheng, L.; Xing, D. Y.
2017-01-01
We propose using ultracold atoms trapped in a one-dimensional periodically driven optical lattice to realize the Harper-Kitaev model, where the on-site energies are periodically kicked. Such a system provides a natural platform to study both Chern insulators and Majorana fermions. Based on calculating the quasienergy spectra, we find that both Floquet Majorana modes and Hall chiral edge modes could appear at the sample boundary in the gaps between the quasienergy bands. We also study the competition of topological superconductor and Chern insulator states in the model. We calculate the {{{Z}}2}× {{{Z}}2} index and Floquet Chern number to characterize the above two different topological states, including the topological phase transitions in the kicked Harper-Kitaev model with the increase in the strength of the kick.
Topological phase transition in the Scheidegger model of river networks
Oppenheim, Jacob N.; Magnasco, Marcelo O.
2012-08-01
Transport networks are found at the heart of myriad natural systems, yet are poorly understood, except for the case of river networks. The Scheidegger model, in which rivers are convergent random walks, has been studied only in the case of flat topography, ignoring the variety of curved geometries found in nature. Embedding this model on a cone, we find a convergent and a divergent phase, corresponding to few, long basins and many, short basins, respectively, separated by a singularity, indicating a phase transition. Quantifying basin shape using Hacks law l˜ah gives distinct values for h, providing a method of testing our hypotheses. The generality of our model suggests implications for vascular morphology, in particular, differing number and shapes of arterial and venous trees.
Topological issues in single-phase power factor correction
2001-01-01
The equipment connected to an electricity distribution network usually needs some kind of power conditioning, typically rectification, which produces a nonsinusoidal line current due to the nonlinear input characteristic. With the steadily increasing use of such equipment, line current harmonics have become a significant problem. Their adverse effects on the power system are well recognized. They include increased magnitudes of neutral currents in three-phase systems, overheating in transform...
Topology and Phase Transitions in the Little-Parks Experiment
Berger, Jorge; Rubinstein, Jacob
1996-01-01
This is an analytic study of the problem of transitions between normal and superconducting phases for a sample which encloses a magnetic flux. A preliminary study of this problem, based on numerical minimization of the free energy for a particular form of the thickness of the sample, was published in Phys. Rev. Lett. {\\bf 75}, 320 (1995). For a sample of uniform thickness the order parameter is uniform, but even infinitesimal deviations from uniform thickness give rise to a singly connected s...
Topological Phases of Interacting Bosons on the Kagome Lattice
Roychowdhury, Krishanu; Bhattacharjee, Subhro; Pollmann, Frank
2015-03-01
We consider an extended Hubbard model of hard core bosons including nearest-neighbour hopping and long range repulsive interactions on a kagome lattice. The system is an insulator at commensurate fillings of 1/6, 1/3 and 1/2 and can be mapped to different dimer models on the triangular lattice (depending on the filling). We focus on the filling of 1/3, which transforms to a fully packed loop (FPL) model, and derive the full phase diagram in the low-energy subspace. Similar to the quantum dimer model and easy-axis kagome antiferromagnetic model studied before, we find an extended region of a gapped Z2 liquid with vison excitations. The gauge fluctuations, responsible for the vison modes, are dictated by the action of an even Ising gauge theory. In the ordered phase, where the vison gap closes, we observe a 3-fold rotationally symmetric loop ordering and present the critical theory for the amplitude fluctuations of the condensed modes. We also speculate the phase diagram for the fermionic counterpart of the model at all the above mentioned fractional fillings.
Ye, Peng; Wen, Xiao-Gang
2014-01-01
Recently, there is a considerable study on gapped symmetric phases of bosons that do not break any symmetry. Even without symmetry breaking, the bosons can still be in many exotic new states of matter, such as symmetry-protected topological (SPT) phases, which are short-range entangled and symmetry-enriched topological (SET) phases, which are long-range entangled. It is well known that noninteracting fermionic topological insulators are SPT states protected by time-reversal symmetry and U(1) fermion number conservation symmetry. In this paper, we construct three-dimensional exotic phases of bosons with time-reversal symmetry and boson number conservation U(1) symmetry by means of fermionic projective construction. We first construct an algebraic bosonic insulator, which is a symmetric bosonic state with an emergent U(1) gapless gauge field. We then obtain many gapped bosonic states that do not break the time-reversal symmetry and boson number conservation via proper dyon condensations. We identify the constructed states by calculating the allowed electric and magnetic charges of their excitations, as well as the statistics and the symmetric transformation properties of those excitations. This allows us to show that our constructed states can be trivial SPT states (i.e., trivial Mott insulators of bosons with symmetry), nontrivial SPT states (i.e., bosonic topological insulators), and SET states (i.e., fractional bosonic topological insulators). In nontrivial SPT states, the elementary monopole (carrying zero electric charge but unit magnetic charge) and elementary dyon (carrying both unit electric charge and unit magnetic charge) are fermionic and bosonic, respectively. In SET states, intrinsic excitations may carry fractional charge.
Belopolski, Ilya; Xu, Su-Yang; Koirala, Nikesh; Liu, Chang; Bian, Guang; Strocov, Vladimir N; Chang, Guoqing; Neupane, Madhab; Alidoust, Nasser; Sanchez, Daniel; Zheng, Hao; Brahlek, Matthew; Rogalev, Victor; Kim, Timur; Plumb, Nicholas C; Chen, Chaoyu; Bertran, François; Le Fèvre, Patrick; Taleb-Ibrahimi, Amina; Asensio, Maria-Carmen; Shi, Ming; Lin, Hsin; Hoesch, Moritz; Oh, Seongshik; Hasan, M Zahid
2017-03-01
Engineered lattices in condensed matter physics, such as cold-atom optical lattices or photonic crystals, can have properties that are fundamentally different from those of naturally occurring electronic crystals. We report a novel type of artificial quantum matter lattice. Our lattice is a multilayer heterostructure built from alternating thin films of topological and trivial insulators. Each interface within the heterostructure hosts a set of topologically protected interface states, and by making the layers sufficiently thin, we demonstrate for the first time a hybridization of interface states across layers. In this way, our heterostructure forms an emergent atomic chain, where the interfaces act as lattice sites and the interface states act as atomic orbitals, as seen from our measurements by angle-resolved photoemission spectroscopy. By changing the composition of the heterostructure, we can directly control hopping between lattice sites. We realize a topological and a trivial phase in our superlattice band structure. We argue that the superlattice may be characterized in a significant way by a one-dimensional topological invariant, closely related to the invariant of the Su-Schrieffer-Heeger model. Our topological insulator heterostructure demonstrates a novel experimental platform where we can engineer band structures by directly controlling how electrons hop between lattice sites.
Topology in the SU(Nf) chiral symmetry restored phase of unquenched QCD and axion cosmology
Azcoiti, Vicente
2016-01-01
We investigate the topological properties of unquenched QCD on the basis of numerical results of simulations at fixed topological charge, recently reported by Borsanyi et al., and analytical predictions of the dilute instanton gas approximation. We demonstrate that the mean value of the chiral condensate at fixed topological charge is, in both cases, inconsistent with the analytical prediction of the large volume expansion around the saddle point, and argue that the most plausible explanation for the failure of the saddle point expansion is a vacuum energy density theta-independent at high temperatures, but surprisingly not too high (T\\sim 2T_c), a result which would imply a vanishing topological susceptibility, and the absence of all physical effects of the U(1) axial anomaly at these temperatures. We also show that under a general assumption concerning the high temperature phase of QCD, where the SU(Nf)_A symmetry is restored, the analytical prediction for the chiral condensate at fixed topological charge i...
Quantum Oscillation Signatures of Pressure-induced Topological Phase Transition in BiTeI.
Park, Joonbum; Jin, Kyung-Hwan; Jo, Y J; Choi, E S; Kang, W; Kampert, E; Rhyee, J-S; Jhi, Seung-Hoon; Kim, Jun Sung
2015-11-02
We report the pressure-induced topological quantum phase transition of BiTeI single crystals using Shubnikov-de Haas oscillations of bulk Fermi surfaces. The sizes of the inner and the outer FSs of the Rashba-split bands exhibit opposite pressure dependence up to P = 3.35 GPa, indicating pressure-tunable Rashba effect. Above a critical pressure P ~ 2 GPa, the Shubnikov-de Haas frequency for the inner Fermi surface increases unusually with pressure, and the Shubnikov-de Haas oscillations for the outer Fermi surface shows an abrupt phase shift. In comparison with band structure calculations, we find that these unusual behaviors originate from the Fermi surface shape change due to pressure-induced band inversion. These results clearly demonstrate that the topological quantum phase transition is intimately tied to the shape of bulk Fermi surfaces enclosing the time-reversal invariant momenta with band inversion.
Zhu, Guo-Yi; Wang, Ziqiang; Zhang, Guang-Ming
2017-05-01
Motivated by the recent observations of nodeless superconductivity in the monolayer CuO2 grown on the Bi2Sr2CaCu2O8+δ substrates, we study the two-dimensional superconducting (SC) phases described by the two-dimensional t\\text-J model in proximity to an antiferromagnetic (AF) insulator. We found that i) the nodal d-wave SC state can be driven via a continuous transition into a nodeless d-wave pairing state by the proximity-induced AF field. ii) The energetically favorable pairing states in the strong field regime have extended s-wave symmetry and can be nodal or nodeless. iii) Between the pure d-wave and s-wave paired phases, there emerge two topologically distinct SC phases with (s+\\text{i}d) symmetry, i.e., the weak and strong pairing phases, and the weak pairing phase is found to be a Z 2 topological superconductor protected by valley symmetry, exhibiting robust gapless nonchiral edge modes. These findings strongly suggest that the high-T c superconductors in proximity to antiferromagnets can realize fully gapped symmetry-protected topological SC.
A Topological Phase Transition in Models of River Networks
Oppenheim, Jacob; Magnasco, Marcelo
2012-02-01
The classical Scheidegger model of river network formation and evolution is investigated on non-Euclidean geometries, which model the effects of regions of convergent and divergent flows - as seen around lakes and drainage off mountains, respectively. These new models may be differentiated by the number of basins formed. Using the divergence as an order parameter, we see a phase transition in the number of distinct basins at the point of a flat landscape. This is a surprising property of the statistics of river networks and suggests significantly different properties for riverine networks in uneven topography and vascular networks of arteries versus those of veins among others.
Using Topological Analysis to Support Event-Guided Exploration in Urban Data.
Doraiswamy, Harish; Ferreira, Nivan; Damoulas, Theodoros; Freire, Juliana; Silva, Cláudio T
2014-12-01
The explosion in the volume of data about urban environments has opened up opportunities to inform both policy and administration and thereby help governments improve the lives of their citizens, increase the efficiency of public services, and reduce the environmental harms of development. However, cities are complex systems and exploring the data they generate is challenging. The interaction between the various components in a city creates complex dynamics where interesting facts occur at multiple scales, requiring users to inspect a large number of data slices over time and space. Manual exploration of these slices is ineffective, time consuming, and in many cases impractical. In this paper, we propose a technique that supports event-guided exploration of large, spatio-temporal urban data. We model the data as time-varying scalar functions and use computational topology to automatically identify events in different data slices. To handle a potentially large number of events, we develop an algorithm to group and index them, thus allowing users to interactively explore and query event patterns on the fly. A visual exploration interface helps guide users towards data slices that display interesting events and trends. We demonstrate the effectiveness of our technique on two different data sets from New York City (NYC): data about taxi trips and subway service. We also report on the feedback we received from analysts at different NYC agencies.
Controlled topological transitions in thin film phase separation
Hennessy, Matthew G; Goriely, Alain; Münch, Andreas; Wagner, Barbara
2014-01-01
In this paper the evolution of a binary mixture in a thin-film geometry with a wall at the top and bottom is considered. By bringing the mixture into its miscibility gap so that no spinodal decomposition occurs in the bulk, a slight energetic bias of the walls towards each one of the constituents ensures the nucleation of thin boundary layers that grow until the constituents have moved into one of the two layers. These layers are separated by an interfacial region where the composition changes rapidly. Conditions that ensure the separation into two layers with a thin interfacial region are investigated based on a phase-field model. Using matched asymptotic expansions a corresponding sharp-interface problem for the location of the interface is established. It is then argued that this newly created two-layer system is not at its energetic minimum but destabilizes into a controlled self-replicating pattern of trapezoidal vertical stripes by minimizing the interfacial energy between the phases while conserving th...
Controlled Topological Transitions in Thin-Film Phase Separation
Hennessy, Matthew G.
2015-01-01
© 2015 Society for Industrial and Applied Mathematics. In this paper the evolution of a binary mixture in a thin-film geometry with a wall at the top and bottom is considered. By bringing the mixture into its miscibility gap so that no spinodal decomposition occurs in the bulk, a slight energetic bias of the walls toward each one of the constituents ensures the nucleation of thin boundary layers that grow until the constituents have moved into one of the two layers. These layers are separated by an interfacial region where the composition changes rapidly. Conditions that ensure the separation into two layers with a thin interfacial region are investigated based on a phase-field model. Using matched asymptotic expansions a corresponding sharp-interface problem for the location of the interface is established. It is then argued that this newly created two-layer system is not at its energetic minimum but destabilizes into a controlled self-replicating pattern of trapezoidal vertical stripes by minimizing the interfacial energy between the phases while conserving their area. A quantitative analysis of this mechanism is carried out via a thin-film model for the free interfaces, which is derived asymptotically from the sharp-interface model.
Bona fide interaction-driven topological phase transition in correlated SPT states
Meng, Zi Yang; He, Yuan-Yao; Wu, Han-Qing; You, Yi-Zhuang; Xu, Cenke; Lu, Zhong-Yi
It is expected the interplay between non-trivial band topology and strong electron correlation will lead to very rich physics. Thus a controlled study of the competition between topology and correlation is of great interest. Here, employing large-scale quantum Monte Carlo simulations, we provide a concrete example of the Kane-Mele-Hubbard model on an AA stacking bilayer honeycomb lattice with inter-layer antiferromagnetic interaction. Our simulation identified several different phases: a quantum spin-Hall insulator (QSH), a xy-plane antiferromagnetic Mott insulator (xy-AFM) and an inter-layer dimer-singlet insulator (dimer-singlet). Most importantly, a bona fide topological phase transition between the QSH and the dimer-singlet insulators, purely driven by the inter-layer antiferromagnetic interaction is found. At the transition, the spin and charge gap of the system close while the single-particle excitations remain gapped, which means that this transition has no mean field analogue and it can be viewed as a transition between bosonic SPT states. At one special point, this transition is described by a (2+1)d O(4) nonlinear sigma model with exact SO(4) symmetry, and a topological term at theta=p. Relevance of this work towards more general interacting SPT states is discussed.
Emergent topology and dynamical quantum phase transitions in two-dimensional closed quantum systems
Bhattacharya, Utso; Dutta, Amit
2017-07-01
Dynamical quantum phase transitions (DQPTs) manifested in the nonanalyticities in the temporal evolution of a closed quantum system generated by the time-independent final Hamiltonian, following a quench (or ramping) of a parameter of the Hamiltonian, is an emerging frontier of nonequilibrium quantum dynamics. We, here, introduce the notion of a dynamical topological order parameter (DTOP) that characterizes these DQPTs occurring in quenched (or ramped) two-dimensional closed quantum systems; this is quite a nontrivial generalization of the notion of DTOP introduced in Budich and Heyl [Phys. Rev. B 93, 085416 (2016), 10.1103/PhysRevB.93.085416] for one-dimensional situations. This DTOP is obtained from the "gauge-invariant" Pancharatnam phase extracted from the Loschmidt overlap, i.e., the modulus of the overlap between the initially prepared state and its time-evolved counterpart reached following a temporal evolution generated by the time-independent final Hamiltonian. This generic proposal is illustrated considering DQPTs occurring in the subsequent temporal evolution following a sudden quench of the staggered mass of the topological Haldane model on a hexagonal lattice where it stays fixed to zero or unity and makes a discontinuous jump between these two values at critical times at which DQPTs occur. What is remarkable is that while the topology of the equilibrium model is characterized by the Chern number, the emergent topology associated with the DQPTs is characterized by a generalized winding number.
T. Santosh Kumar
2014-01-01
Full Text Available This paper presents the detailed model, control and simulation of H-Bridge VSI topology based DSTATCOM. It also describes the control of multilevel inverter supplied by Photovoltaic system and a battery bank which is connected to the supply system. It is well known that the Power Quality of the Multililevel Inverter signals depends upon the number of levels. Basic structure and operating principle of the Cascaded H-Bridge Multilevel Inverter are explored. The phase shifted SPWM is used for reducing the lower order harmonics of the output voltage and the Park’s transformation is employed to decouple the active and reactive power components for regulating the compensation power. The controller equations are such that the phase shifted SPWM pulses are generated automatically for any number of levels. The effectiveness of the proposal method is evaluated in simulation by using Matlab/Simulink. The results of the simulation are analyzed and discussed.
Céolin, René; Rietveld, Ivo B.
2017-04-01
The phase behavior of pharmaceuticals is important for regulatory requirements and dosage form development. Racemic fluoxetine nitrate possesses two crystalline forms for which initial measurements indicated that they have a monotropic relationship with form I the only stable form. By constructing the topological pressure-temperature phase diagram, it has been shown that unexpectedly form II has a stable domain in the phase diagram and can be easily obtained by heating and grinding. The pressure necessary to obtain form II is only 11 MPa, which is much lower than most pressure used for tableting in the pharmaceutical industry.
Phase field model for optimization of multi-material structural topology in two and three dimensions
Zhou, Shiwei
The Optimization of Structural Topology (OST) is a breakthrough in product design because it can optimize size, shape and topology synchronously under different physical constraints. It has promising applications in industry ranging from automobile and aerospace engineering to micro electromechanical system. This dissertation first substitutes the nonlinear diffusion method for filter process in the optimization of structural topology. Filtering has been a major technique used in a homogenization-based method for topology optimization of structures. It plays a key role in regularizing the basic problem into a well-behaved setting. But it has a drawback of smoothing effect around the boundary of material domain. A diffusion technique is presented here as a variational approach to the regularization of the topology optimization problem. A nonlinear or anisotropic diffusion process not only leads to a suitable problem regularization but also exhibits strong "edge"-preserving characteristics. Thus, it shows that the use of the nonlinear diffusions brings desirable effects of boundary preservation and even enhancement of lower-dimensional features such as flow-like structures. The proposed diffusion techniques have a close relationship with the diffusion methods and the phase-field methods of the fields of materials and digital image processing. Then this dissertation introduces a gradient flow in the norm of H-1 for the problem of multi-material structural topology optimization in 2/3D with a generalized Cahn-Hilliard (C-H) model with elasticity. Unlike the traditional C-H model applied to spinodal separation which only has bulk energy and interface energy, the generalized model couples the macroscopic elastic energy (mean compliance) into the total free energy. As a result, the grain morphology is not random islands or zigzag web-like objects but regular truss or bar structure. Although disturbed by elastic energy, the C-H system still keeps its two most important
Dey, Dayasindhu; Saha, Sudip Kumar; Singha Deo, P.; Kumar, Manoranjan; Sarkar, Sujit
2017-07-01
We study the topological quantum phase transition and also the nature of this transition using the density matrix renormalization group method. We observe the existence of topological quantum phase transition for repulsive interaction, however this phase is more stable for the attractive interaction. The length scale dependent study shows many new and important results and we show explicitly that the major contribution to the excitation comes from the edge of the system when the system is in the topological state. We also show the dependence of Majorana localization length for various values of chemical potential.
Signatures of a pressure-induced topological quantum phase transition in BiTeI.
Xi, Xiaoxiang; Ma, Chunli; Liu, Zhenxian; Chen, Zhiqiang; Ku, Wei; Berger, H; Martin, C; Tanner, D B; Carr, G L
2013-10-11
We report the observation of two signatures of a pressure-induced topological quantum phase transition in the polar semiconductor BiTeI using x-ray powder diffraction and infrared spectroscopy. The x-ray data confirm that BiTeI remains in its ambient-pressure structure up to 8 GPa. The lattice parameter ratio c/a shows a minimum between 2.0-2.9 GPa, indicating an enhanced c-axis bonding through p(z) band crossing as expected during the transition. Over the same pressure range, the infrared spectra reveal a maximum in the optical spectral weight of the charge carriers, reflecting the closing and reopening of the semiconducting band gap. Both of these features are characteristics of a topological quantum phase transition and are consistent with a recent theoretical proposal.
Topological Aspects of Entropy and Phase Transition of Kerr Black Holes
YANG Guo-Hong; YAN Ji-Jiang; TIAN Li-Jun; DUAN Yi-Shi
2005-01-01
In the light of topological current and the relationship between the entropy and the Euler characteristic, the topological aspects of entropy and phase transition of Kerr black holes are studied. From Gauss-Bonnet-Chern theorem,it is shown that the entropy of Kerr black holes is determined by the singularities of the Killing vector field of spacetime.By calculating the Hopf indices and Brouwer degrees of the Killing vector field at the singularities, the entropy S = A/4for nonextreme Kerr black holes and S = 0 for extreme ones are obtained, respectively. It is also discussed that, with the change of the ratio of mass to angular momentum for unit mass, the Euler characteristic and the entropy of Kerr black holes will change discontinuously when the singularities on Cauchy horizon merge with the singularities on event horizon, which will lead to the first-order phase transition of Kerr black holes.
Floquet topological phase transitions and chiral edge states in a kagome lattice
He, Chaocheng; Zhang, Zhiyong, E-mail: zyzhang@nju.edu.cn
2014-09-05
The Floquet topological phases and chiral edge states in a kagome lattice under a circularly-polarized driving field are studied. In the off-resonant case, the system exhibits the similar character as the kagome lattice model with staggered magnetic fluxes, but the total band width is damped in oscillation. In the on-resonant case, the degeneracy splitting at the Γ point does not always result in a gap. The positions of the other two gaps are influenced by the flat band. With the field intensity increased, these two gaps undergo closing-then-reopening processes, accompanied with the changing of the winding numbers. - Highlights: • A kagome lattice under a circularly-polarized driving field is studied. • The band structures and chiral edge states are studied via exact Floquet method. • Various modifications of the Floquet band structure are found. • Floquet topological phase transitions appear in both off- and on-resonant cases.
Fermionic Symmetry-Protected Topological Phase in a Two-Dimensional Hubbard Model
Chen, Cheng-Chien; Muechler, Lukas; Car, Roberto; Neupert, Titus; Maciejko, Joseph
2016-08-01
We study the two-dimensional (2D) Hubbard model using exact diagonalization for spin-1 /2 fermions on the triangular and honeycomb lattices decorated with a single hexagon per site. In certain parameter ranges, the Hubbard model maps to a quantum compass model on those lattices. On the triangular lattice, the compass model exhibits collinear stripe antiferromagnetism, implying d -density wave charge order in the original Hubbard model. On the honeycomb lattice, the compass model has a unique, quantum disordered ground state that transforms nontrivially under lattice reflection. The ground state of the Hubbard model on the decorated honeycomb lattice is thus a 2D fermionic symmetry-protected topological phase. This state—protected by time-reversal and reflection symmetries—cannot be connected adiabatically to a free-fermion topological phase.
Emergence of non-centrosymmetric topological insulating phase in BiTeI under pressure.
Bahramy, M S; Yang, B-J; Arita, R; Nagaosa, N
2012-02-14
The spin-orbit interaction affects the electronic structure of solids in various ways. Topological insulators are one example in which the spin-orbit interaction leads the bulk bands to have a non-trivial topology, observable as gapless surface or edge states. Another example is the Rashba effect, which lifts the electron-spin degeneracy as a consequence of the spin-orbit interaction under broken inversion symmetry. It is of particular importance to know how these two effects, that is, the non-trivial topology of electronic states and the Rashba spin splitting, interplay with each other. Here we show through sophisticated first-principles calculations that BiTeI, a giant bulk Rashba semiconductor, turns into a topological insulator under a reasonable pressure. This material is shown to exhibit several unique features, such as a highly pressure-tunable giant Rashba spin splitting, an unusual pressure-induced quantum phase transition, and more importantly, the formation of strikingly different Dirac surface states at opposite sides of the material.
Pre-inflation: origin of the Universe from a topological phase transition
Bellini, Mauricio
2016-01-01
I study a model which describes the birth of the universe using a global topological phase transition with a complex manifold where the time, $\\tau$, is considered as a complex variable. Before the big bang $\\tau$ is a purely imaginary variable so that the space can be considered as Euclidean. The phase transition from a pre-inflation to inflation is examined by studying the dynamical rotation of the time on the complex plane. Back-reaction effects are exactly calculated using Relativistic Quantum Geometry.
Phase-tunable Majorana bound states in a topological N-SNS junction
Hansen, Esben Bork; Danon, Jeroen; Flensberg, Karsten
2016-01-01
We theoretically study the differential conductance of a one-dimensional normal-superconductor-normal-superconductor (N-SNS) junction with a phase bias applied between the two superconductors. We consider specifically a junction formed by a spin-orbit coupled semiconducting nanowire with regions...... of the Majorana modes gives rise to features in the differential conductance that offer a clear distinction between the topologically trivial and nontrivial phases. We calculate the transport properties of the junction numerically and also present a simple analytical model that captures the main properties...
Pre-inflation: Origin of the Universe from a topological phase transition
Bellini, Mauricio
2017-08-01
I study a model which describes the birth of the universe using a global topological phase transition with a complex manifold where the time, τ, is considered as a complex variable. Before the big bang τ is a purely imaginary variable so that the space can be considered as Euclidean. The phase transition from a pre-inflation to inflation is examined by studying the dynamical rotation of the time on the complex plane. Back-reaction effects are exactly calculated using Relativistic Quantum Geometry.
Pre-inflation: Origin of the Universe from a topological phase transition
Mauricio Bellini
2017-08-01
Full Text Available I study a model which describes the birth of the universe using a global topological phase transition with a complex manifold where the time, τ, is considered as a complex variable. Before the big bang τ is a purely imaginary variable so that the space can be considered as Euclidean. The phase transition from a pre-inflation to inflation is examined by studying the dynamical rotation of the time on the complex plane. Back-reaction effects are exactly calculated using Relativistic Quantum Geometry.
Introduction to Topological Phases and Electronic Interactions in (2+1) Dimensions
Nascimento, Leandro O.
2017-04-01
A brief introduction to topological phases is provided, considering several two-band Hamiltonians in one and two dimensions. Relevant concepts of the topological insulator theory, such as: Berry phase, Chern number, and the quantum adiabatic theorem, are reviewed in a basic framework, which is meant to be accessible to non-specialists. We discuss the Kitaev chain, SSH, and BHZ models. The role of the electromagnetic interaction in the topological insulator theory is addressed in the light of the pseudo-quantum electrodynamics (PQED). The well-known parity anomaly for massless Dirac particle is reviewed in terms of the Chern number. Within the continuum limit, a half-quantized Hall conductivity is obtained. Thereafter, by considering the lattice regularization of the Dirac theory, we show how one may obtain the well-known quantum Hall conductivity for a single Dirac cone. The renormalization of the electron energy spectrum, for both small and large coupling regime, is derived. In particular, it is shown that massless Dirac particles may, only in the strong correlated limit, break either chiral or parity symmetries. For graphene, this implies the generation of Landau-like energy levels and the quantum valley Hall effect.
Spaans, M.
2013-01-01
General Relativity is extended into the quantum domain. A thought experiment is explored to derive a specific topological build-up for Planckian spacetime. The presented arguments are inspired by Feynman's path integral for superposition and Wheeler's quantum foam of Planck mass mini black holes (BH
Spaans, M.
2013-01-01
General Relativity is extended into the quantum domain. A thought experiment is explored to derive a specific topological build-up for Planckian spacetime. The presented arguments are inspired by Feynman's path integral for superposition and Wheeler's quantum foam of Planck mass mini black holes (BH
Topological semimetals with triply degenerate nodal points in θ -phase tantalum nitride
Weng, Hongming; Fang, Chen; Fang, Zhong; Dai, Xi
2016-06-01
Using first-principles calculation and symmetry analysis, we propose that θ -TaN is a topological semimetal having a new type of point nodes, i.e., triply degenerate nodal points. Each node is a band crossing between degenerate and nondegenerate bands along the high-symmetry line in the Brillouin zone, and is protected by crystalline symmetries. Such new type of nodes will always generate singular touching points between different Fermi surfaces and three-dimensional spin texture around them. Breaking the crystalline symmetry by external magnetic field or strain leads to various topological phases. By studying the Landau levels under a small field along the c axis, we demonstrate that the system has a new quantum anomaly that we call "helical anomaly.'
Topological insulators and the QCD vacuum: the theta parameter as a Berry phase
Thacker, H B
2013-01-01
There is considerable evidence, based on large $N_c$ chiral dynamics, holographic QCD, and Monte Carlo studies, that the QCD vacuum is permeated by discrete quasivacua separated by domain walls across which the local value of the topological $\\theta$ parameter jumps by $\\pm2\\pi$. In the 2-dimensional $CP^{N-1}$ sigma model, a pointlike charge is a domain wall, and $\\theta$ describes the background electric flux and the polarization of charged pairs in the vacuum. We show that the screening process, and the role of $\\theta$ as an order parameter describing electric polarization, are naturally formulated in terms of Bloch wave eigenstates of the Dirac Hamiltonian in the background gauge field. This formulation is similar to the Berry phase description of electric polarization and quantized charge transport in topological insulators. The Bloch waves are quasiperiodic superpositions of localized Dirac zero modes. They define a Berry connection around the Brillouin zone of the zero mode band which describes the lo...
Topological phases of one-dimensional fermions: An entanglement point of view
Turner, Ari M.; Pollmann, Frank; Berg, Erez
2011-02-01
The effect of interactions on topological insulators and superconductors remains, to a large extent, an open problem. Here, we describe a framework for classifying phases of one-dimensional interacting fermions, focusing on spinless fermions with time-reversal symmetry and particle number parity conservation, using concepts of entanglement. In agreement with an example presented by L. Fidkowski and A. Kitaev [Phys. Rev. BPRBMDO1098-012110.1103/PhysRevB.81.134509 81, 134509 (2010)], we find that in the presence of interactions there are only eight distinct phases which obey a Z8 group structure. This is in contrast to the Z classification in the noninteracting case. Each of these eight phases is characterized by a unique set of bulk invariants, related to the transformation laws of its entanglement (Schmidt) eigenstates under symmetry operations, and has a characteristic degeneracy of its entanglement levels. If translational symmetry is present, the number of distinct phases increases to 16.
Matrix product operators for symmetry-protected topological phases: Gauging and edge theories
Williamson, Dominic J.; Bultinck, Nick; Mariën, Michael; Şahinoǧlu, Mehmet B.; Haegeman, Jutho; Verstraete, Frank
2016-11-01
Projected entangled pair states (PEPS) provide a natural ansatz for the ground states of gapped, local Hamiltonians in which global characteristics of a quantum state are encoded in properties of local tensors. We develop a framework to describe onsite symmetries, as occurring in systems exhibiting symmetry-protected topological (SPT) quantum order, in terms of virtual symmetries of the local tensors expressed as a set of matrix product operators (MPOs) labeled by distinct group elements. These MPOs describe the possibly anomalous symmetry of the edge theory, whose local degrees of freedom are concretely identified in a PEPS. A classification of SPT phases is obtained by studying the obstructions to continuously deforming one set of MPOs into another, recovering the results derived for fixed-point models [Chen et al., Phys. Rev. B 87, 155114 (2013), 10.1103/PhysRevB.87.155114]. Our formalism accommodates perturbations away from fixed-point models, opening the possibility of studying phase transitions between different SPT phases. We also demonstrate that applying the recently developed quantum state gauging procedure to a SPT PEPS yields a PEPS with topological order determined by the initial symmetry MPOs. The MPO framework thus unifies the different approaches to classifying SPT phases, via fixed-point models, boundary anomalies, or gauging the symmetry, into the single problem of classifying inequivalent sets of matrix product operator symmetries that are defined purely in terms of a PEPS.
Magneto-optical response in the arbitrary-Chern number topological phase on square lattice
Wang, Yi-Xiang, E-mail: wangyixiang@jiangnan.edu.cn
2016-07-01
In this work, we investigate the magneto-optical response in the arbitrary-Chern number topological phase. Based on the Dirac theory, we derive the analytic expressions for the magneto-optical response. More importantly, we construct the model on the possible square lattice and make the numerical calculations with the exact diagonalization method. We find the analytical and numerical results are in good agreement with each other. For the optical absorption spectrum, the low-energy absorptive peaks and the corresponding hopping processes are distinct in different Chern number phases, heavily depending on the filling factor of the system. While for the optical Hall conductivities, the physical mechanisms are revealed for the dichroism of the absorption peaks in response to the right- and left-circularly polarized light. We discuss the feasibility of these results in experiment. - Highlights: • The arbitrary-Chern number topological phase is constructed on square lattice. • The optical absorption spectra are distinct in different Chern number phases. • The physical mechanisms are revealed for the dichroism of the absorption peaks.
Topological insulators and topological superconductors
Bernevig, Andrei B
2013-01-01
This graduate-level textbook is the first pedagogical synthesis of the field of topological insulators and superconductors, one of the most exciting areas of research in condensed matter physics. Presenting the latest developments, while providing all the calculations necessary for a self-contained and complete description of the discipline, it is ideal for graduate students and researchers preparing to work in this area, and it will be an essential reference both within and outside the classroom. The book begins with simple concepts such as Berry phases, Dirac fermions, Hall conductance and its link to topology, and the Hofstadter problem of lattice electrons in a magnetic field. It moves on to explain topological phases of matter such as Chern insulators, two- and three-dimensional topological insulators, and Majorana p-wave wires. Additionally, the book covers zero modes on vortices in topological superconductors, time-reversal topological superconductors, and topological responses/field theory and topolo...
Schoop, Leslie M.; Xie, Lilia S.; Chen, Ru; Gibson, Quinn D.; Lapidus, Saul H.; Kimchi, Itamar; Hirschberger, Max; Haldolaarachchige, Neel; Ali, Mazhar N.; Belvin, Carina A.; Liang, Tian; Neaton, Jeffrey B.; Ong, N P; Vishwanath, Ashvin; Cava, R. J.
2015-06-23
Three-dimensionalDirac semimetals (DSMs) arematerials that have masslessDirac electrons and exhibit exotic physical properties. It has been suggested that structurally distorting a DSM can create a topological insulator but this has not yet been experimentally verified. Furthermore, Majorana fermions have been theoretically proposed to exist inmaterials that exhibit both superconductivity and topological surface states. Herewe showthat the cubic Laves phase Au2Pb has a bulk Dirac cone that is predicted to gap on cooling through a structural phase transition at 100 K. The low temperature phase can be assigned a Z(2) = -1 topological index, and this phase becomes superconducting below 1.2 K. These characteristics make Au2Pb a unique platform for studying the transition between bulk Dirac electrons and topological surface states as well as studying the interaction of superconductivity with topological surface states, combining many different properties of emergent materials-superconductivity, bulk Dirac electrons, and a topologically nontrivial Z(2) invariant.
Interaction of the topological phase and the Magnus effect in a multimode fiber
Aleksiev, A.; Modnikova, E.; Fadeyeva, Tatyana A.; Lapayeva, S. N.; Volyar, Alexander V.
1996-04-01
The phenomenon of a light topological birefringence in a multimode fiber has been discussed in papers. The physical mechanism of the topological birefringence, as expected earlier is determined by the interaction of the two effects, namely, the topological Berry's phase and the optical Magnus effect. So, for a square distribution of a refractive index in a fiber cross section the near-meridianal local waves propagate along ray trajectories represented by strongly stretched ellipses of an elliptical helix. A plane made by a fiber axis and a major axis of a ray elliptical helix undergoes a rotation into the fiber, and the rotation hand of this plane is defined by a sign of the wave polarization circularity. If a linear polarized light drops into a fiber input its left-hand polarized component will rotate the major axis of the elliptical helix counterclockwise, and the right-hand polarized component rotates clockwise. Since the angular rates of this rotation are slightly different one from another forthcoming the local waves having counter circulation of a polarization should be collapsed in a single linear polarized local wave. However if the local wave trajectory doesn't lie in a plane then it is a space curve.
Large topological Hall effect in the non-collinear phase of an antiferromagnet.
Sürgers, Christoph; Fischer, Gerda; Winkel, Patrick; Löhneysen, Hilbert V
2014-03-05
Non-trivial spin arrangements in magnetic materials give rise to the topological Hall effect observed in compounds with a non-centrosymmetric cubic structure hosting a skyrmion lattice, in double-exchange ferromagnets and magnetically frustrated systems. The topological Hall effect has been proposed to appear also in presence of non-coplanar spin configurations and thus might occur in an antiferromagnetic material with a highly non-collinear and non-coplanar spin structure. Particularly interesting is a material where the non-collinearity develops not immediately at the onset of antiferromagnetic order but deep in the antiferromagnetic phase. This unusual situation arises in non-cubic antiferromagnetic Mn5Si3. Here we show that a large topological Hall effect develops well below the Néel temperature as soon as the spin arrangement changes from collinear to non-collinear with decreasing temperature. We further demonstrate that the effect is not observed when the material is turned ferromagnetic by carbon doping without changing its crystal structure.
A New Topology of Three-Phase Four-Wire UPQC with a Simplified Control Algorithm
Yash Pal
2012-03-01
Full Text Available In this paper, a simplified control algorithm based on unit vector template generation (UVTG is proposed for a star-delta supported three-phase four-wire (3P-4W unified power quality conditioner (UPQC topology for the improvement of different power quality problems. Different topologies reported in literature for 3P-4W UPQC use active compensation for the mitigation of source neutral current along with other power quality (PQ problems, while the uses of passive elements for the mitigation of source neutral current are advantageous over the active compensation due to ruggedness and less complexity of control. Hence, in this paper a star-delta transformer is connected in shunt near the load for mitigation of source neutral current, while three-leg voltage source inverters (VSIs based shunt and series active power filters (APFs of 3P-4W UPQC mitigate the current and voltage based distortions, respectively. A simple control algorithm based on Unit Vector Template Generation (UVTG is used as a control strategy of UPQC for mitigation of different PQ problems. In this control scheme, the current/voltage control is applied over the fundamental supply currents/load voltages instead of fast changing APFs currents/voltages, thereby reducing the effects of computational delay and the required sensors. The performance of the proposed topology of UPQC is analyzed through simulations results using MATLAB software with its Simulink and Power System Block set toolboxes.
Primordial Inflation Polarization Explorer (Phase 3)
Kogut, Alan
This is the Lead Proposal for the investigation "Primordial Inflation Polarization Explorer (Phase 3)". We propose to complete and fly the Primordial Inflation Polarization Explorer (PIPER) to measure the polarization of the cosmic microwave background (CMB) and search for the imprint of gravitational waves produced during an inflationary epoch in the early universe. Detection of the inflationary signal would have profound consequences for both cosmology and high-energy physics. Not only would it establish inflation as a physical reality, it would provide a direct, model-independent determination of the relevant energy scale, shedding light on physics at energies twelve orders of magnitude beyond those accessible to direct experimentation in particle accelerators. The recent detection of CMB polarization by the BICEP2 instrument brings new urgency to the field. The BICEP2 detection at degree angular scales is consistent with inflation, but the amplitude is a factor of two higher than upper limits set by unpolarized data. A critical test is the rise in power at large angular scales predicted by inflation. Detecting this rise would confirm the signal's inflationary origin, fulfilling a long quest for cosmology while providing new insight into physics at the highest energies. PIPER is the only suborbital instrument capable of measuring CMB polarization on the large angular scales needed to test an inflationary origin for the BICEP2 detection. PIPER is a balloon-borne instrument, optimized to detect the inflationary signal on large angular scales. It consists of two co-aligned telescopes cooled to 1.5 K within a large liquid helium bucket dewar. A variable-delay polarization modulator (VPM) on each telescope chops between linear and circular polarization to isolate the polarized signal while rejecting the much brighter unpolarized emission. Four 32 x 40 element detector arrays provide background-limited sensitivity. A series of flights from mid-latitude sites will map
Park, Sunghun; Recher, Patrik
2015-12-11
A phase from an adiabatic exchange of Majorana bound states (MBS) reveals their exotic anyonic nature. For detecting this exchange phase, we propose an experimental setup consisting of a Corbino geometry Josephson junction on the surface of a topological insulator, in which two MBS at zero energy can be created and rotated. We find that if a metallic tip is weakly coupled to a point on the junction, the time-averaged differential conductance of the tip-Majorana coupling shows peaks at the tip voltages eV=±(α-2πl)ℏ/T_{J}, where α=π/2 is the exchange phase of the two circulating MBS, T_{J} is the half rotation time of MBS, and l an integer. This result constitutes a clear experimental signature of Majorana fermion exchange.
Topological phases of silicene and germanene in an external magnetic field: Quantitative results
Singh, Nirpendra
2014-03-17
We investigate the topological phases of silicene and germanene that arise due to the strong spin-orbit interaction in an external perpendicular magnetic field. Below and above a critical field of 10 T, respectively, we demonstrate for silicene under 3% tensile strain quantum spin Hall and quantum anomalous Hall phases. Not far above the critical field, and therefore in the experimentally accessible regime, we obtain an energy gap in the meV range, which shows that the quantum anomalous Hall phase can be realized experimentally in silicene, in contrast to graphene (tiny energy gap) and germanene (enormous field required). © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Felix: A Topology based Framework for Visual Exploration of Cosmic Filaments
Shivshankar, Nithin; Natarajan, Vijay; van de Weygaert, Rien; Bos, E G Patrick; Rieder, Steven
2015-01-01
The large-scale structure of the universe is comprised of virialized blob-like clusters, linear filaments, sheet-like walls and huge near empty three-dimensional voids. Characterizing the large scale universe is essential to our understanding of the formation and evolution of galaxies. The density range of clusters, walls and voids are relatively well separated, when compared to filaments, which span a relatively larger range. The large scale filamentary network thus forms an intricate part of the cosmic web. In this paper, we describe Felix, a topology based framework for visual exploration of filaments in the cosmic web. The filamentary structure is represented by the ascending manifold geometry of the 2-saddles in the Morse-Smale complex of the density field. We generate a hierarchy of Morse-Smale complexes and query for filaments based on the density ranges at the end points of the filaments. The query is processed efficiently over the entire hierarchical Morse-Smale complex, allowing for interactive visu...
Exploring the dark foldable proteome by considering hydrophobic amino acids topology
Bitard-Feildel, Tristan; Callebaut, Isabelle
2017-01-01
The protein universe corresponds to the set of all proteins found in all organisms. A way to explore it is by taking into account the domain content of the proteins. However, some part of sequences and many entire sequences remain un-annotated despite a converging number of domain families. The un-annotated part of the protein universe is referred to as the dark proteome and remains poorly characterized. In this study, we quantify the amount of foldable domains within the dark proteome by using the hydrophobic cluster analysis methodology. These un-annotated foldable domains were grouped using a combination of remote homology searches and domain annotations, leading to define different levels of darkness. The dark foldable domains were analyzed to understand what make them different from domains stored in databases and thus difficult to annotate. The un-annotated domains of the dark proteome universe display specific features relative to database domains: shorter length, non-canonical content and particular topology in hydrophobic residues, higher propensity for disorder, and a higher energy. These features make them hard to relate to known families. Based on these observations, we emphasize that domain annotation methodologies can still be improved to fully apprehend and decipher the molecular evolution of the protein universe. PMID:28134276
Santos, F. A. N.; da Silva, L. C. B.; Coutinho-Filho, M. D.
2017-01-01
We propose a topological approach suitable to establish a connection between thermodynamics and topology in the microcanonical ensemble. Indeed, we report on results that point to the possibility of describing interacting classical spin systems in the thermodynamic limit, including the occurrence of a phase transition, using topological arguments only. Our approach relies on Morse theory, through the determination of the critical points of the potential energy, which is the proper Morse function. Our main finding is that, in the context of the classical models studied, the Euler characteristic χ (E) embeds the necessary features for a correct description of several magnetic thermodynamic quantities of the systems, such as the magnetization, correlation function, susceptibility, and critical temperature. Despite the classical nature of the models, such quantities are those that do not violate the laws of thermodynamics (with the proviso that van der Waals loop states are mean field (MF) artifacts). We also discuss the subtle connection between our approach using the Euler entropy, defined by the logarithm of the modulus of χ (E) per site, and that using the Boltzmann microcanonical entropy. Moreover, the results suggest that the loss of regularity in the Morse function is associated with the occurrence of unstable and metastable thermodynamic solutions in the MF case. The reliability of our approach is tested in two exactly soluble systems: the infinite-range and the one-dimensional short-range XY models in the presence of a magnetic field. In particular, we confirm that the topological hypothesis holds for both the infinite-range ({{T}c}\
Sahoo, Ranjit Kumar; Warren, Andrew D; Wahlberg, Niklas; Brower, Andrew V Z; Lukhtanov, Vladimir A; Kodandaramaiah, Ullasa
2016-01-01
Despite multiple attempts to infer the higher-level phylogenetic relationships of skipper butterflies (Family Hesperiidae), uncertainties in the deep clade relationships persist. The most recent phylogenetic analysis included fewer than 30% of known genera and data from three gene markers. Here we reconstruct the higher-level relationships with a rich sampling of ten nuclear and mitochondrial markers (7,726 bp) from 270 genera and find two distinct but equally plausible topologies among subfamilies at the base of the tree. In one set of analyses, the nuclear markers suggest two contrasting topologies, one of which is supported by the mitochondrial dataset. However, another set of analyses suggests mito-nuclear conflict as the reason for topological incongruence. Neither topology is strongly supported, and we conclude that there is insufficient phylogenetic evidence in the molecular dataset to resolve these relationships. Nevertheless, taking morphological characters into consideration, we suggest that one of the topologies is more likely.
Ranjit Kumar Sahoo
2016-12-01
Full Text Available Despite multiple attempts to infer the higher-level phylogenetic relationships of skipper butterflies (Family Hesperiidae, uncertainties in the deep clade relationships persist. The most recent phylogenetic analysis included fewer than 30% of known genera and data from three gene markers. Here we reconstruct the higher-level relationships with a rich sampling of ten nuclear and mitochondrial markers (7,726 bp from 270 genera and find two distinct but equally plausible topologies among subfamilies at the base of the tree. In one set of analyses, the nuclear markers suggest two contrasting topologies, one of which is supported by the mitochondrial dataset. However, another set of analyses suggests mito-nuclear conflict as the reason for topological incongruence. Neither topology is strongly supported, and we conclude that there is insufficient phylogenetic evidence in the molecular dataset to resolve these relationships. Nevertheless, taking morphological characters into consideration, we suggest that one of the topologies is more likely.
Phase-Field Relaxation of Topology Optimization with Local Stress Constraints
Stainko, Roman; Burger, Martin
2006-01-01
We introduce a new relaxation scheme for structural topology optimization problems with local stress constraints based on a phase-field method. In the basic formulation we have a PDE-constrained optimization problem, where the finite element and design analysis are solved simultaneously...... parameter decreases to zero. A major advantage of this kind of relaxation opposed to standard approaches is a uniform constraint qualification that is satisfied for any positive value of the penalization parameter. The relaxation scheme yields a large-scale optimization problem with a high number of linear...
Quantum Oscillation Signatures of Pressure-induced Topological Phase Transition in BiTeI
Joonbum Park; Kyung-Hwan Jin; Jo, Y. J.; Choi, E. S.; Kang, W.; Kampert, E.; J.-S. Rhyee; Seung-Hoon Jhi; Jun Sung Kim
2015-01-01
We report the pressure-induced topological quantum phase transition of BiTeI single crystals using Shubnikov-de Haas oscillations of bulk Fermi surfaces. The sizes of the inner and the outer FSs of the Rashba-split bands exhibit opposite pressure dependence up to P = 3.35 GPa, indicating pressure-tunable Rashba effect. Above a critical pressure P ~ 2 GPa, the Shubnikov-de Haas frequency for the inner Fermi surface increases unusually with pressure, and the Shubnikov-de Haas oscillations for t...
Topological phases of two-component bosons in species-dependent artificial gauge potentials
Wu, Ying-Hai; Shi, Tao
2016-08-01
We study bosonic atoms with two internal states in artificial gauge potentials whose strengths are different for the two components. A series of topological phases for such systems is proposed using the composite fermion theory and the parton construction. It is found in exact diagonalization that some of the proposed states may be realized for simple contact interaction between bosons. The ground states and low-energy excitations of these states are modeled using trial wave functions. The effective field theories for these states are also constructed and reveal some interesting properties.
Geometric Phase for Neutral Particle in the Presence of a Topological Defect
Bakke, K; Furtado, C
2008-01-01
In this paper we study the quantum dynamics of a neutral particle in the presence of a topological defect. We investigate the appearance of a geometric phase in the relativistic quantum dynamics of neutral particle which possesses permanent magnetic and electric dipole moments in the presence of an electromagnetic fields in this curved background. The nonrelativistic quantum dynamics are investigated using the Foldy-Wouthuysen expansion. The gravitational Aharonov-Casher and He-Mckellar-Wilkens effects are investigated for a series of electric and magnetic fields configurations.
Jiguang Du
2016-04-01
Full Text Available The interaction natures between Pu and different ligands in several plutonyl (VI complexes are investigated by performing topological analyses of electron density. The geometrical structures in both gaseous and aqueous phases are obtained with B3LYP functional, and are generally in agreement with available theoretical and experimental results when combined with all-electron segmented all-electron relativistic contracted (SARC basis set. The Pu– O y l bond orders show significant linear dependence on bond length and the charge of oxygen atoms in plutonyl moiety. The closed-shell interactions were identified for Pu-Ligand bonds in most complexes with quantum theory of atoms in molecules (QTAIM analyses. Meanwhile, we found that some Pu–Ligand bonds, like Pu–OH−, show weak covalent. The interactive nature of Pu–ligand bonds were revealed based on the interaction quantum atom (IQA energy decomposition approach, and our results indicate that all Pu–Ligand interactions is dominated by the electrostatic attraction interaction as expected. Meanwhile it is also important to note that the quantum mechanical exchange-correlation contributions can not be ignored. By means of the non-covalent interaction (NCI approach it has been found that some weak and repulsion interactions existed in plutonyl(VI complexes, which can not be distinguished by QTAIM, can be successfully identified.
Asorey, Manuel
2016-01-01
An old branch of mathematics, Topology, has opened the road to the discovery of new phases of matter. A hidden topology in the energy spectrum is the key for novel conducting/insulating properties of topological matter.
Miyamoto, K., E-mail: k-miyamoto@faculty.chiba-u.jp [Graduate School of Advanced Integration Science, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522 (Japan); Suizu, K.; Akiba, T. [Department of Electrical, Electronics and Computer Engineering, Chiba Institute of Technology, 2-17-1 Tsudanuma, Narashino, Chiba 275-0016 (Japan); Omatsu, T. [Graduate School of Advanced Integration Science, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522 (Japan); CREST Japan Science and Technology Agency, Sanbancho, Chiyoda-ku, Tokyo 102-0075 (Japan)
2014-06-30
A terahertz (THz) spiral phase plate with high transmission (>90% after Fresnel correction) and low dispersion has been developed based on the Tsurupica olefin polymer. Direct observations of the topological charge (both magnitude and sign) of a THz vortex beam are performed by using a THz camera with tilted lens focusing and radial defect introduction. The vortex outputs with a topological charge of ±1 (or ±2) are obtained at a frequency of 2 (or 4) THz.
Rodriguez, Pedro; Candela, J. I.; Luna, A.;
2009-01-01
This paper presents a new solution for filtering current harmonics in three-phase four-wire networks. The original four-branch star (FBS) filter topology presented in this paper is characterized by a particular layout of single-phase inductances and capacitors, without using any transformer......, a specific implementation of a three-phase four-wire hybrid power filter is presented as an illustrative application of the filtering topology. An extensive evaluation using simulation and experimental results from a DSP-based laboratory prototype is conducted in order to verify and validate the good...
Sheykhi, A.; Naeimipour, F.; Zebarjad, S. M.
2015-06-01
Considering the Lagrangian of the logarithmic nonlinear electrodynamics in the presence of a scalar dilaton field, we obtain a new class of topological black hole solutions of Einstein-dilaton gravity with two Liouville-type dilaton potentials. Black hole horizons and cosmological horizons, in these spacetimes, can be a two-dimensional positive, zero, or negative constant curvature surface. We find that the behavior of the electric field crucially depends on the dilaton coupling constant α . For small α , the electric field diverges near the origin, although its divergency is weaker than the linear Maxwell field. However, with increasing α , the behavior of the electric field, near the origin, approaches to that of the Maxwell field. We also study casual structure, asymptotic behavior, and physical properties of the solutions. We find that, depending on the model parameters, the topological dilaton black holes may have one or two horizons, and even in some cases we encounter a naked singularity without horizon. We compute the conserved and thermodynamic quantities of the spacetime and investigate that these quantities satisfy the first law of thermodynamics. We also probe thermal stability in the canonical and grand canonical ensembles and disclose the effects of the dilaton field as well as nonlinear parameter on the thermal stability of the solutions. Finally, we investigate thermodynamical geometry of the obtained solutions by introducing a new metric and studying the phase transition points due to the divergency of the Ricci scalar. We find that the dilaton field affects the phase transition points of the system.
Beyond Darcy's law: The role of phase topology and ganglion dynamics for two-fluid flow
Armstrong, Ryan T.; McClure, James E.; Berrill, Mark A.; Rücker, Maja; Schlüter, Steffen; Berg, Steffen
2016-10-01
In multiphase flow in porous media the consistent pore to Darcy scale description of two-fluid flow processes has been a long-standing challenge. Immiscible displacement processes occur at the scale of individual pores. However, the larger scale behavior is described by phenomenological relationships such as relative permeability, which typically uses only fluid saturation as a state variable. As a consequence pore scale properties such as contact angle cannot be directly related to Darcy scale flow parameters. Advanced imaging and computational technologies are closing the gap between the pore and Darcy scale, supporting the development of new theory. We utilize fast x-ray microtomography to observe pore-scale two-fluid configurations during immiscible flow and initialize lattice Boltzmann simulations that demonstrate that the mobilization of disconnected nonwetting phase clusters can account for a significant fraction of the total flux. We show that fluid topology can undergo substantial changes during flow at constant saturation, which is one of the underlying causes of hysteretic behavior. Traditional assumptions about fluid configurations are therefore an oversimplification. Our results suggest that the role of fluid connectivity cannot be ignored for multiphase flow. On the Darcy scale, fluid topology and phase connectivity are accounted for by interfacial area and Euler characteristic as parameters that are missing from our current models.
Beyond Darcy's law: The role of phase topology and ganglion dynamics for two-fluid flow.
Armstrong, Ryan T; McClure, James E; Berrill, Mark A; Rücker, Maja; Schlüter, Steffen; Berg, Steffen
2016-10-01
In multiphase flow in porous media the consistent pore to Darcy scale description of two-fluid flow processes has been a long-standing challenge. Immiscible displacement processes occur at the scale of individual pores. However, the larger scale behavior is described by phenomenological relationships such as relative permeability, which typically uses only fluid saturation as a state variable. As a consequence pore scale properties such as contact angle cannot be directly related to Darcy scale flow parameters. Advanced imaging and computational technologies are closing the gap between the pore and Darcy scale, supporting the development of new theory. We utilize fast x-ray microtomography to observe pore-scale two-fluid configurations during immiscible flow and initialize lattice Boltzmann simulations that demonstrate that the mobilization of disconnected nonwetting phase clusters can account for a significant fraction of the total flux. We show that fluid topology can undergo substantial changes during flow at constant saturation, which is one of the underlying causes of hysteretic behavior. Traditional assumptions about fluid configurations are therefore an oversimplification. Our results suggest that the role of fluid connectivity cannot be ignored for multiphase flow. On the Darcy scale, fluid topology and phase connectivity are accounted for by interfacial area and Euler characteristic as parameters that are missing from our current models.
Phase Fluctuations and the Absence of Topological Defects in Photo-excited Charge Ordered Nickelate
Lee, W.S.; Chuang, Y.D.; Moore, R.G.; Zhu, Y.; Patthey, L.; Trigo, M.; Lu, D.H.; Kirchmann, P.S.; Krupin, O.; Yi, M.; Langner, M.; Huse, N.; Robinson, J.S.; Chen, Y.; Zhou, S.Y.; Coslovich, G.; Huber, B.; Reis, D.A.; Kaindl, R.A.; Schoenlein, R.W.; Doering, D.
2012-05-15
The dynamics of an order parameter's amplitude and phase determines the collective behaviour of novel states emerging in complex materials. Time- and momentum-resolved pump-probe spectroscopy, by virtue of measuring material properties at atomic and electronic time scales out of equilibrium, can decouple entangled degrees of freedom by visualizing their corresponding dynamics in the time domain. Here we combine time-resolved femotosecond optical and resonant X-ray diffraction measurements on charge ordered La{sub 1.75}Sr{sub 0.25}NiO{sub 4} to reveal unforeseen photoinduced phase fluctuations of the charge order parameter. Such fluctuations preserve long-range order without creating topological defects, distinct from thermal phase fluctuations near the critical temperature in equilibrium. Importantly, relaxation of the phase fluctuations is found to be an order of magnitude slower than that of the order parameter's amplitude fluctuations, and thus limits charge order recovery. This new aspect of phase fluctuations provides a more holistic view of the phase's importance in ordering phenomena of quantum matter.
Quantum phase transitions between a class of symmetry protected topological states
Tsui, Lokman; Jiang, Hong-Chen; Lu, Yuan-Ming; Lee, Dung-Hai
2015-07-01
The subject of this paper is the phase transition between symmetry protected topological states (SPTs). We consider spatial dimension d and symmetry group G so that the cohomology group, Hd+1(G,U(1)), contains at least one Z2n or Z factor. We show that the phase transition between the trivial SPT and the root states that generate the Z2n or Z groups can be induced on the boundary of a (d+1)-dimensional View the MathML source-symmetric SPT by a View the MathML source symmetry breaking field. Moreover we show these boundary phase transitions can be “transplanted” to d dimensions and realized in lattice models as a function of a tuning parameter. The price one pays is for the critical value of the tuning parameter there is an extra non-local (duality-like) symmetry. In the case where the phase transition is continuous, our theory predicts the presence of unusual (sometimes fractionalized) excitations corresponding to delocalized boundary excitations of the non-trivial SPT on one side of the transition. This theory also predicts other phase transition scenarios including first order transition and transition via an intermediate symmetry breaking phase.
Phase fluctuations and the absence of topological defects in photo-excited charge ordered nickelate
Lee, W.S.; Chuang, Y.D.; Moore, R.G.; Zhu, Y.; Patthey, L.; Trigo, M.; Lu, D.H.; Kirchmann, P.S.; Krupin, O.; Yi, M.; Langner, M.; Huse, N.; Robinson, J.S.; Chen, Y.; Zhou, S.Y.; Coslovich, G.; Huber, B.; Reis, D.A.; Kaindl, R.A.; Schoenlein, R.W.; Doering, D.; Denes, P.; Schlotter, W.F.; Turner, J.J.; Johnson, S.L.; F& #246; rst, M.; Sasagawa, T.; Kung, Y.F.; Sorini, A.P.; Kemper, A.F.; Moritz, B.; Devereaux, T.P.; Lee, D.-H.; Shen, Z.X.; Hussain, Z.
2012-01-01
The dynamics of an order parameter's amplitude and phase determines the collective behaviour of novel states emerging in complex materials. Time- and momentum-resolved pump-probe spectroscopy, by virtue of measuring material properties at atomic and electronic time scales out of equilibrium, can decouple entangled degrees of freedom by visualizing their corresponding dynamics in the time domain. Here we combine time-resolved femotosecond optical and resonant X-ray diffraction measurements on charge ordered La1.75Sr0.25NiO4 to reveal unforeseen photoinduced phase fluctuations of the charge order parameter. Such fluctuations preserve long-range order without creating topological defects, distinct from thermal phase fluctuations near the critical temperature in equilibrium. Importantly, relaxation of the phase fluctuations is found to be an order of magnitude slower than that of the order parameter's amplitude fluctuations, and thus limits charge order recovery. This new aspect of phase fluctuations provides a more holistic view of the phase's importance in ordering phenomena of quantum matter.
Competing orders and topology in the global phase diagram of pyrochlore iridates
Goswami, Pallab; Roy, Bitan; Das Sarma, Sankar
2017-02-01
Strong electronic interactions and spin-orbit coupling can be conducive for realizing novel broken symmetry phases supporting quasiparticles with nontrivial band topology. 227 pyrochlore iridates provide a suitable material platform for studying such emergent phenomena where both topology and competing orders play important roles. In contrast to the most members of this material class, which are thought to display "all-in-all-out" (AIAO) type magnetically ordered low-temperature insulating ground states, Pr2Ir2O7 remains metallic while exhibiting "spin-ice" (SI) correlations at low temperatures. Additionally, this is the only 227 iridate compound, which exhibits a large anomalous Hall effect (AHE) along the [1,1,1] direction below 1.5 K, without possessing any measurable magnetic moment. By focusing on the normal state of 227 iridates, described by a parabolic semimetal with quadratic band touching, we use renormalization group analysis, mean-field theory, and phenomenological Landau theory as three complementary methods to construct a global phase diagram in the presence of generic local interactions among itinerant electrons of Ir ions. While the global phase diagram supports several competing multipolar orders, motivated by the phenomenology of 227 iridates we particularly emphasize the competition between AIAO and SI orders and how it can cause a mixed phase with "three-in-one-out" (3I1O) spin configurations. In terms of topological properties of Weyl quasiparticles of the 3I1O state, we provide an explanation for the magnitude and the direction of the observed AHE in Pr2Ir2O7 . We propose a strain-induced enhancement of the onset temperature for AHE in thin films of Pr2Ir2O7 and additional experiments for studying competing orders in the vicinity of the metal-insulator transition. In addition to providing a theory for competing orders and magnetic properties of Pr2Ir2O7 , the theoretical framework developed in this work should also be useful for a better
Sorokin, A. V.; Aparicio Alcalde, M.; Bastidas, V. M.; Engelhardt, G.; Angelakis, D. G.; Brandes, T.
2016-09-01
In this work we study a one-dimensional lattice of Lipkin-Meshkov-Glick models with alternating couplings between nearest-neighbors sites, which resembles the Su-Schrieffer-Heeger model. Typical properties of the underlying models are present in our semiclassical-topological hybrid system, allowing us to investigate an interplay between semiclassical bifurcations at mean-field level and topological phases. Our results show that bifurcations of the energy landscape lead to diverse ordered quantum phases. Furthermore, the study of the quantum fluctuations around the mean-field solution reveals the existence of nontrivial topological phases. These are characterized by the emergence of localized states at the edges of a chain with free open-boundary conditions.
Dyon condensation: an effective way to construct topological phases with symmetry
Ye, Peng; Wen, Xiao-Gang
2014-03-01
In this work, we construct three-dimensional exotic phases of bosons with time-reversal symmetry and boson number conservation U(1) symmetry by means of fermionic projective construction. We first construct an algebraic bosonic insulator which is a symmetric bosonic state with an emergent U(1) gapless gauge field. We then obtain many gapped bosonic states that do not break the time-reversal symmetry and boson number conservation via proper dyon condensations. We identify the constructed states by calculating the allowed electric and magnetic charges of their excitations, as well as the statistics and the symmetric transformation properties of those excitations. This allows us to show that our constructed states can be trivial SPT states (i.e. trivial Mott insulators of bosons with symmetry), non-trivial SPT states (i.e. bosonic topological insulators) and SET states (i.e. fractional bosonic topological insulators). In non-trivial SPT states, the elementary monopole (carrying zero electric charge but unit magnetic charge) and elementary dyon (carrying both unit electric charge and unit magnetic charge) are fermionic and bosonic, respectively. In SET states, intrinsic excitations may carry fractional charge.
Oh, Yong-Geun
2012-01-01
The main purpose of this note is to rectify the incomplete proof given in arXiv:1111.5992 of the following result, when $\\dim M = 2$. High dimensional cases will be treated elsewhere: For any \\emph{contractible topological Hamiltonian loop} $\\phi_F$, $$ f_{\\underline{\\mathbb F}} \\equiv 0, \\quad \\mathbb F(t,x,y) := F(t,x) $$ where $f_{\\underline{\\mathbb F}} := \\lim_{i \\to \\infty} f_{\\underline{\\mathbb F_i}}$ for an approximating sequence $F_i$ of $F$. Here $f_{\\underline{\\mathbb F_i}}$ is the basic phase function of the Lagrangian submanifold $\\phi_{\\mathbb F_i}^1(o_\\Delta) = \\Graph \\phi_{F_i}^1$ which is the graph selector previously constructed by Lagrangian Floer theory. A complete revision of the paper "Homotopy invariance of spectral invariants of topological Hamiltonian flows and its Lagrangian analog" in dimension 2, which combines Part I of arXiv:1111.5992(v5) and this note, is available in the author's homepage (http://www.math.wisc.edu/~oh/preprints.html).
Lateral phase drift of the topological charge density in stochastic optical fields
Roux, FS
2012-03-01
Full Text Available The statistical distributions of optical vortices or topological charge in stochastic optical fields can be inhomogeneous in both transverse directions. Such two-dimensional inhomogeneous vortex or topological charge distributions evolve in a...
Multi-Dimensional Phase Space Methods for Mass Measurements and Decay Topology Determination
Altunkaynak, Baris; Klimek, Matthew D
2016-01-01
Collider events with multi-stage cascade decays fill out the kinematically allowed region in phase space with a density that is enhanced at the boundary. The boundary encodes all available information about the spectrum and is well populated even with moderate signal statistics due to this enhancement. In previous work, the improvement in the precision of mass measurements for cascade decays with three visible and one invisible particles was demonstrated when the full boundary information is used instead of endpoints of one-dimensional projections. We extend these results to cascade decays with four visible and one invisible particles. We also comment on how the topology of the cascade decay can be determined from the differential distribution of events in these scenarios.
Bulk-boundary correspondence in (3+1)-dimensional topological phases
Chen, Xiao; Tiwari, Apoorv; Ryu, Shinsei
2016-07-01
We discuss (2+1)-dimensional gapless surface theories of bulk (3+1)-dimensional topological phases, such as the BF theory at level K , and its generalization. In particular, we put these theories on a flat (2+1)-dimensional torus T3 parameterized by its modular parameters, and compute the partition functions obeying various twisted boundary conditions. We show the partition functions are transformed into each other under S L (3 ,Z ) modular transformations, and furthermore establish the bulk-boundary correspondence in (3+1) dimensions by matching the modular S and T matrices computed from the boundary field theories with those computed in the bulk. We also propose the three-loop braiding statistics can be studied by constructing the modular S and T matrices from an appropriate boundary field theory.
Shape and Topology Optimization in Stokes Flow with a Phase Field Approach
Garcke, Harald, E-mail: harald.garcke@mathematik.uni-regensburg.de; Hecht, Claudia, E-mail: claudia.hecht@mathematik.uni-regensburg.de [Universität Regensburg, Fakultät für Mathematik (Germany)
2016-02-15
In this paper we introduce a new formulation for shape optimization problems in fluids in a diffuse interface setting that can in particular handle topological changes. By adding the Ginzburg–Landau energy as a regularization to the objective functional and relaxing the non-permeability outside the fluid region by introducing a porous medium approach we hence obtain a phase field problem where the existence of a minimizer can be guaranteed. This problem is additionally related to a sharp interface problem, where the permeability of the non-fluid region is zero. In both the sharp and the diffuse interface setting we can derive necessary optimality conditions using only the natural regularity of the minimizers. We also pass to the limit in the first order conditions.
Ochiai, Tetsuyuki
2016-01-01
We show the presence of Floquet-Weyl and Floquet-topological-insulator phases in a stacked two-dimensional ring-network lattice. The Weyl points in the three-dimensional Brillouin zone and Fermi-arc surface states are clearly demonstrated in the quasienergy spectrum of the system in the Weyl phase. In addition, chiral surface states coexist in this phase. The Floquet-topological-insulator phase is characterized by the winding number of two in the reflection matrices of the semi-infinite system and resulting two gapless surface states in the quasienergy g ap of the bulk. The phase diagram of the system is derived in the two-parameter space of hopping S-matrices among the rings. We also discuss a possible optical realization of the system together with the introduction of synthetic gauge fields.
Ochiai, Tetsuyuki
2016-10-01
We show the presence of Floquet-Weyl and Floquet-topological-insulator phases in a stacked two-dimensional ring-network lattice. The Weyl points in the three-dimensional Brillouin zone and Fermi-arc surface states are clearly demonstrated in the quasienergy spectrum of the system in the Floquet-Weyl phase. In addition, chiral surface states coexist in this phase. The Floquet-topological-insulator phase is characterized by the winding number of two in the reflection matrices of the semi-infinite system and resulting two gapless surface states in the quasienergy gap of the bulk. The phase diagram of the system is derived in the two-parameter space of hopping S-matrices among the rings. We also discuss a possible optical realization of the system together with the introduction of synthetic gauge fields.
Kim, Ki-Seok
2016-01-01
We develop a gravity reformulation for a topological phase transition of the Kitaev superconductor model in one dimension. Applying the Wilson's renormalization group procedure repeatedly, we find an effective theory with a renormalized coupling function, where the repetition index of the renormalization group transformation is identified with an extra dimension. Solving the renormalization group equation, we obtain an effective interaction vertex as a function of the extra dimension. The topological quantum phase transition is encoded into the gravity description as follows: First, the inter-site correlation (hopping and pairing) strength of spinless fermions given by a ferromagnetic coupling constant in the transverse-field Ising model is renormalized to vanish in a topologically trivial p-wave superconducting state, adiabatically connected to a trivial insulating behavior. Second, the inter-site correlation strength does not evolve at a quantum critical point, giving rise to a conformal field theory that d...
Wang, Yunhua; Liu, Yulan; Wang, Biao
2017-01-01
Periodically driven nontrivial quantum states open another door to engineer topological phases in solid systems by light. Here we show, based on the Floquet-Bloch theory, that the on-resonant linearly and circularly polarized infrared light brings in the exotic Floquet quantum spin Hall state and half-metal in two-dimensional Metal-organic frameworks (2D MOFs) because of the unbroken and broken time-reversal symmetry, respectively. We also observe that the off-resonant light triggers topological quantum phase transitions and induces semimetals with pseudospin-1 Dirac-Weyl fermions via the photon-dressed topological band structures of 2D MOFs. This work paves a way to design light-controlled spintronics and optoelectronics based on 2D MOFs. PMID:28134315
Wang, Yunhua; Liu, Yulan; Wang, Biao
2017-01-01
Periodically driven nontrivial quantum states open another door to engineer topological phases in solid systems by light. Here we show, based on the Floquet-Bloch theory, that the on-resonant linearly and circularly polarized infrared light brings in the exotic Floquet quantum spin Hall state and half-metal in two-dimensional Metal-organic frameworks (2D MOFs) because of the unbroken and broken time-reversal symmetry, respectively. We also observe that the off-resonant light triggers topological quantum phase transitions and induces semimetals with pseudospin-1 Dirac-Weyl fermions via the photon-dressed topological band structures of 2D MOFs. This work paves a way to design light-controlled spintronics and optoelectronics based on 2D MOFs.
Exploring Landmark Placement Strategies for Topology-Based Localization in Wireless Sensor Networks
Alexandre Brandwajn
2008-04-01
Full Text Available In topology-based localization, each node in a network computes its hop-count distance to a finite number of reference nodes, or Ã¢Â€ÂœlandmarksÃ¢Â€Â. This paper studies the impact of landmark placement on the accuracy of the resulting coordinate systems. The coordinates of each node are given by the hop-count distance to the landmarks. We show analytically that placing landmarks on the boundary of the topology yields more accurate coordinate systems than when landmarks are placed in the interior. Moreover, under some conditions, we show that uniform landmark deployment on the boundary is optimal. This work is also the first empirical study to consider not only uniform, synthetic topologies, but also nonuniform topologies resembling more concrete deployments. Our simulation results show that, in general, if enough landmarks are used, random landmark placement yields comparative performance to placing landmarks on the boundary randomly or equally spaced. This is an important result since boundary placement, especially at equal distances, may turn out to be infeasible and/or prohibitively expensive (in terms of communication, processing overhead, and power consumption in networks of nodes with limited capabilities.
Phase transitions in charged topological black holes dressed with a scalar hair
Martínez, Cristián; Montecinos, Alejandra
2010-12-01
Phase transitions in charged topological black holes dressed with a scalar field are studied. These black holes are solutions of the Einstein-Maxwell theory with a negative cosmological constant and a conformally coupled real self-interacting scalar field. Comparing, in the grand canonical ensemble, the free energies of the hairy and undressed black holes two different phase transitions are found. The first of them is one of second-order type and it occurs at a temperature defined by the value of the cosmological constant. Below this temperature an undressed black hole spontaneously acquires a scalar hair. The other phase transition is one of first-order type. The corresponding critical temperature, which is bounded from above by the one of the previous case, strongly depends on the coupling constant of the quartic self-interaction potential, and this transition only appears when the coupling constant is less than a certain value. In this case, below the critical temperature the undressed black hole is thermodynamically favored. However, when the temperature exceeds the critical value a hairy black hole is likely to be occur.
Phase transitions in charged topological black holes dressed with a scalar hair
Martinez, Cristian
2010-01-01
Phase transitions in charged topological black holes dressed with a scalar field are studied. These black holes are solutions of the Einstein-Maxwell theory with a negative cosmological constant and a conformally coupled real self-interacting scalar field. Comparing, in the grand canonical ensemble, the free energies of the hairy and undressed black holes two different phase transitions are found. The first of them is one of second-order type and it occurs at a temperature defined by the value of the cosmological constant. Below this temperature an undressed black hole spontaneously acquires a scalar hair. The other phase transition is one of first-order type. The corresponding critical temperature, which is bounded from above by the one of the previous case, strongly depends on the coupling constant of the quartic self-interaction potential, and this transition only appears when the coupling constant is less than a certain value. In this case, below the critical temperature the undressed black is thermodynam...
A Hybrid Computational Model to Explore the Topological Characteristics of Epithelial Tissues.
González-Valverde, Ismael; García Aznar, José Manuel
2017-03-01
Epithelial tissues show a particular topology where cells resemble a polygon-like shape, but some biological processes can alter this tissue topology. During cell proliferation, mitotic cell dilation deforms the tissue and modifies the tissue topology. Additionally, cells are reorganized in the epithelial layer and these rearrangements also alter the polygon distribution. We present here a computer-based hybrid framework focused on the simulation of epithelial layer dynamics that combines discrete and continuum numerical models. In this framework, we consider topological and mechanical aspects of the epithelial tissue. Individual cells in the tissue are simulated by an off-lattice agent-based model, which keeps the information of each cell. In addition, we model the cell-cell interaction forces and the cell cycle. Otherwise, we simulate the passive mechanical behaviour of the cell monolayer using a material that approximates the mechanical properties of the cell. This continuum approach is solved by the finite element method, which uses a dynamic mesh generated by the triangulation of cell polygons. Forces generated by cell-cell interaction in the agent-based model are also applied on the finite element mesh. Cell movement in the agent-based model is driven by the displacements obtained from the deformed finite element mesh of the continuum mechanical approach. We successfully compare the results of our simulations with some experiments about the topology of proliferating epithelial tissues in Drosophila. Our framework is able to model the emergent behaviour of the cell monolayer that is due to local cell-cell interactions, which have a direct influence on the dynamics of the epithelial tissue.
Topological phase transitions and chiral inelastic transport induced by the squeezing of light
Peano, Vittorio; Houde, Martin; Brendel, Christian; Marquardt, Florian; Clerk, Aashish A.
2016-01-01
There is enormous interest in engineering topological photonic systems. Despite intense activity, most works on topological photonic states (and more generally bosonic states) amount in the end to replicating a well-known fermionic single-particle Hamiltonian. Here we show how the squeezing of light can lead to the formation of qualitatively new kinds of topological states. Such states are characterized by non-trivial Chern numbers, and exhibit protected edge modes, which give rise to chiral elastic and inelastic photon transport. These topological bosonic states are not equivalent to their fermionic (topological superconductor) counterparts and, in addition, cannot be mapped by a local transformation onto topological states found in particle-conserving models. They thus represent a new type of topological system. We study this physics in detail in the case of a kagome lattice model, and discuss possible realizations using nonlinear photonic crystals or superconducting circuits. PMID:26931620
Strongly Correlated Topological Insulators
2016-02-03
Research Triangle Park , NC 27709-2211 Condensed Matter, Topological Phases of Matter REPORT DOCUMENTATION PAGE 11. SPONSOR/MONITOR’S REPORT NUMBER(S...Strongly Correlated Topological Insulators In the past year, the grant was used for work in the field of topological phases, with emphasis on finding...surface of topological insulators. In the past 3 years, we have started a new direction, that of fractional topological insulators. These are materials
Lapa, Matthew F.; Hughes, Taylor L.
2017-09-01
We study perturbative and global anomalies at the boundaries of bosonic analogs of integer quantum Hall (BIQH) and topological insulator (BTI) phases using a description of the boundaries of these phases in terms of a nonlinear sigma model (NLSM) with Wess-Zumino term. One of the main results of the paper is that these anomalies are robust against arbitrary smooth deformations of the target space of the NLSM which describes the phase, provided that the deformations also respect the symmetry of the phase. In the first part of the paper, we discuss the perturbative U(1 ) anomaly at the boundary of BIQH states in all odd (space-time) dimensions. In the second part, we study global anomalies at the boundary of BTI states in even dimensions. In a previous work [Lapa et al., Phys. Rev. B 95, 035149 (2017), 10.1103/PhysRevB.95.035149] we argued that the boundary of the BTI phase exhibits a global anomaly which is an analog of the parity anomaly of Dirac fermions in three dimensions. Here, we elevate this argument to a proof for the boundary of the two-dimensional BTI state by explicitly computing the partition function of the gauged NLSM describing the boundary. We then use the powerful equivariant localization technique to show that this global anomaly is robust against all smooth deformations of the target space of the NLSM which preserve the U(1 ) ⋊Z2 symmetry of the BTI state. We also comment on the difficulties of generalizing this latter proof to higher dimensions. Finally, we discuss the expected low-energy behavior of the boundary theories studied in this paper when the coupling constants are allowed to flow under the renormalization group.
Haghshenas, R; Langari, A; Rezakhani, A T
2014-11-12
We study different phases of the one-dimensional bond-alternating spin-1/2 Heisenberg model by using the symmetry fractionalization mechanism. We employ the infinite matrix-product state representation of the ground state (through the infinite-size density matrix renormalization group algorithm) to obtain inequivalent projective representations and commutation relations of the (unbroken) symmetry groups of the model, which are used to identify the different phases. We find that the model exhibits trivial as well as symmetry-protected topological phases. The symmetry-protected topological phases are Haldane phases on even/odd bonds, which are protected by the time-reversal (acting on the spin as σ → -σ), parity (permutation of the chain about a specific bond), and dihedral (π-rotations about a pair of orthogonal axes) symmetries. Additionally, we investigate the phases of the most general two-body bond-alternating spin-1/2 model, which respects the time-reversal, parity, and dihedral symmetries, and obtain its corresponding twelve different types of the symmetry-protected topological phases.
Hybrid QTAIM and electrostatic potential-based quantum topology phase diagrams for water clusters.
Kumar, Anmol; Gadre, Shridhar R; Chenxia, Xiao; Tianlv, Xu; Kirk, Steven Robert; Jenkins, Samantha
2015-06-21
The topological diversity of sets of isomers of water clusters (W = H2O)n, 7 ≤ n ≤ 10, is analyzed employing the scalar fields of total electronic charge density ρ(r) and the molecular electrostatic potential (MESP). The features uncovered by the MESP are shown to be complementary to those revealed by the theory of atoms in molecules (QTAIM) analysis. The MESP is known to exhibit the electron localizations such as lone pairs that are central to water cluster behavior. Therefore, a 'hybrid' QTAIM and MESP quantum topology phase diagram (QTPD) for Wn, 7 ≤ n ≤ 10, is introduced in addition to the QTPD. The 'spanning' QTPD with upper and lower bounds is constructed from the solutions of the Poincaré-Hopf relation involving the non-degenerate critical points. The changing subtle balance between the planar and three dimensional character of the growing water clusters Wn, 4 ≤ n ≤ 10, is revealed. Characterization of the structure of the QTPDs, possible with new tools, demonstrated the migration of the position of the global minimum on the spanning QTPD from the lower bound to upper bound as the Wn, 4 ≤ n ≤ 10, cluster grows in size. Differences in the structure of the QTPD are found between the clusters containing even versus odd monomers for Wn, n = 7-10. The energetic stability of the clusters which possess even number of monomers viz. n = 8, 10 is higher than that of the n = 7, 9 clusters due to relatively higher numbers of hydrogen-bond BCPs in the n = 8, 10 clusters, in agreement with energetic results reported in the literature. A 'hybrid' QTPD is created from a new chemical relation bHB + l ≥ 2n for Wn that relates the number of hydrogen-bond bond critical points (bHB) with the number of oxygen lone pairs exclusively specified by the negative valued MESP (3,+3) critical points (l). The topologies of the subset bHB + l = 2n for Wn, point the way to the discovery of unknown 'missing' lower energy isomers. A discussion of the relative merits and
Spaans, Marco
2013-01-01
General Relativity is extended into the quantum domain. A thought experiment is explored to derive a specific topological build-up for Planckian space-time. The presented arguments are inspired by Feynman's path integral for superposition and Wheeler's quantum foam of Planck mass mini black holes/wormholes. Paths are fundamental and prime 3-manifolds like T^3, S^1xS^2 and S^3 are used to construct quantum space-time. A physical principle is formulated that causes observed paths to multiply: It takes one to know one. So topological fluctuations on the Planck scale take the form of multiple copies of any homeomorphically distinct path through quantum space-time. The discrete time equation of motion for this topological quantum gravity is derived by counting distinct paths globally. The equation of motion is solved to derive some properties of dark energy and inflation. The dark energy density depends linearly on the number of macroscopic black holes in the universe and is time dependent in a manner consistent w...
Spaans, M.
2013-08-01
General Relativity is extended into the quantum domain. A thought experiment is explored to derive a specific topological build-up for Planckian spacetime. The presented arguments are inspired by Feynman's path integral for superposition and Wheeler's quantum foam of Planck mass mini black holes (BHs)/wormholes. Paths are fundamental and prime three-manifolds like T3, S1 × S2 and S3 are used to construct quantum spacetime. A physical principle is formulated that causes observed paths to multiply: It takes one to know one. So topological fluctuations on the Planck scale take the form of multiple copies of any homeomorphically distinct path through quantum spacetime. The discrete time equation of motion for this topological quantum gravity is derived by counting distinct paths globally. The equation of motion is solved to derive some properties of dark energy and inflation. The dark energy density depends linearly on the number of macroscopic BHs in the universe and is time-dependent in a manner consistent with current astrophysical observations, having an effective equation of state w ≈ -1.1 for redshifts smaller than unity. Inflation driven by mini BHs proceeds over n ≈ 55 e-foldings, without strong inhomogeneity. A discrete time effect visible in the cosmic microwave background is suggested.
Zhang, G; Stillinger, F H; Torquato, S
2016-12-28
Disordered hyperuniform many-particle systems have attracted considerable recent attention, since they behave like crystals in the manner in which they suppress large-scale density fluctuations, and yet also resemble statistically isotropic liquids and glasses with no Bragg peaks. One important class of such systems is the classical ground states of "stealthy potentials." The degree of order of such ground states depends on a tuning parameter χ. Previous studies have shown that these ground-state point configurations can be counterintuitively disordered, infinitely degenerate, and endowed with novel physical properties (e.g., negative thermal expansion behavior). In this paper, we focus on the disordered regime (0 two-phase media by circumscribing each point with a possibly overlapping sphere of a common radius a: the "particle" and "void" phases are taken to be the space interior and exterior to the spheres, respectively. The hyperuniformity of such two-phase media depends on the sphere sizes: While it was previously analytically proven that the resulting two-phase media maintain hyperuniformity if spheres do not overlap, here we show numerically that they lose hyperuniformity whenever the spheres overlap. We study certain transport properties of these systems, including the effective diffusion coefficient of point particles diffusing in the void phase as well as static and time-dependent characteristics associated with diffusion-controlled reactions. Besides these effective transport properties, we also investigate several related structural properties, including pore-size functions, quantizer error, an order metric, and percolation thresholds. We show that these transport, geometrical, and topological properties of our two-phase media derived from decorated stealthy ground states are distinctly different from those of equilibrium hard-sphere systems and spatially uncorrelated overlapping spheres. As the extent of short-range order increases, stealthy disordered
Ozfidan, Isil; Vladisavljevic, Milos; Korkusinski, Marek; Hawrylak, Pawel
2015-12-01
We present a theory of the electronic and optical properties of a charged artificial benzene ring (ABR). The ABR is described by the extended Hubbard model solved using exact diagonalization methods in both real and Fourier space as a function of the tunneling matrix element t , Hubbard on-site repulsion U , and interdot interaction V . In the strongly interacting case, we discuss exact analytical results for the spectrum of the hole in a half-filled ABR dressed by the spin excitations of the remaining electrons. The spectrum is interpreted in terms of the appearance of a topological phase associated with an effective gauge field piercing through the ring. We show that the maximally spin-polarized (S =5 /2 ) and maximally spin-depolarized (S =1 /2 ) states are the lowest energy, orbitally nondegenerate, states. We discuss the evolution of the phase diagram and level crossings as interactions are switched off and the ground state becomes spin nondegenerate but orbitally degenerate S =1 /2 . We present a theory of optical absorption spectra and show that the evolution of the ground and excited states, level crossings, and presence of artificial gauge can be detected optically.
Amplitude-Phase Modulation, Topological Horseshoe and Scaling Attractor of a Dynamical System
Li, Chun-Lai; Li, Wen; Zhang, Jing; Xie, Yuan-Xi; Zhao, Yi-Bo
2016-09-01
A three-dimensional autonomous chaotic system is discussed in this paper. Some basic dynamical properties of the system, including phase portrait, Poincaré map, power spectrum, Kaplan-Yorke dimension, Lyapunov exponent spectra, signal amplitude and topological horseshoe are studied theoretically and numerically. The main finding by analysis is that the signal amplitude can be modulated via controlling the coefficients of the linear term, cross-product term and squared term simultaneously or respectively, and the phase of x3 can be modulated by the product of the coefficients of the linear term and cross-product term. Furthermore, scaling chaotic attractors of this system are achieved by modified projective synchronization with an optimization-based linear coupling method, which is safer for secure communications than the existed synchronization scheme since the scaling factors can be regarded as the security encoding key. Supported by Hunan Provincial Natural Science Foundation of China under Grant No. 2016JJ4036, University Natural Science Foundation of Jiangsu Province under Grant No. 14KJB120007 and the National Natural Science Foundation of China under Grant Nos. 11504176 and 11602084
Optical image encryption topology.
Yong-Liang, Xiao; Xin, Zhou; Qiong-Hua, Wang; Sheng, Yuan; Yao-Yao, Chen
2009-10-15
Optical image encryption topology is proposed based on the principle of random-phase encoding. Various encryption topological units, involving peer-to-peer, ring, star, and tree topologies, can be realized by an optical 6f system. These topological units can be interconnected to constitute an optical image encryption network. The encryption and decryption can be performed in both digital and optical methods.
Saadatmand, S. N.; McCulloch, I. P.
2016-09-01
Using density-matrix renormalization-group calculations for infinite cylinders, we elucidate the properties of the spin-liquid phase of the spin-1/2 J1-J2 Heisenberg model on the triangular lattice. We find four distinct ground states characteristic of a nonchiral, Z2 topologically ordered state with vison and spinon excitations. We shed light on the interplay of topological ordering and global symmetries in the model by detecting fractionalization of time-reversal and space-group dihedral symmetries in the anyonic sectors, which leads to the coexistence of symmetry protected and intrinsic topological order. The anyonic sectors, and information on the particle statistics, can be characterized by degeneracy patterns and symmetries of the entanglement spectrum. We demonstrate the ground states on finite-width cylinders are short-range correlated and gapped; however, some features in the entanglement spectrum suggest that the system develops gapless spinonlike edge excitations in the large-width limit.
Franz, Marcel
2013-01-01
Topological Insulators, volume six in the Contemporary Concepts of Condensed Matter Series, describes the recent revolution in condensed matter physics that occurred in our understanding of crystalline solids. The book chronicles the work done worldwide that led to these discoveries and provides the reader with a comprehensive overview of the field. Starting in 2004, theorists began to explore the effect of topology on the physics of band insulators, a field previously considered well understood. However, the inclusion of topology brings key new elements into this old field. Whereas it was
Lacevic, N; Gee, R; Saab, A; Maxwell, R
2008-04-24
Molecular dynamics simulations have been performed in order to study the effects of nanoscale filler cross-linking topologies and loading levels on the mechanical properties of a model elastomeric nanocomposite. The model system considered here is constructed from octa-functional polyhedral oligomeric silsesquioxane (POSS) dispersed in a poly(dimethylsiloxane) (PDMS) matrix. Shear moduli, G, have been computed for pure and for filled and unfilled PDMS as a function of cross-linking density, POSS fill loading level, and polymer network topology. The results reported here show that G increases as the cross-linking (covalent bonds formed between the POSS and the PDMS network) density increases. Further, G is found to have a strong dependence on cross-linking topology. The increase in shear modulus, G, for POSS filled PDMS is significantly higher than that for unfilled PDMS cross-linked with standard molecular species, suggesting an enhanced reinforcement mechanism for POSS. In contrast, in blended systems (POSS/PDMS mixture with no cross-linking) G was not observed to significantly increase with POSS loading. Finally, we find intriguing differences in the structural arrangement of bond strains between the cross-linked and the blended systems. In the unfilled PDMS the distribution of highly strained bonds appears to be random, while in the POSS filled system, the strained bonds form a net-like distribution that spans the network. Such a distribution may form a structural network 'holding' the composite together and resulting in increases in G compared to an unfilled, cross-linked system. These results are of importance for engineering of new POSS-based multifunctional materials with tailor-made mechanical properties.
Lacevic, Naida; Gee, Richard H; Saab, Andrew; Maxwell, Robert
2008-09-28
Molecular dynamics simulations have been performed in order to study the effects of nanoscale filler cross-linking topologies and loading levels on the mechanical properties of a model elastomeric nanocomposite. The model system considered here is constructed from octafunctional polyhedral oligomeric silsesquioxane (POSS) dispersed in a poly(dimethylsiloxane) (PDMS) matrix. Shear moduli, G, have been computed for pure and for filled and unfilled PDMS as a function of cross-linking density, POSS fill loading level, and polymer network topology. The results reported here show that G increases as the cross-linking (covalent bonds formed between the POSS and the PDMS network) density increases. Further, G is found to have a strong dependence on cross-linking topology. The increase in shear modulus, G, for POSS filled PDMS is significantly higher than that for unfilled PDMS cross-linked with standard molecular species, suggesting an enhanced reinforcement mechanism for POSS. In contrast, in blended systems (POSS/PDMS mixture with no cross-linking) G was not observed to significantly increase with POSS loading. Finally, we find intriguing differences in the structural arrangement of bond strains between the cross-linked and the blended systems. In the unfilled PDMS the distribution of highly strained bonds appears to be random, while in the POSS filled system, the strained bonds form a netlike distribution that spans the network. Such a distribution may form a structural network "holding" the composite together and resulting in increases in G compared to an unfilled, cross-linked system. These results are of importance for engineering of new POSS-based multifunctional materials with tailor-made mechanical properties.
Chung, Chung-Hou; Lee, Der-Hau; Chao, Sung-Po
2014-07-01
We study the quantum phases and phase transitions of the Kane-Mele Hubbard (KMH) model on a zigzag ribbon of honeycomb lattice at a finite size via the weak-coupling renormalization group (RG) approach. In the noninteracting limit, the Kane-Mele (KM) model is known to support topological edge states where electrons show helical property with orientations of the spin and momentum being locked. The effective interedge hopping terms are generated due to finite-size effect. In the presence of an on-site Coulomb (Hubbard) interaction and the interedge hoppings, special focus is put on the stability of the topological edge states (TI phase) in the KMH model against (i) the charge and spin gaped (II) phase, (ii) the charge gaped but spin gapless (IC) phase, and (iii) the spin gaped but charge gapless (CI) phase depending on the number (even/odd) of the zigzag ribbons, doping level (electron filling factor) and the ratio of the Coulomb interaction to the interedge tunneling. We discuss different phase diagrams for even and odd numbers of zigzag ribbons. We find the TI-CI, II-IC, and II-CI quantum phase transitions are of the Kosterlitz-Thouless (KT) type. By computing various correlation functions, we further analyze the nature and leading instabilities of these phases. The relevance of our results for graphene is discussed.
A new high-efficiency single-phase transformerless PV inverter topology
Kerekes, Tamas; Teodorescu, Remus; Rodriguez, Pedro;
2011-01-01
There is a strong trend in the photovoltaic (PV) inverter technology to use transformerless topologies in order to acquire higher efficiencies combining with very low ground leakage current. In this paper a new topology, based on the H-Bridge with a new AC bypass circuit consisting in a diode rec...
Guruvidyathri, K.; Hari Kumar, K. C.; Yeh, J. W.; Murty, B. S.
2017-09-01
One of the major challenges in high entropy alloy (HEA) research is to obtain single-phase solid solutions by proper selection of components and processing techniques. Often one encounters situations where topologically close-packed (TCP) phases are present in the HEA microstructures. TCP phases are a class of intermetallic phases that are in general considered undesirable. The ability to predict these phases in HEAs using the Calphad (CALculation of PHAse Diagrams) method has been shown to accelerate the identification of promising compositions. In this review, an analysis of the reported Calphad studies and corresponding microstructural information on HEAs is done to evaluate the success of the Calphad method for TCP phases. A total of 52 alloys with 123 post-heat treatment microstructures reported so far have been compared. Challenges and issues in experiments and calculations are brought out with a possible way forward.
The influence of topological phase transition on the superfluid density of overdoped copper oxides.
Shaginyan, V R; Stephanovich, V A; Msezane, A Z; Japaridze, G S; Popov, K G
2017-08-23
We show that a quantum phase transition, generating flat bands and altering Fermi surface topology, is a primary reason for the exotic behavior of the overdoped high-temperature superconductors represented by La2-xSrxCuO4, whose superconductivity features differ from what is predicted by the classical Bardeen-Cooper-Schrieffer theory. This observation can open avenues for chemical preparation of high-Tc materials. We demonstrate that (1) at temperature T = 0, the superfluid density ns turns out to be considerably smaller than the total electron density; (2) the critical temperature Tc is controlled by ns rather than by doping, and is a linear function of the ns; (3) at T > Tc the resistivity ρ(T) varies linearly with temperature, ρ(T) ∝ αT, where α diminishes with Tc → 0, whereas in the normal (non superconducting) region induced by overdoping, Tc = 0, and ρ(T) ∝ T(2). Our results are in good agreement with recent experimental observations.
Superconductivity in the amorphous phase of topological insulator Bi x Sb100-x alloys
Barzola-Quiquia, J.; Lauinger, C.; Zoraghi, M.; Stiller, M.; Sharma, S.; Häussler, P.
2017-01-01
In this work we investigated the electrical properties of rapidly quenched amorphous Bi x Sb{}100-x alloys in the temperature range of 1.2 K to 345 K. The resistance reveals that for a broad range of different compositions, including that for the topological insulator (TI), a superconducting state in the amorphous phase is present. After crystallization and annealing at an intermediate temperature, we found that in pure Bi and Bi x Sb{}100-x alloys with composition corresponding to the TI, the superconductivity persists, but the transition shifts to a lower temperature. The highest superconducting transition temperature {T}{{C}0} was found for pure Bi and those TI’s, with a shift to low temperatures when the Sb content is increased. After annealing at a maximum temperature of T = 345 K, the samples are non-superconducting within the experimental range and the behavior changes from semiconducting-like for pure Bi, to metallic-like for pure Sb. Transition temperature {T}{{C}0} of the amorphous Bi x Sb{}100-x alloys have been calculated in the BCS-Eliashberg-McMillan framework, modified for binary alloys. The results can explain the experimental results and show that amorphous Bi x Sb{}100-x exhibits a strong to intermediate electron-phonon coupling.
Macroscopic Quantum Phenomena and Topological Phase Interference Effects in Single-Domain Magnets
L(U) Rong; ZHU Jialin
2001-01-01
The tunneling of macroscopic object is one of the most fascinating phenomena in condensed matter physics.During the last decade,the problem of quantum tunneling of magnetization in nanometer-scale magnets has attracted a great deal of theoretical and experimental interest.A review of recent theoretical research of the macroscopic quantum phenomena in nanometer-scale single-domain magnets is presented in this paper.It includes macroscopic quantum tunneling (MQT) and coherence (MQC) in single-domain magnetic particles,the topological phase interference or spin-parity effects,and tunneling of magnetization in an arbitrarily directed magnetic field.The general formulas are shown to evaluate the tunneling rate and the tunneling level splitting for single-domain AFM particles.A nontrivial generalization of Kramers degeneracy for double-well system is provided to coherently spin tunneling for spin systems with m-fold rotational symmetry.The effects induced by the external magnetic field have been studied,where the field is along the easy,medium,hard axis,or arbitrary direction.
A high-temperature ferromagnetic topological insulating phase by proximity coupling
Katmis, Ferhat; Lauter, Valeria; Nogueira, Flavio S.; Assaf, Badih A.; Jamer, Michelle E.; Wei, Peng; Satpati, Biswarup; Freeland, John W.; Eremin, Ilya; Heiman, Don; Jarillo-Herrero, Pablo; Moodera, Jagadeesh S.
2016-05-09
Topological insulators are insulating materials that display conducting surface states protected by time-reversal symmetry(1,)2, wherein electron spins are locked to their momentum. This unique property opens up new opportunities for creating next-generation electronic, spintronic and quantum computation devices(3-5). Introducing ferromagnetic order into a topological insulator system without compromising its distinctive quantum coherent features could lead to the realization of several predicted physical phenomena(6,7). In particular, achieving robust long-range magnetic order at the surface of the topological insulator at specific locations without introducing spin-scattering centres could open up new possibilities for devices. Here we use spin-polarized neutron reflectivity experiments to demonstrate topologically enhanced interface magnetism by coupling a ferromagnetic insulator (EuS) to a topological insulator (Bi2Se3) in a bilayer system. This interfacial ferromagnetism persists up to room temperature, even though the ferromagnetic insulator is known to order ferromagnetically only at low temperatures (<17 K). The magnetism induced at the interface resulting from the large spin-orbit interaction and the spin-momentum locking of the topological insulator surface greatly enhances the magnetic ordering (Curie) temperature of this bilayer system. The ferromagnetism extends similar to 2 nm into the Bi2Se3 from the interface. Owing to the short-range nature of the ferromagnetic exchange interaction, the time-reversal symmetry is broken only near the surface of a topological insulator, while leaving its bulk states unaffected. The topological magneto-electric response originating in such an engineered topological insulator(2,8) could allow efficient manipulation of the magnetization dynamics by an electric field, providing an energy-efficient topological control mechanism for future spin-based technologies.
Introduction to topological quantum matter & quantum computation
Stanescu, Tudor D
2017-01-01
What is -topological- about topological quantum states? How many types of topological quantum phases are there? What is a zero-energy Majorana mode, how can it be realized in a solid state system, and how can it be used as a platform for topological quantum computation? What is quantum computation and what makes it different from classical computation? Addressing these and other related questions, Introduction to Topological Quantum Matter & Quantum Computation provides an introduction to and a synthesis of a fascinating and rapidly expanding research field emerging at the crossroads of condensed matter physics, mathematics, and computer science. Providing the big picture, this book is ideal for graduate students and researchers entering this field as it allows for the fruitful transfer of paradigms and ideas amongst different areas, and includes many specific examples to help the reader understand abstract and sometimes challenging concepts. It explores the topological quantum world beyond the well-know...
Lawler, Michael
I generalize the theory of phonon topological band structures of isostatic lattices to highly frustrated antiferromagnets. I achieve this with a discovery of a many-body supersymmetry (SUSY) in the phonon problem of balls and springs which also applies to geometrically frustrated magnets. The Witten index of the SUSY model, when restricted to the single body problem (meaningful for linearized phonons), is then shown to be the Calladine-Kane-Lubensky index of mechanical structures that forms the cornerstone of the phonon topological band structure theory. ``Spontaneous supersymmetry breaking'' is then identified as the need to gap all modes in the bulk to create the topological state. The many-body SUSY formulation shows that the topology is not restricted to a band structure problem but extends to systems of coupled bosons and fermions that are in principle also realizable in solid state systems. The analogus supersymmetry of the magnon problem turns out to be particularly useful for highly frustrated magnets with the kagome family of antiferromagnets an analog of topological isostatic lattices. Thus, a solid state realization of the theory of phonon topological band structure may be found in highly frustrated magnets. However, our results show that this topology is protected not
Ilias Chlis
2014-01-01
Full Text Available This paper reports comparative analyses of phase noise in Hartley, Colpitts, and common-source cross-coupled differential pair LC oscillator topologies in 28 nm CMOS technology. The impulse sensitivity function is used to carry out both qualitative and quantitative analyses of the phase noise exhibited by each circuit component in each circuit topology with oscillation frequency ranging from 1 to 100 GHz. The comparative analyses show the existence of four distinct frequency regions in which the three oscillator topologies rank unevenly in terms of best phase noise performance, due to the combined effects of device noise and circuit node sensitivity.
Chlis, Ilias; Pepe, Domenico; Zito, Domenico
2014-01-01
This paper reports comparative analyses of phase noise in Hartley, Colpitts, and common-source cross-coupled differential pair LC oscillator topologies in 28 nm CMOS technology. The impulse sensitivity function is used to carry out both qualitative and quantitative analyses of the phase noise exhibited by each circuit component in each circuit topology with oscillation frequency ranging from 1 to 100 GHz. The comparative analyses show the existence of four distinct frequency regions in which the three oscillator topologies rank unevenly in terms of best phase noise performance, due to the combined effects of device noise and circuit node sensitivity.
Lin, S.; Zhang, G.; Li, C.; Song, Z.
2016-08-01
We study the tight-binding model for a graphene tube with perimeter N threaded by a magnetic field. We show exactly that this model has different nontrivial topological phases as the flux changes. The winding number, as an indicator of topological quantum phase transition (QPT) fixes at N/3 if N/3 equals to its integer part [N/3], otherwise it jumps between [N/3] and [N/3] + 1 periodically as the flux varies a flux quantum. For an open tube with zigzag boundary condition, exact edge states are obtained. There exist two perfect midgap edge states, in which the particle is completely located at the boundary, even for a tube with finite length. The threading flux can be employed to control the quantum states: transferring the perfect edge state from one end to the other, or generating maximal entanglement between them.
Topological Phase Transition in Layered GaS and GaSe
Zhu, Zhiyong
2012-06-29
By fully relativistic first principles calculations, we predict that appropriate strain engineering of layered GaX (X=S, Se) leads to a new class of three-dimensional topological insulators with an excitation gap of up to 135 meV. Our results provide a new perspective on the formation of three-dimensional topological insulators. Band inversion can be induced by strain only, without considering any spin-orbit coupling. The latter, however, is indispensable for the formation of local band gaps at the crossing points of the inverted bands. Our study indicates that three-dimensional topological insulators can also be realized in materials which comprise light elements only.
Hida, Kazuo
2016-12-01
A series of symmetry-protected topological (SPT) and trivial spin-gap phases in the spin-1/2 ferromagnetic-antiferromagnetic alternating Heisenberg chain with alternating next-nearest-neighbour interaction are investigated using two kinds of entanglement spectra defined by different divisions of the whole chain. In case one of the next-nearest-neighbor interactions vanishes, the model reduces to the Δ-chain in which a series of spin-gap phases are found, as shown in J. Phys. Soc. Jpn. 77, 044707 (2008). From the degeneracy of the entanglement spectra, these phases are identified as the SPT and trivial phases. It is found that the ground-state phase boundaries are insensitive to the strength of the alternation in the next-nearest-neighbor interaction. These results are consistent with the analysis based on the nonlinear σ model and exact solution on the ferromagnetic-nonmagnetic phase boundary.
Hida, Kazuo
2016-02-01
The topological classification of a series of frustration-induced spin-gap phases in the spin-1/2 ferromagnetic-antiferromagnetic alternating Heisenberg chain with next-nearest-neighbour interaction reported in J. Phys. Soc. Jpn. 82, 064703 (2013) is confirmed using two kinds of entanglement spectra defined by different divisions of the whole chain. For the numerical calculation, the iDMRG method is used. The results are consistent with the valence bond solid picture proposed in the previous paper.
Qi, Yanpeng; Shi, Wujun; Naumov, Pavel G; Kumar, Nitesh; Sankar, Raman; Schnelle, Walter; Shekhar, Chandra; Chou, Fang-Cheng; Felser, Claudia; Yan, Binghai; Medvedev, Sergey A
2017-03-06
A pressure-induced topological quantum phase transition has been theoretically predicted for the semiconductor bismuth tellurohalide BiTeI with giant Rashba spin splitting. In this work, evolution of the electrical transport properties in BiTeI and BiTeBr is investigated under high pressure. The pressure-dependent resistivity in a wide temperature range passes through a minimum at around 3 GPa, indicating the predicted topological quantum phase transition in BiTeI. Superconductivity is observed in both BiTeI and BiTeBr, while resistivity at higher temperatures still exhibits semiconducting behavior. Theoretical calculations suggest that superconductivity may develop from the multivalley semiconductor phase. The superconducting transition temperature, Tc , increases with applied pressure and reaches a maximum value of 5.2 K at 23.5 GPa for BiTeI (4.8 K at 31.7 GPa for BiTeBr), followed by a slow decrease. The results demonstrate that BiTeX (X = I, Br) compounds with nontrivial topology of electronic states display new ground states upon compression.
Spanning QTAIM topology phase diagrams of water isomers W4, W5 and W6.
Jenkins, Samantha; Restrepo, Albeiro; David, Jorge; Yin, Dulin; Kirk, Steven R
2011-06-28
Structural and chemical properties of the small water clusters W(4), W(5) and W(6) are investigated with the theory of atoms and molecules (QTAIM). For the W(4), W(5) and W(6) clusters, nine, fourteen and twenty-seven conformers, respectively, have been analyzed. For the W(4), W(5) and W(6) clusters one, two and three of these structures, respectively, have not been reported before. We then proceed to extend the W(4), W(5) and W(6) water cluster topology space using QTAIM; the Poincaré-Hopf topological sum rules are applied to create rules to identify the spanning set of conformer topologies, this includes finding three, ten and eight new distinct topologies that satisfy the Poincaré-Hopf relation for W(4), W(5) and W(6) respectively. The topological stability of degenerate solutions to the Poincaré-Hopf relation is compared by evaluating the proximity to rupturing of critical points of the gradient vector field of the charge density. We introduce a QTAIM topology space to replace the inconsistent use of Euclidean geometry to determine whether a cluster is 1-, 2- or 3-D. We show from the topology of the charge density that the conformers of the W(4), W(5) clusters are more energetically stable in less compact, planar forms, conversely the conformers of W(6) are more energetically stable with compact 3-D topologies. Quantifying the degree of covalent character in the hydrogen bonding for the W(4), W(5) and W(6) clusters independently verifies this finding. Differences in simple rules for the number of hydrogen bonds obeying the Bernal-Fowler ice rules between W(4), W(5) and W(6) reflect the transition from 2-D to 3-D structures being more energetically stable. In addition, we identify a new class of O-O bonding interactions that are up to 48% longer than the inter-nuclear separation and appear to be failed hydrogen bonds.
Elastic phases of Ge(x)Sb(x)Se(100-2x) ternary glasses driven by topology.
Gunasekera, Kapila; Boolchand, P; Micoulaut, M
2013-08-29
Topology offers a practical set of computational tools to accurately predict certain physical and chemical properties of materials including transformations under deformation. In network glasses with increased cross-linking three generic elastic phases are observed. We examine ternary Ge(x)Sb(x)Se(100-2x) glasses in Raman scattering, modulated DSC and volumetric measurements, and observe the rigidity transition, x = x(c)(1) = 14.9% that separates the flexible phase from the Intermediate phase, and the stress transition, x = x(c)(2) = 17.5% that separate the intermediate phase from the stressed rigid one. Raman scattering provides evidence of the structural motifs populated in these networks. Using size increasing cluster agglomeration, we have calculated the rigidity and stress transitions to occur near x(c)(1)(t) = 15.2% and x(c)(2)(t) = 17.5%, respectively. Theory predicts and experiments confirm that these two transitions will coalesce if edge-sharing Ge-tetrahedral motifs were absent in the structure, a circumstance that prevails in the Ge-deficient Ge7Sb(x)Se(93-x) ternary, underscoring the central role played by topology in network glasses. We have constructed a global elastic phase diagram of the Ge-Sb-Se ternary that provides a roadmap to network functionality. In this diagram, regions labeled A, B, and C comprise networks that are flexible, rigid but unstressed, and stressed-rigid, respectively.
Pressure-induced phase transition in Bi2Se3 at 3 GPa: electronic topological transition or not?
Bera, Achintya; Pal, Koushik; Muthu, D V S; Waghmare, U V; Sood, A K
2016-03-16
In recent years, a low pressure transition around P3 GPa exhibited by the A2B3-type 3D topological insulators is attributed to an electronic topological transition (ETT) for which there is no direct evidence either from theory or experiments. We address this phase transition and other transitions at higher pressure in bismuth selenide (Bi2Se3) using Raman spectroscopy at pressure up to 26.2 GPa. We see clear Raman signatures of an isostructural phase transition at P2.4 GPa followed by structural transitions at ∼ 10 GPa and 16 GPa. First-principles calculations reveal anomalously sharp changes in the structural parameters like the internal angle of the rhombohedral unit cell with a minimum in the c/a ratio near P3 GPa. While our calculations reveal the associated anomalies in vibrational frequencies and electronic bandgap, the calculated Z2 invariant and Dirac conical surface electronic structure remain unchanged, showing that there is no change in the electronic topology at the lowest pressure transition.
Lapa, Matthew F.; Hughes, Taylor L.
2017-08-01
We canonically quantize O (D +2 ) nonlinear sigma models (NLSMs) with a theta term on arbitrary smooth, closed, connected, oriented D -dimensional spatial manifolds M , with the goal of proving the suitability of these models for describing symmetry-protected topological (SPT) phases of bosons in D spatial dimensions. We show that in the disordered phase of the NLSM, and when the coefficient θ of the theta term is an integer multiple of 2 π , the theory on M has a unique ground state and a finite energy gap to all excitations. We also construct the ground state wave functional of the NLSM in this parameter regime, and we show that it is independent of the metric on M and given by the exponential of a Wess-Zumino term for the NLSM field, in agreement with previous results on flat space. Our results show that the NLSM in the disordered phase and at θ =2 π k , k ∈Z , has a symmetry-preserving ground state but no topological order (i.e., no topology-dependent ground state degeneracy), making it an ideal model for describing SPT phases of bosons. Thus, our work places previous results on SPT phases derived using NLSMs on solid theoretical ground. To canonically quantize the NLSM on M , we use Dirac's method for the quantization of systems with second class constraints, suitably modified to account for the curvature of space. In a series of four Appendixes, we provide the technical background needed to follow the discussion in the main sections of the paper.
Topological phase transitions in finite-size periodically driven translationally invariant systems
Ge, Yang; Rigol, Marcos
2017-08-01
It is known that, in the thermodynamic limit, the Chern number of a translationally invariant system cannot change under unitary time evolutions that are smooth in momentum space. Yet a real-space counterpart of the Chern number, the Bott index, has been shown to change in periodically driven systems with open boundary conditions. Here we prove that the Bott index and the Chern number are identical in translationally invariant systems in the thermodynamic limit. Using the Bott index, we show that, in finite-size translationally invariant systems, a Fermi sea under a periodic drive that is turned on slowly can acquire a different topology from that of the initial state. This can happen provided that the gap-closing points in the thermodynamic limit are absent in the discrete Brillouin zone of the finite system. Hence, in such systems, a periodic drive can be used to dynamically prepare topologically nontrivial states starting from topologically trivial ones.
El-Batanouny, Maged
2015-08-03
We propose to investigate the surface structural, dynamics and magnetic properties of the novel class of topological insulator crystals, as well as crystals that exhibit multiferroicity, magnetoelectricity and thermoelectricity. Topological insulators (TIs) are a new class of insulators in which a bulk gap for electronic excitations is generated because of the strong spin-orbit coupling inherent to these systems. These materials are distinguished from ordinary insulators by the presence of gapless metallic surface states, resembling chiral edge modes in quantum Hall systems, but with unconventional spin textures. These exotic metallic states are formed by topological conditions that also render the electrons travelling on such surfaces insensitive to scattering by impurities. The electronic quasi-particles populating the topological surface state are Dirac fermions; they have a linear dispersion and thus are massless just like photons. We propose to investigate the interaction of these massless Dirac fermions with the massive lattice in the newly discovered crystals, Bi2Se3, Bi2Te3 and Sb2Te3. We shall use inelastic helium beam scattering from surfaces to search for related signatures in surface phonon dispersions mappings that cover the entire surface Brillouin zone of these materials. Our recent investigations of the (001) surface of the multiferroic crystals (Li/Na)Cu2O2 revealed an anomalous surface structural behavior where surface Cu$^{2+}$ row rise above the surface plane as the crystal was cooled. Subsequent worming revealed the onset of a thermally activated incommensurate surface phase, driven by the elevated rows. We are currently investigating the structure of the magnetic phases in these quasi-one-dimensional magnetic rows. Multiferroics are excellent candidates for large magnetoelectric response. We propose to extend this investigation to the class of delafossites which are also multiferroics and have been investigated as good candidates for
Nittala S K Sastry
2012-06-01
Full Text Available This paper presents a new PWM Multi phase DC-DC converter under current mode control with an auxiliary circuit which provides zero voltage switching in order to meet the power supply requirements of the processors of modern electronic equipments like laptops, mobiles, and PDAs etc which require more than 70 A current, lower voltage and better transient response.The multi phase topology benefits in high current, good efficiency and better current transient response. High current multi phase buck converters found applications in advanced data control, solid state lasers, communication equipment and Pentium processors etc. In this paper designed of three phase DC-DC converter 100W, 12V/1V under current mode control is discussed in detail and the simulation results are presented to support the theoretical analysis.
Hanke, J.-P.; Freimuth, F.; Nandy, A. K.; Zhang, H.; Blügel, S.; Mokrousov, Y.
2016-09-01
We address the importance of the modern theory of orbital magnetization for spintronics. Based on an all-electron first-principles approach, we demonstrate that the predictive power of the routinely employed "atom-centered" approximation is limited to materials like elemental bulk ferromagnets, while the application of the modern theory of orbital magnetization is crucial in chemically or structurally inhomogeneous systems such as magnetic thin films, and materials exhibiting nontrivial topology in reciprocal and real space, e.g., Chern insulators or noncollinear systems. We find that the modern theory is particularly crucial for describing magnetism in a class of materials that we suggest here—topological orbital ferromagnets.
Amundsen, Morten; Ouassou, Jabir Ali; Linder, Jacob
2017-01-01
Multiterminal Josephson junctions have recently been proposed as a route to artificially mimic topological matter with the distinct advantage that its properties can be controlled via the superconducting phase difference, giving rise to Weyl points in 4-terminal geometries. A key goal is to accurately determine when the system makes a transition from a gapped to non-gapped state as a function of the phase differences in the system, the latter effectively playing the role of quasiparticle momenta in conventional topological matter. We here determine the proximity gap phase diagram of diffusive n-terminal Josephson junctions (), both numerically and analytically, by identifying a class of solutions to the Usadel equation at zero energy in the full proximity effect regime. We present an analytical equation which provides the phase diagram for an arbitrary number of terminals n. After briefly demonstrating the validity of the analytical approach in the previously studied 2- and 3-terminal cases, we focus on the 4-terminal case and map out the regimes where the electronic excitations in the system are gapped and non-gapped, respectively, demonstrating also in this case full agreement between the analytical and numerical approach.
On time-reversal anomaly of 2+1d topological phases
Tachikawa, Yuji
2016-01-01
We describe a method to find the anomaly of the time-reversal symmetry of 2+1d topological quantum field theories, by computing the fractional anomalous momentum on the cross-cap background. This allows us, for example, to identify the parameter $\
More on time-reversal anomaly of 2+1d topological phases
Tachikawa, Yuji
2016-01-01
We prove an explicit formula conjectured recently by Wang and Levin for the anomaly of time-reversal symmetry in 2+1 dimensional fermionic topological quantum field theories. The crucial step is to determine the crosscap state in terms of the modular S matrix and $\\mathsf{T}^2$ eigenvalues, generalizing the recent analysis by Barkeshli et al. in the bosonic case.
Bi, Zhen; BenTov, Yoni; Xu, Cenke
2016-01-01
Motivated by recent studies of symmetry protected topological (SPT) phases, we explore the possible gapless quantum disordered phases in the $(2+1)d$ nonlinear sigma model defined on the Grassmannian manifold $\\frac{U(N)}{U(n)\\times U(N - n)}$ with a Wess-Zumino-Witten (WZW) term at level $k$, which is the effective low energy field theory of the boundary of certain $(3+1)d$ SPT states. With $k = 0$, this model has a well-controlled large-$N$ limit, $i.e.$ its renormalization group equations can be computed exactly with large-$N$. However, with the WZW term, the large-$N$ and large-$k$ limit alone is not sufficient for a reliable study of the nature of the quantum disordered phase. We demonstrate that at least for $n = 1$, through a combined large-$N$, large-$k$ and $3-\\epsilon$ generalization, a stable fixed point in the quantum disordered phase can be reliably located, which corresponds to a $(2+1)d$ strongly interacting conformal field theory. Extension of our method to $n > 1$ will also be discussed.
On the topological stability of magnetostatic equilibria
Tsinganos, K. C.; Rosner, R.; Distler, J.
1984-01-01
The topological stability of MHD equilibria is investigated by exploring the formal analogy, in the ideal MHD limit, between the topology of magnetic lines of force in coordinate space and the topology of integral surfaces of one- and two-dimensional Hamiltonian systems in phase space. It is demonstrated that in an astrophysical setting, symmetric magnetostatic equilibria satisfying the ideal MHD equations are exceptional. The principal result of the study is that previous infinitesimal perturbation theory calculations can be generalized to include finite-amplitude and symmetry-breaking effects. The effect of the ergodicity of perturbed symmetric equilibria on heat dispersal in magnetically dominated plasmas is discussed.
Matsuno, Genki; Omori, Yukiko; Eguchi, Takaaki; Kobayashi, Akito
2016-09-01
The topological domain wall and valley Hall effect are theoretically investigated in the molecular conductor α-(BEDT-TTF)2I3. By using the mean-field theory in an extended Hubbard model, it is demonstrated under a cylinder boundary condition that a domain wall emerges in the charge ordered phase, and exhibits a topological nature near the phase transition to the massless Dirac Fermion phase. The topological nature is well characterized by the Berry curvature, which has opposite signs in two charge ordered phases divided by the domain wall, and gives rise to the valley Hall conductivity with opposite signs, enabling these phases to be distinguished. It is also found that the valley Hall conductivity in the tilted Dirac cones exhibits a characteristic double-peak structure as a function of chemical potential using the semi classical formalism.
The topology of geology 1: Topological analysis
Thiele, Samuel T.; Jessell, Mark W.; Lindsay, Mark; Ogarko, Vitaliy; Wellmann, J. Florian; Pakyuz-Charrier, Evren
2016-10-01
Topology has been used to characterise and quantify the properties of complex systems in a diverse range of scientific domains. This study explores the concept and applications of topological analysis in geology. We have developed an automatic system for extracting first order 2D topological information from geological maps, and 3D topological information from models built with the Noddy kinematic modelling system, and equivalent analyses should be possible for other implicit modelling systems. A method is presented for describing the spatial and temporal topology of geological models using a set of adjacency relationships that can be expressed as a topology network, thematic adjacency matrix or hive diagram. We define three types of spatial topology (cellular, structural and lithological) that allow us to analyse different aspects of the geology, and then apply them to investigate the geology of the Hamersley Basin, Western Australia.
Qi, Yanpeng; Shi, Wujun; Naumov, Pavel G.; Kumar, Nitesh; Sankar, Raman; Schnelle, Walter; Shekhar, Chandra; Chou, F. C.; Felser, Claudia; Yan, Binghai; Medvedev, Sergey A.
2016-01-01
A pressure-induced topological quantum phase transition has been theoretically predicted for the semiconductor BiTeI with giant Rashba spin splitting. In this work, the evolution of the electrical transport properties in BiTeI and BiTeBr is investigated under high pressure. The pressure-dependent resistivity in a wide temperature range passes through a minimum at around 3 GPa, indicating the predicted transition in BiTeI. Superconductivity is observed in both BiTeI and BiTeBr while the resist...
Zhang, Shu-Bo; Lai, Jian-Huang
2016-07-15
Measuring the similarity between pairs of biological entities is important in molecular biology. The introduction of Gene Ontology (GO) provides us with a promising approach to quantifying the semantic similarity between two genes or gene products. This kind of similarity measure is closely associated with the GO terms annotated to biological entities under consideration and the structure of the GO graph. However, previous works in this field mainly focused on the upper part of the graph, and seldom concerned about the lower part. In this study, we aim to explore information from the lower part of the GO graph for better semantic similarity. We proposed a framework to quantify the similarity measure beneath a term pair, which takes into account both the information two ancestral terms share and the probability that they co-occur with their common descendants. The effectiveness of our approach was evaluated against seven typical measurements on public platform CESSM, protein-protein interaction and gene expression datasets. Experimental results consistently show that the similarity derived from the lower part contributes to better semantic similarity measure. The promising features of our approach are the following: (1) it provides a mirror model to characterize the information two ancestral terms share with respect to their common descendant; (2) it quantifies the probability that two terms co-occur with their common descendant in an efficient way; and (3) our framework can effectively capture the similarity measure beneath two terms, which can serve as an add-on to improve traditional semantic similarity measure between two GO terms. The algorithm was implemented in Matlab and is freely available from http://ejl.org.cn/bio/GOBeneath/. Copyright © 2016 Elsevier B.V. All rights reserved.
Zhou, Jian, E-mail: jzhou2@vcu.edu, E-mail: pjena@vcu.edu; Jena, Puru, E-mail: jzhou2@vcu.edu, E-mail: pjena@vcu.edu [Department of Physics, Virginia Commonwealth University, Richmond, Virginia 23284 (United States); Zhang, Shunhong [Center for Applied Physics and Technology, College of Engineering, Peking University, Beijing 100871 (China); Wang, Qian [Center for Applied Physics and Technology, College of Engineering, Peking University, Beijing 100871 (China); Department of Physics, Virginia Commonwealth University, Richmond, Virginia 23284 (United States)
2016-06-20
Motivated by the growth of superconducting atomic hexagonal Ga layers on GaN surface we have calculated the electronic properties of Hf intercalated honeycomb Ga layers using first-principles theory. In contrast to the hexagonal Ga layers where substrate is necessary for their stability, we find the above structure to be dynamically stable in its freestanding form with small formation energy. In particular, six Dirac cones composed of Hf-d{sub xy}/d{sub x2-y2} orbitals are observed in the first Brillouin zone, slightly below the Fermi energy. Spin-orbit coupling opens a large band gap of 177 meV on these Dirac cones. By calculating its mirror Chern number, we demonstrate that this band gap is topologically nontrivial and protected by mirror symmetry. Such mirror symmetry protected band gaps are rare in hexagonal lattice. A large topological crystalline quantum spin Hall conductance σ{sub SH} ∼ −4 e{sup 2}/h is also revealed. Moreover, electron-phonon coupling calculations reveal that this material is superconducting with a transition temperature T{sub c} = 2.4 K, mainly contributed by Ga out-of-plane vibrations. Our results provide a route toward manipulating quantum spin Hall and superconducting behaviors in a single material which helps to realize Majorana fermions and topological superconductors.
Magnetoconductance in InN/GaN quantum wells in topological insulator phase
Bardyszewski, W.; Rodak, D.; Łepkowski, S. P.
2017-04-01
We present a theoretical study of the magnetic-field effect on the electronic properties of the two-dimensional, hypothetical topological insulator based on the InN/GaN quantum well system. Using the effective two-dimensional Hamiltonian, we have modelled magneto-transport in mesoscopic, symmetric samples of such materials. It turns out that, as in the case of the other two-dimensional topological insulators, the magnetoconductance in such samples is quantized due to the presence of helical edge states for magnetic fields below a certain critical value and for fairly small disorder strength. However, in our case the helical edge transport is much more prone to the disorder than, for example, in the case of topological insulators based on the HgTe/CdTe quantum wells. At low enough level of disorder and for the Fermi energy located in the energy gap of an infinite planar quantum well, we may expect an interesting phenomenon of non-monotonic dependence of the conductance on the magnetic field caused by the complicated interplay of couplings between the heavy hole, light hole and conduction subbands.
Lee, W. S.; Chuang, Y. D.; Moore, R. G.; Zhu, Y.; Patthey, L.; Trigo, M.; Lu, D. H.; Kirchmann, P. S.; Krupin, O.; Yi, M.; Langner, M.; Huse, N.; Robinson, J. S.; Chen, Y.; Zhou, S. Y.; Coslovich, G.; Huber, B.; Reis, D. A.; Kaindl, R. A.; Schoenlein, R. W.; Doering, D.; Denes, P.; Schlotter, W. F.; Turner, J. J.; Johnson, S. L.; Först, M.; Sasagawa, T.; Kung, Y. F.; Sorini, A. P.; Kemper, A. F.; Moritz, B.; Devereaux, T. P.; Lee, D. -H.; Shen, Z. X.; Hussain, Z.
2012-05-15
The dynamics of an order parameter's amplitude and phase determines the collective behaviour of novel states emerging in complex materials. Time- and momentum-resolved pump-probe spectroscopy, by virtue of measuring material properties at atomic and electronic time scales out of equilibrium, can decouple entangled degrees of freedom by visualizing their corresponding dynamics in the time domain. Here we combine time-resolved femotosecond optical and resonant X-ray diffraction measurements on charge ordered La1.75Sr0.25NiO4 to reveal unforeseen photoinduced phase fluctuations of the charge order parameter. Such fluctuations preserve long-range order without creating topological defects, distinct from thermal phase fluctuations near the critical temperature in equilibrium. Importantly, relaxation of the phase fluctuations is found to be an order of magnitude slower than that of the order parameter's amplitude fluctuations, and thus limits charge order recovery. This new aspect of phase fluctuations provides a more holistic view of the phase's importance in ordering phenomena of quantum matter.
Colloquium: Topological band theory
Bansil, A.; Lin, Hsin; Das, Tanmoy
2016-04-01
The first-principles band theory paradigm has been a key player not only in the process of discovering new classes of topologically interesting materials, but also for identifying salient characteristics of topological states, enabling direct and sharpened confrontation between theory and experiment. This review begins by discussing underpinnings of the topological band theory, which involve a layer of analysis and interpretation for assessing topological properties of band structures beyond the standard band theory construct. Methods for evaluating topological invariants are delineated, including crystals without inversion symmetry and interacting systems. The extent to which theoretically predicted properties and protections of topological states have been verified experimentally is discussed, including work on topological crystalline insulators, disorder and interaction driven topological insulators (TIs), topological superconductors, Weyl semimetal phases, and topological phase transitions. Successful strategies for new materials discovery process are outlined. A comprehensive survey of currently predicted 2D and 3D topological materials is provided. This includes binary, ternary, and quaternary compounds, transition metal and f -electron materials, Weyl and 3D Dirac semimetals, complex oxides, organometallics, skutterudites, and antiperovskites. Also included is the emerging area of 2D atomically thin films beyond graphene of various elements and their alloys, functional thin films, multilayer systems, and ultrathin films of 3D TIs, all of which hold exciting promise of wide-ranging applications. This Colloquium concludes by giving a perspective on research directions where further work will broadly benefit the topological materials field.
Lapa, Matthew F.; Cho, Gil Young; Hughes, Taylor L.
2016-12-01
We construct a bosonic analog of a two-dimensional topological Dirac semimetal (DSM). The low-energy description of the most basic 2D DSM model consists of two Dirac cones at positions ±k0 in momentum space. The local stability of the Dirac cones is guaranteed by a composite symmetry Z2TI, where T is time reversal and I is inversion. This model also exhibits interesting time-reversal and inversion symmetry breaking electromagnetic responses. In this work we construct a bosonic version by replacing each Dirac cone with a copy of the O (4 ) nonlinear sigma model (NLSM) with topological theta term and theta angle θ =±π . One copy of this NLSM also describes the gapless surface termination of the 3D bosonic topological insulator (BTI). We compute the time-reversal and inversion symmetry breaking electromagnetic responses for our model and show that they are twice the value one gets in the DSM case matching what one might expect from, for example, a bosonic Chern insulator. We also investigate the stability of the BSM model and find that the composite Z2TI symmetry again plays an important role. Along the way we clarify many aspects of the surface theory of the BTI including the electromagnetic response, the charges and statistics of vortex excitations, and the stability to symmetry-allowed perturbations. We briefly comment on the relation between the various descriptions of the O (4 ) NLSM with θ =π used in this paper (a dual vortex description and a description in terms of four massless fermions) and the recently proposed dual description of the BTI surface in terms of 2 +1 -dimensional quantum electrodynamics with two flavors of fermion (N =2 QED3). In a set of four Appendixes we review some of the tools used in the paper and also derive some of the more technical results.
Gillot, J.; Lepoutre, S.; Gauguet, A.; Büchner, M.; Vigué, J.
2013-07-01
In this Letter, we report a measurement of the He-McKellar-Wilkens (HMW) topological phase by atom interferometry. The experiment is done with our lithium atom interferometer, and in order to suppress the stray effects present in our first experiment, we use optical pumping of the Li7 atoms in their F=2, mF=+2 (or -2) ground state sublevel. In these conditions, the measured phase shift is the sum of the HMW phase and of the Aharonov-Casher phase, which are separated due to their different mF dependence. The HMW phase has been measured for different lithium beam velocities and the results are in very good agreement with a phase independent of the atom velocity, as expected for a topological phase.
Phase transition and thermodynamic stability of topological black holes in Hořava-Lifshitz gravity
Ma, Meng-Sen; Zhao, Ren; Liu, Yan-Song
2017-08-01
On the basis of horizon thermodynamics, we study the thermodynamic stability and P-V criticality of topological black holes constructed in Hořava-Lifshitz (HL) gravity without the detailed-balance condition (with general ɛ). In the framework of horizon thermodynamics, we do not need the concrete black hole solution (the metric function) and the concrete matter fields. It is shown that the HL black hole for k=0 is always thermodynamically stable. For k=1 , the thermodynamic behaviors and P-V criticality of the HL black hole are similar to those of RN-AdS black hole for some \
Observation of topological transitions in interacting quantum circuits.
Roushan, P; Neill, C; Chen, Yu; Kolodrubetz, M; Quintana, C; Leung, N; Fang, M; Barends, R; Campbell, B; Chen, Z; Chiaro, B; Dunsworth, A; Jeffrey, E; Kelly, J; Megrant, A; Mutus, J; O'Malley, P J J; Sank, D; Vainsencher, A; Wenner, J; White, T; Polkovnikov, A; Cleland, A N; Martinis, J M
2014-11-13
Topology, with its abstract mathematical constructs, often manifests itself in physics and has a pivotal role in our understanding of natural phenomena. Notably, the discovery of topological phases in condensed-matter systems has changed the modern conception of phases of matter. The global nature of topological ordering, however, makes direct experimental probing an outstanding challenge. Present experimental tools are mainly indirect and, as a result, are inadequate for studying the topology of physical systems at a fundamental level. Here we employ the exquisite control afforded by state-of-the-art superconducting quantum circuits to investigate topological properties of various quantum systems. The essence of our approach is to infer geometric curvature by measuring the deflection of quantum trajectories in the curved space of the Hamiltonian. Topological properties are then revealed by integrating the curvature over closed surfaces, a quantum analogue of the Gauss-Bonnet theorem. We benchmark our technique by investigating basic topological concepts of the historically important Haldane model after mapping the momentum space of this condensed-matter model to the parameter space of a single-qubit Hamiltonian. In addition to constructing the topological phase diagram, we are able to visualize the microscopic spin texture of the associated states and their evolution across a topological phase transition. Going beyond non-interacting systems, we demonstrate the power of our method by studying topology in an interacting quantum system. This required a new qubit architecture that allows for simultaneous control over every term in a two-qubit Hamiltonian. By exploring the parameter space of this Hamiltonian, we discover the emergence of an interaction-induced topological phase. Our work establishes a powerful, generalizable experimental platform to study topological phenomena in quantum systems.
Lunar Quest in Second Life, Lunar Exploration Island, Phase II
Ireton, F. M.; Day, B. H.; Mitchell, B.; Hsu, B. C.
2010-12-01
Linden Lab’s Second Life is a virtual 3D metaverse created by users. At any one time there may be 40,000-50,000 users on line. Users develop a persona and are seen on screen as a human figure or avatar. Avatars move through Second Life by walking, flying, or teleporting. Users form communities or groups of mutual interest such as music, computer graphics, and education. These groups communicate via e-mail, voice, and text within Second Life. Information on downloading the Second Life browser and joining can be found on the Second Life website: www.secondlife.com. This poster details Phase II in the development of Lunar Exploration Island (LEI) located in Second Life. Phase I LEI highlighted NASA’s LRO/LCROSS mission. Avatars enter LEI via teleportation arriving at a hall of flight housing interactive exhibits on the LRO/ LCROSS missions including full size models of the two spacecraft and launch vehicle. Storyboards with information about the missions interpret the exhibits while links to external websites provide further information on the mission, both spacecraft’s instrument suites, and related EPO. Other lunar related activities such as My Moon and NLSI EPO programs. A special exhibit was designed for International Observe the Moon Night activities with links to websites for further information. The sim includes several sites for meetings, a conference stage to host talks, and a screen for viewing NASATV coverage of mission and other televised events. In Phase II exhibits are updated to reflect on-going lunar exploration highlights, discoveries, and future missions. A new section of LEI has been developed to showcase NASA’s Lunar Quest program. A new exhibit hall with Lunar Quest information has been designed and is being populated with Lunar Quest information, spacecraft models (LADEE is in place) and kiosks. A two stage interactive demonstration illustrates lunar phases with static and 3-D stations. As NASA’s Lunar Quest program matures further
Mera, Bruno; Vlachou, Chrysoula; Paunković, Nikola; Vieira, Vítor R.
2017-09-01
We perform the fidelity analysis for Boltzmann-Gibbs-like states in order to investigate whether the topological order of 1D fermionic systems at zero temperature is maintained at finite temperatures. We use quantum walk protocols that are known to simulate topological phases and the respective quantum phase transitions for chiral symmetric Hamiltonians. Using the standard approaches of the fidelity analysis and the study of edge states, we conclude that no thermal-like phase transitions occur as temperature increases, i.e. the topological behaviour is washed out gradually. We also show that the behaviour of the Uhlmann geometric factor associated to the considered fidelity exhibits the same behaviour as the latter, thus confirming the results obtained using the previously established approaches.
Thanyanan Phuphachong
2017-01-01
Full Text Available Topological crystalline insulators (TCIs are topological materials that have Dirac surface states occurring at crystalline symmetric points in the Brillouin zone. This topological state has been experimentally shown to occur in the lead–tin salts Pb1−xSnxSe and Pb1−xSnxTe. More recent works also took interest in studying the topological phase transition from trivial to non-trivial topology that occurs in such materials as a function of increasing Sn content. A peculiar property of these materials is the fact that their bulk bands disperse following a massive Dirac dispersion that is linear at low energies above the energy gap. This makes Pb1−xSnxSe and Pb1−xSnxTe ideal platforms to simultaneously study 3D and 2D Dirac physics. In this review, we will go over infrared magneto-optical studies of the Landau level dispersion of Pb1−xSnxSe and Pb1−xSnxTe for both the bulk and surface bands and summarize work that has been done on this matter. We will review recent work on probing the topological phase transition in TCI. We will finally present our views on prospects and open questions that have yet to be addressed in magneto-optical spectroscopy studies on Pb1-xSnxSe and Pb1−xSnxTe.
Łepkowski, S P; Bardyszewski, W
2017-02-08
Combining the k · p method with the third-order elasticity theory, we perform a theoretical study of the pressure-induced topological phase transition and the pressure evolution of topologically protected edge states in InN/GaN and In-rich InGaN/GaN quantum wells. We show that for a certain range of the quantum well parameters, thanks to a negative band gap pressure coefficient, it is possible to continuously drive the system from the normal insulator state through the topological insulator into the semimetal phase. The critical pressure for the topological phase transition depends not only on the quantum well thickness but also on the width of the Hall bar, which determines the coupling between the edge states localized at the opposite edges. We also find that in narrow Hall bar structures, near the topological phase transition, a significant Rashba-type spin splitting of the lower and upper branches of the edge state dispersion curve appears. This effect originates from the lack of the mirror symmetry of the quantum well potential caused by the built-in electric field, and can be suppressed by increasing the Hall bar width. When the pressure increases, the energy dispersion of the edge states becomes more parabolic-like and the spin splitting decreases. A further increase of pressure leads to the transition to a semimetal phase, which occurs due to the closure of the indirect 2D bulk band gap. The difference between the critical pressure at which the system becomes semimetallic, and the pressure for the topological phase transition, correlates with the variation of the pressure coefficient of the band gap in the normal insulator state.
Łepkowski, S. P.; Bardyszewski, W.
2017-02-01
Combining the k · p method with the third-order elasticity theory, we perform a theoretical study of the pressure-induced topological phase transition and the pressure evolution of topologically protected edge states in InN/GaN and In-rich InGaN/GaN quantum wells. We show that for a certain range of the quantum well parameters, thanks to a negative band gap pressure coefficient, it is possible to continuously drive the system from the normal insulator state through the topological insulator into the semimetal phase. The critical pressure for the topological phase transition depends not only on the quantum well thickness but also on the width of the Hall bar, which determines the coupling between the edge states localized at the opposite edges. We also find that in narrow Hall bar structures, near the topological phase transition, a significant Rashba-type spin splitting of the lower and upper branches of the edge state dispersion curve appears. This effect originates from the lack of the mirror symmetry of the quantum well potential caused by the built-in electric field, and can be suppressed by increasing the Hall bar width. When the pressure increases, the energy dispersion of the edge states becomes more parabolic-like and the spin splitting decreases. A further increase of pressure leads to the transition to a semimetal phase, which occurs due to the closure of the indirect 2D bulk band gap. The difference between the critical pressure at which the system becomes semimetallic, and the pressure for the topological phase transition, correlates with the variation of the pressure coefficient of the band gap in the normal insulator state.
Li, Huai-Fan; Zhao, Hui-Hua; Zhang, Li-Chun; Zhao, Ren [Shanxi Datong University, Institute of Theoretical Physics, Datong (China); Shanxi Datong University, Department of Physics, Datong (China)
2017-05-15
Using Maxwell's equal area law, we discuss the phase transition of higher dimensional charged topological dilaton AdS black hole with a nonlinear source. The coexisting region of the two phases is found and we depict the coexistence region in the P-v diagrams. The two-phase equilibrium curves in the P-T diagrams are plotted, and we take the first order approximation of volume v in the calculation. To better compare with a general thermodynamic system, the Clapeyron equation is derived for a higher dimensional charged topological black hole with a nonlinear source. The latent heat of an isothermal phase transition is investigated. We also study the effect of the parameters of the black hole on the region of two-phase coexistence. The results show that the black hole may go through a small-large phase transition similar to those of usual non-gravity thermodynamic systems. (orig.)
Li, Huai-Fan; Zhang, Li-Chun; Zhao, Ren
2016-01-01
Using Maxwell's equal area law, we discuss the phase transition of higher dimensional charged topological dilaton AdS black holes with a nonlinear source. The coexisting region of the two phases is found and we depict the coexistence region in $P-v$ diagrams. The two-phase equilibrium curves in $P-T$ diagrams are plotted, and we take the first order approximation of volume $v$ in the calculation. To better compare with a general thermodynamic system, the Clapeyron equation is derived for higher dimensional charged topological black hole with a nonlinear source. The latent heat of isothermal phase transition is investigated. We also study the effect of the parameters of the black hole on the region of two-phases coexistence. The results show that the black hole may go through a small-large phase transition similar to those of usual non-gravity thermodynamic systems.
The topological phase diagram of cimetidine: A case of overall monotropy.
Céolin, R; Rietveld, I B
2017-03-01
Cimetidine is a histamine H2-receptor antagonist used against peptic ulcers. It is known to exhibit crystalline polymorphism. Forms A and D melt within 0.35 degrees from each other and the enthalpies of fusion are similar as well. The present paper demonstrates how to construct a pressure-temperature phase diagram with only calorimetric and volumetric data available. The phase diagram provides the stability domains and the phase equilibria for the phases A, D, the liquid and the vapor. Cimetidine is overall monotropic with form D the only stable solid phase.
Nagarajan, Mahesh B.; Coan, Paola; Huber, Markus B.; Diemoz, Paul C.; Wismüller, Axel
2014-03-01
Current assessment of cartilage is primarily based on identification of indirect markers such as joint space narrowing and increased subchondral bone density on x-ray images. In this context, phase contrast CT imaging (PCI-CT) has recently emerged as a novel imaging technique that allows a direct examination of chondrocyte patterns and their correlation to osteoarthritis through visualization of cartilage soft tissue. This study investigates the use of topological and geometrical approaches for characterizing chondrocyte patterns in the radial zone of the knee cartilage matrix in the presence and absence of osteoarthritic damage. For this purpose, topological features derived from Minkowski Functionals and geometric features derived from the Scaling Index Method (SIM) were extracted from 842 regions of interest (ROI) annotated on PCI-CT images of healthy and osteoarthritic specimens of human patellar cartilage. The extracted features were then used in a machine learning task involving support vector regression to classify ROIs as healthy or osteoarthritic. Classification performance was evaluated using the area under the receiver operating characteristic (ROC) curve (AUC). The best classification performance was observed with high-dimensional geometrical feature vectors derived from SIM (0.95 ± 0.06) which outperformed all Minkowski Functionals (p analysis of chondrocyte patterns in human patellar cartilage matrix involving SIM-derived geometrical features can distinguish between healthy and osteoarthritic tissue with high accuracy.
Noguchi, Yuki; Yamamoto, Takashi; Yamada, Takayuki; Izui, Kazuhiro; Nishiwaki, Shinji
2017-09-01
This papers proposes a level set-based topology optimization method for the simultaneous design of acoustic and structural material distributions. In this study, we develop a two-phase material model that is a mixture of an elastic material and acoustic medium, to represent an elastic structure and an acoustic cavity by controlling a volume fraction parameter. In the proposed model, boundary conditions at the two-phase material boundaries are satisfied naturally, avoiding the need to express these boundaries explicitly. We formulate a topology optimization problem to minimize the sound pressure level using this two-phase material model and a level set-based method that obtains topologies free from grayscales. The topological derivative of the objective functional is approximately derived using a variational approach and the adjoint variable method and is utilized to update the level set function via a time evolutionary reaction-diffusion equation. Several numerical examples present optimal acoustic and structural topologies that minimize the sound pressure generated from a vibrating elastic structure.
Tan, Maxine; Pu, Jiantao; Zheng, Bin
2014-01-01
In the field of computer-aided mammographic mass detection, many different features and classifiers have been tested. Frequently, the relevant features and optimal topology for the artificial neural network (ANN)-based approaches at the classification stage are unknown, and thus determined by trial-and-error experiments. In this study, we analyzed a classifier that evolves ANNs using genetic algorithms (GAs), which combines feature selection with the learning task. The classifier named "Phased Searching with NEAT in a Time-Scaled Framework" was analyzed using a dataset with 800 malignant and 800 normal tissue regions in a 10-fold cross-validation framework. The classification performance measured by the area under a receiver operating characteristic (ROC) curve was 0.856 ± 0.029. The result was also compared with four other well-established classifiers that include fixed-topology ANNs, support vector machines (SVMs), linear discriminant analysis (LDA), and bagged decision trees. The results show that Phased Searching outperformed the LDA and bagged decision tree classifiers, and was only significantly outperformed by SVM. Furthermore, the Phased Searching method required fewer features and discarded superfluous structure or topology, thus incurring a lower feature computational and training and validation time requirement. Analyses performed on the network complexities evolved by Phased Searching indicate that it can evolve optimal network topologies based on its complexification and simplification parameter selection process. From the results, the study also concluded that the three classifiers - SVM, fixed-topology ANN, and Phased Searching with NeuroEvolution of Augmenting Topologies (NEAT) in a Time-Scaled Framework - are performing comparably well in our mammographic mass detection scheme.
Jupiter Icy Moons Explorer: mission status after the Definition Phase
Titov, Dmitri; Barabash, Stas; Bruzzone, Lorenzo; Dougherty, Michele; Erd, Christian; Fletcher, Leigh; Gare, Philippe; Gladstone, Randall; Grasset, Olivier; Gurvits, Leonid; Hartogh, Paul; Hussmann, Hauke; Iess, Luciano; Jaumann, Ralf; Langevin, Yves; Palumbo, Pasquale; Piccioni, Giuseppe; Sarri, Giuseppe; Wahlund, Jan-Erik; Witasse, Olivier
2015-04-01
ultraviolet to the sub-millimetre wavelengths (MAJIS, UVS, SWI). A geophysical package consists of a laser altimeter (GALA) and a radar sounder (RIME) for exploring the surface and subsurface of the moons, and a radio science experiment (3GM) to probe the atmospheres of Jupiter and its satellites and to perform measurements of the gravity fields. An in situ package comprises a powerful particle environment package (PEP), a magnetometer (J-MAG) and a radio and plasma wave instrument (RPWI), including electric fields sensors and a Langmuir probe. An experiment (PRIDE) using ground-based Very-Long-Baseline Interferometry (VLBI) will provide precise determination of the moons ephemerides. The mission scenario will include a Jovian tour with multiple flybys of Callisto and Ganymede, the phase with more than 20 degrees inclination orbits, and two Europa flybys. The Ganymede tour will include high (5000 km) and low (500 km) almost polar orbits around the moon. The mission scenario has evolved slightly during the definition phase, reassuring that the mission will still be able to fulfil all major science objectives. The talk will give an overview of the mission status at the end of the definition phase, focusing on the evolution of science performance and payload synergies in achieving the mission goals.
Open-phase operating modes of power flow control topologies in a Smart Grid Distribution Network
Astashev, M. G.; Novikov, M. A.; Panfilov, D. I.; Rashitov, P. A.; Remizevich, T. V.; Fedorova, M. I.
2015-12-01
The power flow regulating circuit node in an alternating current system is reviewed. The circuit node is accomplished based on a thyristor controlled phase angle regulator (TCPAR) with controlled thyristor switch. Research results of the individual phase control of the output voltage for the TCPAR are presented. Analytical expressions for the overvoltage factor calculation in the thyristor switch circuit for open-phase operating modes are received. Based on evaluation of overvoltage in operational and emergency modes, the implementability conditions of the individual phase control of the output voltage are determined. Under these conditions, maximal performance and complete controllability are provided.
Ezawa, Motohiko
2017-07-01
We propose a simple scheme to construct a model whose Fermi surface is comprised of crossing-line nodes. The Hamiltonian consists of a normal hopping term and an additional term which is odd under the mirror reflection. The line nodes appear along the mirror-invariant planes, where each line node carries the quantized Berry magnetic flux. We explicitly construct a model with the N -fold rotational symmetry, where the 2 N line nodes merge at the north and south poles. When we apply photoirradiation along the kz axis, there emerge point nodes carrying the monopole charge ±N at these poles, while all the line nodes disappear. In this model, photoirradiation induces a topological phase transition from a crossing-line nodal semimetal to a multiple-Weyl semimetal, where the surface state turns from a drumhead state into a Fermi-arc state.
Narimani, Mitra; Nourbakhsh, Zahra
2017-03-01
The electronic, thermodynamic and optical properties of XPtSb (X=Lu, Sc) half Heusler compounds are studied based on density functional theory. The calculations are carried out in the presence of spin orbit interaction. The exchange correlation part of total energy is calculated within local density approximation, generalized gradient approximation, Engel-Vosco generalized gradient approximation and modified Becke and Johnson exchange potential with the correlation potential of the generalized gradient approximation. The effect of pressure on the electron density of states and linear coefficient of the electronic specific heat is studied. Using the band structure calculations at different pressures, the band inversion strength and topological phase transition of these compounds are investigated. Some thermodynamic properties of XPtSb compounds by different thermal models using the non-equilibrium Gibbs function are studied and compared with experiment. Furthermore the effect of pressure on dielectric function of XPtSb (X=Lu, Sc) compounds is investigated.
Topological Quantum Field Theory, Nonlocal Operators, and Gapped Phases of Gauge Theories
Gukov, Sergei
2013-01-01
We revisit the role of loop and surface operators as order parameters for gapped phases of four-dimensional gauge theories. We show that in some cases surface operators are confined, and that this fact can be used to distinguish phases which are not distinguished by the Wilson-'t Hooft criterion. The long-distance behavior of loop and surface operators which are neither confined nor screened is controlled by a 4d TQFT. We construct these TQFTs for phases which are characterized by the presence of electrically and/or magnetically charged condensates. Interestingly, the TQFT describing a phase with a nonabelian monopole condensate is based on the theory of nonabelian gerbes. We also show that in phases with a dyonic condensate the low-energy theta-angle is quantized.
Thomas Hammerschmidt
2016-02-01
Full Text Available The moments of the electronic density-of-states provide a robust and transparent means for the characterization of crystal structures. Using d-valent canonical tight-binding, we compute the moments of the crystal structures of topologically close-packed (TCP phases as obtained from density-functional theory (DFT calculations. We apply the moments to establish a measure for the difference between two crystal structures and to characterize volume changes and internal relaxations. The second moment provides access to volume variations of the unit cell and of the atomic coordination polyhedra. Higher moments reveal changes in the longer-ranged coordination shells due to internal relaxations. Normalization of the higher moments leads to constant (A15,C15 or very similar (χ, C14, C36, μ, and σ higher moments of the DFT-relaxed TCP phases across the 4d and 5d transition-metal series. The identification and analysis of internal relaxations is demonstrated for atomic-size differences in the V-Ta system and for different magnetic orderings in the C14-Fe 2 Nb Laves phase.
Phase topology of a NR/BR elastomer blend with active filler
Plavšić Milenko B.
2003-01-01
Full Text Available The relations between the structure and mechanical properties of a polymer blend of natural (NR and polybutadiene (BR rubber (i.e. a NR/BR blend with the weight ratio of the components 70/30 filled with active carbon black were analysed. The properties of the individual phases in the blend were resolved by modeling the stress-strain relationship according to the Bauer procedure for high extensions. The obtained results indicated that BR is the dispersed phase, having a higher modulus, which was also confirmed by the much better fit of the experimental data to the series type of phase coupling according to the Takanayagy theory.
Luis Gerardo González-Morales
2014-01-01
Full Text Available Este artículo presenta el diseño de un sistema de conversión de energía eléctrica (SCEE para el aprovechamiento de energía solar y luego acondicionamiento e inyección de energía a la red eléctrica comercial. Se utiliza un inversor puente completo monofásico con la topología sin transformador H5 acoplado a un filtro LCL. El sistema es identificado mediante el modelo de estado promediado y de pequeña señal, el esquema de control presenta un control en cascada sintonizado mediante la asignación de polos, además de un algoritmo de seguimiento de máxima potencia de tipo perturbar y observar que permite aumentar la eficiencia del sistema, operando en el punto óptimo de funcionamiento del panel solar. En el diseño se describen aspectos técnicos fundamentales en el dimensionamiento y selección de componentes para su desarrollo experimental, así como el diseño de la estructura de control para un buen desempeño ante perturbaciones del sistema.
Slagle, Kevin
2015-03-01
Using determinant quantum Monte Carlo simulations, we demonstrate that an extended Hubbard model on a bilayer honeycomb lattice has two novel quantum phase transitions, each with connections to symmetry protected topological states. 1) The first is a continuous phase transition between the weakly interacting gapless Dirac fermion phase and a strongly interacting fully gapped and symmetric trivial phase. Because there is no spontaneous symmetry breaking, this transition cannot be described by the standard Gross-Neveu model. We argue that this phase transition is related to the Z16 classification of the topological superconductor 3He-B phase with interactions. 2) The second is a quantum critical point between a quantum spin Hall insulator with spin Sz conservation and the previously mentioned strongly interacting gapped phase. At the critical point the single particle excitations remain gapped, while spin and charge gaps close. We argue that this transition is described by a bosonic O(4) nonlinear sigma model field theory with a topological Θ-term.
Spaans, M.
2013-01-01
General Relativity is extended into the quantum domain. A thought experiment is ex- plored to derive a specific topological build-up for Planckian space-time. The presented arguments are inspired by Feynman’s path integral for superposition andWheeler’s quan- tum foam of Planck mass mini black holes
Caporaso, Nicola; Cirafici, Michele; Griguolo, Luca; Pasquetti, Sara; Seminara, Domenico; Szabo, Richard J.
2006-01-01
We examine the problem of counting bound states of BPS black holes on local Calabi-Yau threefolds which are fibrations over a Riemann surface by computing the partition function of q-deformed Yang-Mills theory on the Riemann surface. We study in detail the genus zero case and obtain, at finite N, the instanton expansion of the gauge theory. It can be written exactly as the partition function for U(N) Chern-Simons gauge theory on a Lens space, summed over all non-trivial vacua, plus a tower of non-perturbative instanton contributions. The correspondence between two and three dimensional gauge theories is elucidated by an explicit mapping between two-dimensional Yang-Mills instantons and flat connections on the Lens space. In the large N limit we find a peculiar phase structure in the model. At weak string coupling the theory reduces exactly to the trivial flat connection sector with instanton contributions exponentially suppressed, and the topological string partition function on the resolved conifold is reproduced in this regime. At a certain critical point all non-trivial vacua contribute, instantons are enhanced and the theory appears to undergo a phase transition into a strong coupling regime. We rederive these results by performing a saddle-point approximation to the exact partition function. We obtain a q-deformed version of the Douglas-Kazakov equation for two-dimensional Yang-Mills theory on the sphere, whose one-cut solution below the transition point reproduces the resolved conifold geometry. Above the critical point we propose a two-cut solution that should reproduce the chiral-antichiral dynamics found for black holes on the Calabi-Yau threefold and the Gross-Taylor string in the undeformed limit. The transition from the strong coupling phase to the weak coupling phase appears to be of third order.
Exploring the QCD phase diagram through relativistic heavy ion collisions
Mohanty, Bedangadas
2013-01-01
We present a review of the studies related to establishing the QCD phase diagram through high energy nucleus-nucleus collisions. We particularly focus on the experimental results related to the formation of a quark-gluon phase, crossover transition and search for a critical point in the QCD phase diagram.
Ma, Meng-Sen; Liu, Yan-Song
2016-01-01
On the basis of horizon thermodynamics we study the thermodynamic stability and $P-V$ criticality of topological black holes constructed in Ho\\v{r}ava-Lifshitz (HL) gravity without the detailed-balance condition (with general $\\epsilon$). In the framework of horizon thermodynamics, the temperature $T$ and pressure $P$ are independent quantities. It is not necessary to derive $T$ according to the metric function and $P$ according to any matter content. It is shown that the HL black hole for $k=0$ is always thermodynamically stable. For $k=1$, the temperature of HL black hole can be classified in five different cases. In one case, the thermodynamic behaviors of HL black hole is similar to that of Reissner- Nordstr\\"{o}m (RN) black hole. There are larger/smaller black hole phase transition and smaller/larger black hole phase transition in different cases. For $k=-1$, there are six cases for the temperature of HL black hole, in one of which the HL black hole exhibits itself like Schwarzschild-AdS black hole. It i...
Topology optimization of piezo modal transducers with null-polarity phases
Donoso, A.; Sigmund, O.
2016-01-01
Piezo modal transducers in 2d can be designed theoretically by tailoring polarity of the surface electrodes. However, it is also necessary to include null-polarity phases of known width separating areas of opposite polarity in the manufacturing process in order to avoid short-circuiting. Otherwise...
Topology optimization approaches
Sigmund, Ole; Maute, Kurt
2013-01-01
Topology optimization has undergone a tremendous development since its introduction in the seminal paper by Bendsøe and Kikuchi in 1988. By now, the concept is developing in many different directions, including “density”, “level set”, “topological derivative”, “phase field”, “evolutionary...
Kang, Chang-Jong; Choi, Hong Chul; Kim, Kyoo; Min, B I
2015-04-24
We have investigated temperature-dependent behaviors of electronic structure and resistivity in a mixed-valent golden phase of SmS, based on the dynamical mean-field-theory band-structure calculations. Upon cooling, the coherent Sm 4f bands are formed to produce the hybridization-induced pseudogap near the Fermi level, and accordingly the topology of the Fermi surface is changed to exhibit a Lifshitz-like transition. The surface states emerging in the bulk gap region are found to be not topologically protected states but just typical Rashba spin-polarized states, indicating that SmS is not a topological Kondo semimetal. From the analysis of anomalous resistivity behavior in SmS, we have identified universal energy scales, which characterize the Kondo-mixed-valent semimetallic systems.
SU(3) quantum critical model emerging from a spin-1 topological phase
Rao, Wen-Jia; Zhu, Guo-Yi; Zhang, Guang-Ming
2016-04-01
Different from the spin-1 Haldane gapped phase, we propose an SO(3) spin-1 matrix product state (MPS), whose parent Hamiltonian includes three-site spin interactions. From the entanglement spectrum of a single block with l sites, an enlarged SU(3) symmetry is identified in the edge states, which are conjugate to each other for the l =even block but identical for the l =odd block. By blocking this state, the blocked MPS explicitly displays the SU(3) symmetry with two distinct structures. Under a symmetric bulk bipartition with a sufficient large block length l =even , the entanglement Hamiltonian (EH) of the reduced system characterizes a spontaneous dimerized phase with twofold degeneracy. However, for the block length l =odd , the corresponding EH represents an SU(3) quantum critical point with delocalized edge quasiparticles, and the critical field theory is described by the SU(3) level-1 Wess-Zumino-Witten conformal field theory.
Pseudo-self-organized topological phases in glassy selenides for IR photonics
Shpotyuk, O. [Lviv Institute of Materials of Scientific Research Company ' ' Carat' ' 202, Stryjska str., 79031 Lviv (Ukraine); Institute of Physics of Jan Dlugosz University 13/15, al. Armii Krajowej, 42201 Czestochowa (Poland); Golovchak, R. [Lviv Institute of Materials of Scientific Research Company ' ' Carat' ' 202, Stryjska str., 79031 Lviv (Ukraine)
2011-09-15
Network-forming cluster approach is applied to As-Se and Ge-Se glasses to justify their tendency to self-organization. It is shown that reversibility windows determined by temperature-modulated differential scanning calorimetry using short-term aged or as-prepared samples do not necessary coincide with self-organized phase in these materials. The obtained results testify also pseudo-self-organization phenomenon in Ge-Se glasses: over-constrained outrigger raft structural units built of two edge- and four corner-shared tetrahedra are interconnected via optimally-constrained {identical_to}Ge-Se-Se-Ge{identical_to} bridges within the range of compositions identified previously as self-organized phase by temperature modulated differential scanning calorimetry technique. (copyright 2011 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
Clay, Adam
2016-01-01
This book deals with the connections between topology and ordered groups. It begins with a self-contained introduction to orderable groups and from there explores the interactions between orderability and objects in low-dimensional topology, such as knot theory, braid groups, and 3-manifolds, as well as groups of homeomorphisms and other topological structures. The book also addresses recent applications of orderability in the studies of codimension-one foliations and Heegaard-Floer homology. The use of topological methods in proving algebraic results is another feature of the book. The book was written to serve both as a textbook for graduate students, containing many exercises, and as a reference for researchers in topology, algebra, and dynamical systems. A basic background in group theory and topology is the only prerequisite for the reader.
Photonic Floquet Topological Insulators
Rechtsman, Mikael C; Plotnik, Yonatan; Lumer, Yaakov; Nolte, Stefan; Segev, Mordechai; Szameit, Alexander
2012-01-01
The topological insulator is a fundamentally new phase of matter, with the striking property that the conduction of electrons occurs only on its surface, not within the bulk, and that conduction is topologically protected. Topological protection, the total lack of scattering of electron waves by disorder, is perhaps the most fascinating and technologically important aspect of this material: it provides robustness that is otherwise known only for superconductors. However, unlike superconductivity and the quantum Hall effect, which necessitate low temperatures or magnetic fields, the immunity to disorder of topological insulators occurs at room temperature and without any external magnetic field. For this reason, topological protection is predicted to have wide-ranging applications in fault-tolerant quantum computing and spintronics. Recently, a large theoretical effort has been directed towards bringing the concept into the domain of photonics: achieving topological protection of light at optical frequencies. ...
Engineering topological materials in microwave cavity arrays
Anderson, Brandon M; Owens, Clai; Schuster, David I; Simon, Jonathan
2016-01-01
We present a scalable architecture for the exploration of interacting topological phases of photons in arrays of microwave cavities, using established techniques from cavity and circuit quantum electrodynamics. A time-reversal symmetry breaking (non-reciprocal) flux is induced by coupling the microwave cavities to ferrites, allowing for the production of a variety of topological band structures including the $\\alpha=1/4$ Hofstadter model. Effective photon-photon interactions are included by coupling the cavities to superconducting qubits, and are sufficient to produce a $\
Brillouin-Wigner theory for Floquet topological phase transitions in spin-orbit-coupled materials
Mohan, Priyanka; Saxena, Ruchi; Kundu, Arijit; Rao, Sumathi
2016-12-01
We develop the high-frequency expansion based on the Brillouin-Wigner (B-W) perturbation theory for driven systems with spin-orbit coupling which is applicable to the cases of silicene, germanene, and stanene. We compute the effective Hamiltonian in the zero-photon subspace not only to order O (ω-1) but by keeping all the important terms to order O (ω-2) and obtain the photoassisted correction terms to both the hopping and the spin-orbit terms, as well as longer-ranged hopping terms. We then use the effective static Hamiltonian to compute the phase diagram in the high-frequency limit and compare it with the results of direct numerical computation of the Chern numbers of the Floquet bands and show that at sufficiently large frequencies, the B-W theory high-frequency expansion works well even in the presence of spin-orbit-coupling terms.
Hida, Kazuo; Takano, Ken'ichi; Suzuki, Hidenori
2013-06-01
The spin-1/2 ferromagnetic--antiferromagnetic alternating Heisenberg chain with ferromagnetic next-nearest-neighbour (NNN) interaction is investigated. The ground state is the Haldane phase for weak NNN interaction, and is the ferromagnetic phase for weak antiferromagnetic interaction. We find a series of topologically distinct spin-gap phases with various magnitudes of edge spins for strong NNN interaction. The phase boundaries between these phases are determined on the basis of the DMRG calculation with additional spins that compensate the edge spins. It is found that each of the exact solutions with short-range antiferromagnetic correlation on the ferromagnetic--nonmagnetic phase boundary is representative of each spin gap phase.
Topological aspects of the multi-language phases of the Naming Game on community-based networks
Palombi, Filippo
2016-01-01
The Naming Game is an agent-based model where individuals communicate to name an initially unnamed object. On a large class of networks continual pairwise interactions lead the system to an ultimate consensus state, in which agents converge on a globally shared name. Soon after the introduction of the model, it was observed in literature that on community-based networks the path to consensus passes through metastable multi-language states. Subsequently, it was proposed to use this feature as a mean to discover communities in a given network. In this paper we show that metastable states correspond to genuine multi-language phases, emerging in the thermodynamic limit when the fraction of links connecting communities drops below critical thresholds. In particular, we study the transition to multi-language states in the stochastic block model and on networks with community overlap. We also examine the scaling of critical thresholds under variations of topological properties of the network, such as the number and ...
Caporaso, N; Griguolo, L; Pasquetti, S; Seminara, D; Szabó, R J; Caporaso, Nicola; Cirafici, Michele; Griguolo, Luca; Pasquetti, Sara; Seminara, Domenico; Szabo, Richard J.
2006-01-01
We examine the problem of counting bound states of BPS black holes on local Calabi-Yau threefolds which are fibrations over a Riemann surface by computing the partition function of $q$-deformed Yang-Mills theory on the Riemann surface. We study in detail the genus zero case and obtain, at finite $N$, the instanton expansion of the gauge theory. It can be written exactly as the partition function for $U(N)$ Chern-Simons gauge theory on a Lens space, summed over all non-trivial vacua, plus a tower of non-perturbative instanton contributions. The correspondence between two and three dimensional gauge theories is elucidated by an explicit mapping between two-dimensional Yang-Mills instantons and flat connections on the Lens space. In the large $N$ limit we find a peculiar phase structure in the model. At weak string coupling the theory reduces exactly to the trivial flat connection sector with instanton contributions exponentially suppressed, and the topological string partition function on the resolved conifold ...
Topological Aspects of the Multi-Language Phases of the Naming Game on Community-Based Networks
Filippo Palombi
2017-02-01
Full Text Available The Naming Game is an agent-based model where individuals communicate to name an initially unnamed object. On a large class of networks continual pairwise interactions lead the system to an ultimate consensus state, in which agents onverge on a globally shared name. Soon after the introduction of the model, it was observed in literature that on community-based networks the path to consensus passes through metastable multi-language states. Subsequently, it was proposed to use this feature as a mean to discover communities in a given network. In this paper we show that metastable states correspond to genuine multi-language phases, emerging in the thermodynamic limit when the fraction of links connecting communities drops below critical thresholds. In particular, we study the transition to multi-language states in the stochastic block model and on networks with community overlap. We also xamine the scaling of critical thresholds under variations of topological properties of the network, such as the number and relative size of communities and the structure of intra-/inter-community links. Our results provide a theoretical justification for the proposed use of the model as a community-detection algorithm.
Somogyvári, Zoltán; Érdi, Péter
2017-07-01
The neural topodynamics theory of Tozzi et al. [13] has two main foci: metastable brain dynamics and the topological approach based on the Borsuk-Ulam theorem (BUT). Briefly, metastable brain dynamics theory hypothesizes that temporary stable synchronization and desynchronization of large number of individual dynamical systems, formed by local neural circuits, are responsible for coding of complex concepts in the brain and sudden changes of these synchronization patterns correspond to operational steps. But what dynamical network could form the substrate for this metastable dynamics, capable of entering into a combinatorially high number of metastable synchronization patterns and exhibit rapid transient changes between them? The general problem is related to the discrimination between ;Black Swans; and ;Dragon Kings;. While BSs are related to the theory of self-organized criticality, and suggests that high-impact extreme events are unpredictable, Dragon-kings are associated with the occurrence of a phase transition, whose emergent organization is based on intermittent criticality [9]. Widening the limits of predictability is one of the big open problems in the theory and practice of complex systems (Sect. 9.3 of Érdi [2]).
Altenbach, Christian; López, Carlos J; Hideg, Kálmán; Hubbell, Wayne L
2015-01-01
Structural and dynamical characterization of proteins is of central importance in understanding the mechanisms underlying their biological functions. Site-directed spin labeling (SDSL) combined with continuous-wave electron paramagnetic resonance (CW EPR) spectroscopy has shown the capability of providing this information with site-specific resolution under physiological conditions for proteins of any degree of complexity, including those associated with membranes. This chapter introduces methods commonly employed for SDSL and describes selected CW EPR-based methods that can be applied to (1) map secondary and tertiary protein structure, (2) determine membrane protein topology, (3) measure protein backbone flexibility, and (4) reveal the existence of conformational exchange at equilibrium.
Controlling Penguins : an estimate of penguin topologies contributing to the weak phase $\\phi$s.
AUTHOR|(INSPIRE)INSPIRE-00392811; Koppenburg, P.
The main focus of the current thesis is to provide the required ingredients for a high precision measurement of the weak phase φs. The latter is an important parameter related to CP violation, which, as explained throughout the current chapter, is related to the matter-antimatter asymmetry in the universe. Measuring φs enables one to look for de- viations from the established theory of elementary particles. Given the state of the art measurement of φs [1], it is clear that in order to probe potential deviations, φs needs to be measured with increased precision. However, entering this high precision regime one finds out that there are sub-leading contributions that need to be controlled first. Unless this is achieved, a high precision measurement of φs can not provide insight on possible deviations. While measuring φs is based on the analysis of B0s → J/ψφ decays, controlling these sub-leading contributions requires a different decay channel, like B0s → J/ψK∗0, which plays the role of a control ...
Design of Mott and topological phases on buckled 3d-oxide honeycomb lattices
Pentcheva, Rossitza
The honeycomb lattice, as realized e.g. in graphene, has rendered a robust platform for innovative science and potential applications. A much richer generalization of this lattice arises in (111)-oriented bilayers of perovskites, adding the complexity of the strongly correlated, multiorbital nature of electrons in transition metal oxides. Based on first principles calculations with an on-site Coulomb repulsion, here we provide trends in the evolution of ground states versus band filling in (111)-oriented (La XO3)2 /(LaAlO3)4 superlattices, with X spanning the entire 3d transition metal series. The competition between local quasi-cubic and global triangular symmetry triggers unanticipated broken symmetry phases, with mechanisms ranging from Jahn-Teller distortion, to charge-, spin-, and orbital-ordering. LaMnO3 and LaCoO3 bilayers, where spin-orbit coupling opens a sizable gap in the Dirac-point Fermi surface, emerge as much desired oxide-based Chern insulators, the latter displaying a gap capable of supporting room-temperature applications Further realizations of the honeycomb lattice and geometry patterns beyond the perovskite structure will be addressed. Research supported by the DFG, SFB/TR80.
Of topology and low-dimensionality
2016-11-01
The 2016 Nobel Prize in Physics has been awarded to David Thouless, Duncan Haldane and Michael Kosterlitz ``for theoretical discoveries of topological phase transitions and topological phases of matter''.
Grusdt, Fabian; Abanin, Dmitry; Demler, Eugene
2013-05-01
Recently experiments with ultracold atoms started to explore topological phases in 1D optical lattices. While transport measurements are challenging in these systems, ways to directly measure topological quantum numbers using a combination of Bloch oscillations and Ramsey interferometry have been explored (Atala et al., arXiv:1212.0572). In this talk I will present ways to measure the Z2 topological quantum numbers of two and three dimensional time-reversal invariant (TR) topological insulators. In this case non-Abelian Bloch oscillations can be combined with Ramsey interferometry to map out the topological properties of a given band-structure. Our method is very general and works even in the presence of accidental degeneracies. The applicability of the scheme is discussed for different theoretically proposed implementations of TR topological insulators using ultracold atoms. F. G. is grateful to Harvard University for hospitality and acknowledges financial support from Graduate School Materials Science in Mainz (MAINZ).
Using a Spreadsheet To Explore Melting, Dissolving and Phase Diagrams.
Goodwin, Alan
2002-01-01
Compares phase diagrams relating to the solubilities and melting points of various substances in textbooks with those generated by a spreadsheet using data from the literature. Argues that differences between the diagrams give rise to new chemical insights. (Author/MM)
Finite-Size and Composition-Driven Topological Phase Transition in (Bi1-xInx)2Se3 Thin Films.
Salehi, Maryam; Shapourian, Hassan; Koirala, Nikesh; Brahlek, Matthew J; Moon, Jisoo; Oh, Seongshik
2016-09-14
In a topological insulator (TI), if its spin-orbit coupling (SOC) strength is gradually reduced, the TI eventually transforms into a trivial insulator beyond a critical point of SOC, at which point the bulk gap closes: this is the standard description of the topological phase transition (TPT). However, this description of TPT, driven solely by the SOC (or something equivalent) and followed by closing and reopening of the bulk band gap, is valid only for infinite-size samples, and little is known how TPT occurs for finite-size samples. Here, using both systematic transport measurements on interface-engineered (Bi1-xInx)2Se3 thin films and theoretical simulations (with animations in the Supporting Information), we show that description of TPT in finite-size samples needs to be substantially modified from the conventional picture of TPT due to surface-state hybridization and bulk confinement effects. We also show that the finite-size TPT is composed of two separate transitions, topological-normal transition (TNT) and metal-insulator transition (MIT), by providing a detailed phase diagram in the two-dimensional phase space of sample size and SOC strength.
Parisi, Filippo; Sciascia, Luciana; Princivalle, Francesco; Merli, Marcello
2012-02-01
In order to characterize the pressure-induced decomposition of ringwoodite (γ-Mg2SiO4), the topological analysis of the electron density ρ( r), based upon the theory of atoms in molecules (AIM) developed by Bader in the framework of the catastrophe theory, has been performed. Calculations have been carried out by means of the ab initio CRYSTAL09 code at the HF/DFT level, using Hamiltonians based on the Becke- LYP scheme containing hybrid Hartree-Fock/density functional exchange-correlation terms. The equation of state at 0 K has been constructed for the three phases involved in the post-spinel phase transition (ringwoodite → Mg-perovskite + periclase) occurring at the transition zone-lower mantel boundary. The topological results show that the decomposition of the ringwoodite at high pressures is caused by a conflict catastrophe. Furthermore, topological evidences of the central role played by the oxygen atoms to facilitate the pressure-induced ringwoodite decomposition and the subsequent phase transition have been noticed.
Interactive Topology Optimization
Nobel-Jørgensen, Morten
software where the users are assumed to be well-educated both in the finite element method and topology optimization. This dissertation describes how various topology optimization methods have been used for creating cross-platform applications with high performance. The user interface design is based......Interactivity is the continuous interaction between the user and the application to solve a task. Topology optimization is the optimization of structures in order to improve stiffness or other objectives. The goal of the thesis is to explore how topology optimization can be used in applications...... in an interactive and intuitive way. By creating such applications with an intuitive and simple user interface we allow non-engineers like designers and architects to easily experiment with boundary conditions, design domains and other optimization settings. This is in contrast to commercial topology optimization...
2013-01-01
The chapter provides an introduction to the basic concepts of Algebraic Topology with an emphasis on motivation from applications in the physical sciences. It finishes with a brief review of computational work in algebraic topology, including persistent homology.
Momentum space topology of QCD
Zubkov, M A
2016-01-01
We discuss the possibility to consider quark matter as the topological material. In our consideration we concentrate on the hadronic phase (HP), on the quark - gluon plasma phase (QGP), and on the color - flavor locking (CFL) phase. In those phases we identify the relevant topological invariants in momentum space. The formalism is developed, which relates those invariants and massless fermions that reside on vortices and at the interphases. This formalism is illustrated by the example of vortices in the CFL phase.
Exploring first-order phase transitions with population annealing
Barash, Lev Yu.; Weigel, Martin; Shchur, Lev N.; Janke, Wolfhard
2017-03-01
Population annealing is a hybrid of sequential and Markov chain Monte Carlo methods geared towards the efficient parallel simulation of systems with complex free-energy landscapes. Systems with first-order phase transitions are among the problems in computational physics that are difficult to tackle with standard methods such as local-update simulations in the canonical ensemble, for example with the Metropolis algorithm. It is hence interesting to see whether such transitions can be more easily studied using population annealing. We report here our preliminary observations from population annealing runs for the two-dimensional Potts model with q > 4, where it undergoes a first-order transition.
Conducting state of GeTe by defect-induced topological insulating order
Kim, Jinwoong; Jhi, Seung-Hoon
2012-02-01
Topological insulating order protected by time-reversal symmetry is robust under structural disorder. Interestingly, recent studies on phase change materials like GeSbTe showed that their topological insulating order is sensitive to atomic stacking sequences. It was also shown that their structural phase transition is correlated with topological insulating order. GeTe, a well-known phase change material, is trivial insulator in its equilibrium structure. In this study, we discuss how atomic defects such as Ge tetrahedral defect observed in amorphous GeTe can change its topological insulating order based on first-principles calculations and model Hamiltonian. We also investigated the critical density of such tetrahedral defects to induce topological insulating order in GeTe. Our study will help explore hidden orders in GeTe.
Lin, Jian-Yu; Shen, Yi; Ding, Hang; Liu, Nan-Sheng; Lu, Xi-Yun
2017-01-01
We develop a robust cut-cell method for numerical simulation of compressible two-phase flows with topology change of the fluid-fluid interface. In cut cell methods the flows can be solved in the finite volume framework and the jump conditions at the interface are resolved by solving a local Riemann problem. Therefore, cut cell methods can obtain interface evolution with high resolution, and at the same time satisfactorily maintain the conservation of flow quantities. However, it remains a challenge for the cut cell methods to handle interfaces with topology change or very high curvature, where the mesh is not sufficiently fine to resolve the interface. Inappropriate treatment could give rise to either distorted interface advection or unphysical oscillation of flow variables, especially when the regularization process (e.g. reinitialization in the level set methods) is implemented. A robust cut-cell method is proposed here, with the interface being tracked by a level set function. The local unphysical oscillation of flow variables in the presence of topology change is shown to be greatly suppressed by using a delayed reinitialization. The method can achieve second-order accuracy with respect to the interface position in the absence of topology changes of interface, while locally degrading to first-order at the interface region where topology change occurs. Its performance is examined through a variety of numerical tests, such as Rayleigh collapse, shock-bubble interaction, and shock-induced bubble collapse in water. Numerical results are compared against either benchmark solutions or experimental observations, and good agreement has been achieved qualitatively and/or quantitatively. Finally, we apply the method to investigating the collapse process of two tandem bubbles in water.
Standard Model as the topological material
Volovik, G E
2016-01-01
Study of the Weyl and Dirac topological materials (topological semimetals, insulators, superfluids and superconductors) opens the route for the investigation of the topological quantum vacua of relativistic fields. The symmetric phase of the Standard Model (SM), where both electroweak and chiral symmetry are not broken, represents the topological semimetal. The vacua of the SM (and its extensions) in the phases with broken Electroweak symmetry represent the topological insulators of different types. We discuss in details the topological invariants in both symmetric and broken phases and establish their relation to the stability of vacuum.
Savcheva, Antonia; Tassev, Svetlin; DeLuca, Edward E.; Gibson, Sarah; Fan, Yuhong
2016-05-01
Knowledge of the 3D magnetic filed structure at the time of major solar eruptions is vital to the understanding of the space weather effects of these eruptions. Multiple data-constrained techniques that reconstruct the 3D coronal field based on photospheric magnetograms have been used to achieve this goal. In particular, we have used the flux rope insertion method to obtain the coronal magnetic field of multiple regions containing flux ropes or sheared arcades based on line-of-sight magnetograms and X-ray and EUV observations of coronal loops. For the purpose of developing statistical measures of the goodness of fit of these models to the observations, here we present our modeling of flux ropes based on synthetic magnetograms obtained from aFan & Gibson emerging flux rope simulation. The goal is to study the effect of of different input flux rope parameters on the geometry of currents, field line connectivity, and topology, in a controled setting. For this purpose we create a large grid of models with the flux rope insertion method with different combinations of axial and poloidal flux, which give us different morphology of the flux rope. We create synthetic images of these flux ropes in AIA passbands with the FORWARD forward-fitting code. The present parametric study will later be used to get a better handle on the initial condition for magnetofrictional and MHD simulations of observed regions containing flux ropes, such as sigmoids and polar-crown filaments.
Two Paths Diverged: Exploring Trajectories, Protocols, and Dynamic Phases
Gingrich, Todd Robert
-dimensional state space, the trajectory space may also be analytically studied using methods of large deviation theory. We review these methods and introduce a simple class of dynamical models whose dynamical fluctuations we compute exactly. The simplest such model is an asymmetric random walker on a one-dimensional ring with a single heterogeneous link connecting two sites of the ring. We derive conditions for the existence of a dynamic phase transition, which separates two dynamical phases---one localized and the other delocalized. The presence of distinct classes trajectories results in profoundly non-Gaussian fluctuations in dynamical quantities. We discuss the implications of such large dynamical fluctuations in the context of simple stochastic models for biological growth.
M. N. H. Khan
2015-03-01
Full Text Available The Photovoltaic (PV is a part and parcel and well known for cost-effective and easy to operatefeatures when it is used with transformer-less inverter-based grid-tied distribution generation systems. It reduces the leakage current issue that actually occurs making paths from PV penal to ground. In this paper has been addressed this issue as main problem for reducing leakage current. Moreover, here iscompared the proposed topology’s results to AC and DC-based transformer-less topologies. The possibilities of larger number of leakage current paths indicatepower loss, which is the focus of work in this paper for different switching conditions. The results on leakage current paths using PSpice with different parasitic capacitance values from inverters of different topologies are compared with the simulation results of the topology proposed in this paper.
Topological phononic insulator with robust pseudospin-dependent transport
Xia, Bai-Zhan; Liu, Ting-Ting; Huang, Guo-Liang; Dai, Hong-Qing; Jiao, Jun-Rui; Zang, Xian-Guo; Yu, De-Jie; Zheng, Sheng-Jie; Liu, Jian
2017-09-01
Topological phononic states, which facilitate unique acoustic transport around defects and disorders, have significantly revolutionized our scientific cognition of acoustic systems. Here, by introducing a zone folding mechanism, we realize the topological phase transition in a double Dirac cone of the rotatable triangular phononic crystal with C3 v symmetry. We then investigate the distinct topological edge states on two types of interfaces of our phononic insulators. The first one is a zigzag interface which simultaneously possesses a symmetric mode and an antisymmetric mode. Hybridization of the two modes leads to a robust pseudospin-dependent one-way propagation. The second one is a linear interface with a symmetric mode or an antisymmetric mode. The type of mode is dependent on the topological phase transition of the phononic insulators. Based on the rotatability of triangular phononic crystals, we consider several complicated contours defined by the topological zigzag interfaces. Along these contours, the acoustic waves can unimpededly transmit without backscattering. Our research develops a route for the exploration of the topological phenomena in experiments and provides an excellent framework for freely steering the acoustic backscattering-immune propagation within topological phononic structures.
Exploring phase space using smartphone acceleration and rotation sensors simultaneously
Monteiro, Martín; Cabeza, Cecilia; Martí, Arturo C.
2014-07-01
A paradigmatic physical system as the physical pendulum is experimentally studied using the acceleration and rotation (gyroscope) sensors available on smartphones and other devices such as iPads and tablets. A smartphone is fixed to the outside of a bicycle wheel whose axis is kept horizontal and fixed. The compound system, wheel plus smartphone, defines a physical pendulum which can rotate, giving full turns in one direction, or oscillate about the equilibrium position (performing either small or large oscillations). Measurements of the radial and tangential acceleration and the angular velocity obtained with smartphone sensors allow a deep insight into the dynamics of the system to be gained. In addition, thanks to the simultaneous use of the acceleration and rotation sensors, trajectories in the phase space are directly obtained. The coherence of the measures obtained with the different sensors and by traditional methods is remarkable. Indeed, due to their low cost and increasing availability, smartphone sensors are valuable tools that can be used in most undergraduate laboratories.
Computing the topological susceptibility from fixed topology QCD simulations
Dromard, Arthur; Cichy, Krzysztof; Wagner, Marc
2016-01-01
The topological susceptibility is an important quantity in QCD, which can be computed using lattice methods. However, at a fine lattice spacing, or when using high quality chirally symmetric quarks, algorithms which proceed in small update steps --- in particular the HMC algorithm --- tend to get stuck in a single topological sector. In such cases, the computation of the topological susceptibility is not straightforward. Here, we explore two methods to extract the topological susceptibility from lattice QCD simulations restricted to a single topological sector. The first method is based on the correlation function of the topological charge density, while the second method relies on measuring the topological charge within spacetime subvolumes. Numerical results for two-flavor QCD obtained by using both methods are presented.
Ezawa, Motohiko, E-mail: ezawa@ap.t.u-tokyo.ac.jp
2014-03-01
The Chern number is a genuine topological number. On the other hand, a symmetry protected topological (SPT) charge is a topological number only when a symmetry exists. We propose a formula for the SPT charge as a derivative of the Chern number in terms of the Green function in such a way that it is valid and related to the associated Hall current even when the symmetry is broken. We estimate the amount of deviation from the quantized value as a function of the strength of the broken symmetry. We present two examples. First, we consider Dirac electrons with the spin–orbit coupling on honeycomb lattice, where the SPT charges are given by the spin-Chern, valley-Chern and spin-valley-Chern numbers. Though the spin-Chern charge is not quantized in the presence of the Rashba coupling, the deviation is estimated to be 10{sup −7} in the case of silicene, a silicon cousin of graphene. Second, we analyze the effect of the mirror-symmetry breaking of the mirror-Chern number in a thin-film of topological crystalline insulator.
Liu, Xiong; Wang, Peng; Loh, Poh Chiang
2011-01-01
Single-phase stand-alone PV system is suitable for household applications in remote area. Hybrid battery/ultra-capacitor energy storage can reduce charge and discharge cycles and avoid deep discharges of battery. This paper proposes a compact seven switches structure for stand-alone PV system......, which otherwise needs nine switches configuration, inclusive of one switch for boost converter, four switches for single-phase inverter and four switches for two DC/DC converters of battery and ultra-capacitor. It is well-known that a bulky DC-link capacitor is always required to absorb second......-order harmonic current caused by single-phase inverter. In the proposed compact topology, a small size DC-link capacitor can achieve the same function through charging/discharging control of ultra-capacitor to mitigate second-order ripple current. Simulation results are provided to validate the effectiveness...
Carrander, Claes; Mousavi, Seyed Ali; Engdahl, G. öran
2017-02-01
In many transformer applications, it is necessary to have a core magnetization model that takes into account both magnetic and electrical effects. This becomes particularly important in three-phase transformers, where the zero-sequence impedance is generally high, and therefore affects the magnetization very strongly. In this paper, we demonstrate a time-step topological simulation method that uses a lumped-element approach to accurately model both the electrical and magnetic circuits. The simulation method is independent of the used hysteresis model. In this paper, a hysteresis model based on the first-order reversal-curve has been used.
Zloshchastiev, K G
1999-01-01
In the spirit of the well-known analogy between inviscid fluids and pseudo-Riemannian manifolds we study spherical thin shells in the static superfluid. Thin shells turn to be the interfaces dividing the superfluid into the pairs of domains, for instance, phases ``superfluid A - superfluid B'' or ``impurity - superfluid''. It is shown that such shells form the acoustic lenses. The exact equations of motion of the lens interfaces are obtained. Also we consider the quantum mechanical aspects, thereby energy spectra for bound states of the lenses are calculated taking into account the spatial topology of the black hole and wormhole type.
Goodman, Sue E
2009-01-01
Beginning Topology is designed to give undergraduate students a broad notion of the scope of topology in areas of point-set, geometric, combinatorial, differential, and algebraic topology, including an introduction to knot theory. A primary goal is to expose students to some recent research and to get them actively involved in learning. Exercises and open-ended projects are placed throughout the text, making it adaptable to seminar-style classes. The book starts with a chapter introducing the basic concepts of point-set topology, with examples chosen to captivate students' imaginations while i
Microscopic phase-space exploration modeling of $^{258}$Fm spontaneous fission
Tanimura, Yusuke; Ayik, Sakir
2016-01-01
We show that the total kinetic energy (TKE) of nuclei after the spontaneous fission of $^{258}$Fm can be well reproduced using simple assumptions on the quantum collective phase-space explored by the nucleus after passing the fission barrier. Assuming energy conservation and phase-space exploration according to the stochastic mean-field approach, a set of initial densities is generated. Each density is then evolved in time using the nuclear time-dependent density-functional theory. This approach goes beyond mean-field by allowing spontaneous symmetry breaking as well as a wider dynamical phase-space exploration leading to larger fluctuations in collective space. The total kinetic energy and mass distributions are calculated. New information on the fission process: fluctuations in scission time, strong correlation between TKE and collective deformation of daughter nuclei as well as pre- and post-scission particle emission, are obtained.
Topological Insulators in α-Graphyne
WANG Guo-Xiang; HOU Jing-Min
2013-01-01
In this paper,we investigate topological phases of α-graphyne with tight-binding method.By calculating the topological invariant Z2 and the edge states,we identify topological insulators.We present the phase diagrams of α-graphyne with different filling fractions as a function of spin-orbit interaction and the nearest-neighbor hopping energy.We find there exist topological insulators in α-graphyne.We analyze and discuss the characteristics of topological phases of α-graphyne.
The birth of topological insulators.
Moore, Joel E
2010-03-11
Certain insulators have exotic metallic states on their surfaces. These states are formed by topological effects that also render the electrons travelling on such surfaces insensitive to scattering by impurities. Such topological insulators may provide new routes to generating novel phases and particles, possibly finding uses in technological applications in spintronics and quantum computing.
Szczesniak, Pawel
2013-01-01
AC voltage frequency changes is one of the most important functions of solid state power converters. The most desirable features in frequency converters are the ability to generate load voltages with arbitrary amplitude and frequency, sinusoidal currents and voltages waveforms; the possibility of providing unity power factor for any load; and, finally, a simple and compact power circuit. Over the past decades, a number of different frequency converter topologies have appeared in the literature, but only the converters with either a voltage or current DC link are commonly used in industrial app
Topological nodal line semimetals
Fang, Chen; Weng, Hongming; Dai, Xi; Fang, Zhong
2016-11-01
We review the recent, mainly theoretical, progress in the study of topological nodal line semimetals in three dimensions. In these semimetals, the conduction and the valence bands cross each other along a one-dimensional curve in the three-dimensional Brillouin zone, and any perturbation that preserves a certain symmetry group (generated by either spatial symmetries or time-reversal symmetry) cannot remove this crossing line and open a full direct gap between the two bands. The nodal line(s) is hence topologically protected by the symmetry group, and can be associated with a topological invariant. In this review, (i) we enumerate the symmetry groups that may protect a topological nodal line; (ii) we write down the explicit form of the topological invariant for each of these symmetry groups in terms of the wave functions on the Fermi surface, establishing a topological classification; (iii) for certain classes, we review the proposals for the realization of these semimetals in real materials; (iv) we discuss different scenarios that when the protecting symmetry is broken, how a topological nodal line semimetal becomes Weyl semimetals, Dirac semimetals, and other topological phases; and (v) we discuss the possible physical effects accessible to experimental probes in these materials. Project partially supported by the National Key Research and Development Program of China (Grant Nos. 2016YFA0302400 and 2016YFA0300604), partially by the National Natural Science Foundation of China (Grant Nos. 11274359 and 11422428), the National Basic Research Program of China (Grant No. 2013CB921700), and the “Strategic Priority Research Program (B)” of the Chinese Academy of Sciences (Grant No. XDB07020100).
Zahid Hasan, M.; Hsieh, David; Xia, Yuqi; Wray, L. Andrew; Qian, Dong; Dil, J. Hugo; Meier, Fabian; Patthey, Luc; Osterwalder, Jurg; Fedorov, Alexei; Lin, Hsin; Bansil, Arun; Grauer, David; Hor, Yewsan; Cava, Robert
2010-03-01
The topological insulator is a fundamentally new state of quantum matter that exhibits exotic quantum-Hall-like behavior even in the absence of an applied magnetic field. In this talk, I will present new results on the topological insulator in Bi1-xSbx beyond Ref-[1,2], and then report our discovery and findings of a new generation of topological insulators with a single spin-helical surface Dirac cone that can be gated by chemical tuning of the surface [3,4,5]. A method would be discussed how superconducting and magnetic interactions [6] can be realized within the topological matrix. [1] ``A topological Dirac insulator in a quantum spin Hall phase'', D. Hsieh et al., Nature 452, 970 (2008). [2] ``Observation of unconventional quantum spin textures in topological insulators'', D. Hsieh et al., Science 323, 919 (2009). [3] ``Observation of a large-gap topologicalinsulator class with a single Dirac cone on the surface'', Y. Xia et al., Nature Phys. 5, 398 (2009). [4] D. Hsieh et al., Phys. Rev. Lett., 103, 146401 (2009). [5] ``A tunable topological insulator in the spin helical Dirac transport regime'', D. Hsieh et al., Nature 460, 1101 (2009). [6] Preprint (2009).
Topological phases and transitions in condensed matter systems%凝聚态材料中的拓扑相与拓扑相变--2016年诺贝尔物理学奖解读
戴希
2016-01-01
Two months ago, three physicists won the Nobel physics prize for their discov-ery of topological phases and transitions. In this paper, we review the origin of the concept of topol-ogy in condensed matter physics, then present a brief introduction to the main classes of topologi-cal states in solid-state materials, including topological insulators, the quantum anomalous Hall ef-fect, topological crystalline insulators, and topological semimetals.%凝聚态物理中拓扑相变和拓扑物态的发现，获得了2016年度诺贝尔物理学奖。文章系统介绍了凝聚态物理中拓扑性的起源，并简要介绍了目前凝聚态物理中发现的主要几类拓扑态：拓扑绝缘体、量子反常霍尔效应、拓扑晶体绝缘体和拓扑半金属。
QCD as topologically ordered system
Zhitnitsky, Ariel R
2013-01-01
We argue that QCD belongs to a topologically ordered phase similar to many well-known condensed matter systems with a gap such as topological insulators or superconductors. Our arguments are based on analysis of the so-called ``deformed QCD" which is a weakly coupled gauge theory, but nevertheless preserves all crucial elements of strongly interacting QCD, including confinement, nontrivial $\\theta$ dependence, degeneracy of the topological sectors, etc. Specifically, we construct the so-called topological ``BF" action which reproduces the well known infrared features of the theory such as non-dispersive contribution to the topological susceptibility which can not be associated with any propagating degrees of freedom. Furthermore, we interpret the well known resolution of the celebrated $U(1)_A$ problem when would be $\\eta'$ Goldstone boson generates its mass as a result of mixing of the Goldstone field with a topological auxiliary field characterizing the system. We identify the non-propagating auxiliary topo...
Buchstaber, Victor M
2015-01-01
This book is about toric topology, a new area of mathematics that emerged at the end of the 1990s on the border of equivariant topology, algebraic and symplectic geometry, combinatorics, and commutative algebra. It has quickly grown into a very active area with many links to other areas of mathematics, and continues to attract experts from different fields. The key players in toric topology are moment-angle manifolds, a class of manifolds with torus actions defined in combinatorial terms. Construction of moment-angle manifolds relates to combinatorial geometry and algebraic geometry of toric v
Pąk Karol
2015-02-01
Full Text Available Let us recall that a topological space M is a topological manifold if M is second-countable Hausdorff and locally Euclidean, i.e. each point has a neighborhood that is homeomorphic to an open ball of E n for some n. However, if we would like to consider a topological manifold with a boundary, we have to extend this definition. Therefore, we introduce here the concept of a locally Euclidean space that covers both cases (with and without a boundary, i.e. where each point has a neighborhood that is homeomorphic to a closed ball of En for some n.
Warner, S
1989-01-01
Aimed at those acquainted with basic point-set topology and algebra, this text goes up to the frontiers of current research in topological fields (more precisely, topological rings that algebraically are fields).The reader is given enough background to tackle the current literature without undue additional preparation. Many results not in the text (and many illustrations by example of theorems in the text) are included among the exercises. Sufficient hints for the solution of the exercises are offered so that solving them does not become a major research effort for the reader. A comprehensive bibliography completes the volume.
He, Cheng; Lin, Liang; Sun, Xiao-Chen; Liu, Xiao-Ping; Lu, Ming-Hui; Chen, Yan-Feng
2014-01-01
As exotic phenomena in optics, topological states in photonic crystals have drawn much attention due to their fundamental significance and great potential applications. Because of the broken time-reversal symmetry under the influence of an external magnetic field, the photonic crystals composed of magneto-optical materials will lead to the degeneracy lifting and show particular topological characters of energy bands. The upper and lower bulk bands have nonzero integer topological numbers. The gapless edge states can be realized to connect two bulk states. This topological photonic states originated from the topological property can be analogous to the integer quantum Hall effect in an electronic system. The gapless edge state only possesses a single sign of gradient in the whole Brillouin zone, and thus the group velocity is only in one direction leading to the one-way energy flow, which is robust to disorder and impurity due to the nontrivial topological nature of the corresponding electromagnetic states. Furthermore, this one-way edge state would cross the Brillouin center with nonzero group velocity, where the negative-zero-positive phase velocity can be used to realize some interesting phenomena such as tunneling and backward phase propagation. On the other hand, under the protection of time-reversal symmetry, a pair of gapless edge states can also be constructed by using magnetic-electric coupling meta-materials, exhibiting Fermion-like spin helix topological edge states, which can be regarded as an optical counterpart of topological insulator originating from the spin-orbit coupling. The aim of this article is to have a comprehensive review of recent research literatures published in this emerging field of photonic topological phenomena. Photonic topological states and their related phenomena are presented and analyzed, including the chiral edge states, polarization dependent transportation, unidirectional waveguide and nonreciprocal optical transmission, all
Mukherjee, Amiya
2015-01-01
This book presents a systematic and comprehensive account of the theory of differentiable manifolds and provides the necessary background for the use of fundamental differential topology tools. The text includes, in particular, the earlier works of Stephen Smale, for which he was awarded the Fields Medal. Explicitly, the topics covered are Thom transversality, Morse theory, theory of handle presentation, h-cobordism theorem, and the generalised Poincaré conjecture. The material is the outcome of lectures and seminars on various aspects of differentiable manifolds and differential topology given over the years at the Indian Statistical Institute in Calcutta, and at other universities throughout India. The book will appeal to graduate students and researchers interested in these topics. An elementary knowledge of linear algebra, general topology, multivariate calculus, analysis, and algebraic topology is recommended.
Gaitan, F.; Shenoy, S.R. [International Center for Theoretical Physics, P. O. Box 586, Miramare, 34100 Trieste (Italy)
1996-06-01
We examine the consequences of Berry{close_quote}s phase for the dynamics of Josephson junctions and junction arrays in which moving vortices are present. For both a large annular Josephson junction and a 2D junction array, Berry{close_quote}s phase produces a new current drive in the superconducting phase dynamics of these weak link systems. This Berry phase effect is shown to be physically inequivalent to a known effect in junction arrays associated with the Aharonov-Casher phase. {copyright} {ital 1996 The American Physical Society.}
Electronic properties of SnTe-class topological crystalline insulator materials
Wang, Jianfeng; Wang, Na; Huang, Huaqing; Duan, Wenhui
2016-11-01
The rise of topological insulators in recent years has broken new ground both in the conceptual cognition of condensed matter physics and the promising revolution of the electronic devices. It also stimulates the explorations of more topological states of matter. Topological crystalline insulator is a new topological phase, which combines the electronic topology and crystal symmetry together. In this article, we review the recent progress in the studies of SnTe-class topological crystalline insulator materials. Starting from the topological identifications in the aspects of the bulk topology, surface states calculations, and experimental observations, we present the electronic properties of topological crystalline insulators under various perturbations, including native defect, chemical doping, strain, and thickness-dependent confinement effects, and then discuss their unique quantum transport properties, such as valley-selective filtering and helicity-resolved functionalities for Dirac fermions. The rich properties and high tunability make SnTe-class materials promising candidates for novel quantum devices. Project supported by the Ministry of Science and Technology of China (Grant No. 2016YFA0301000) and the National Natural Science Foundation of China (Grant No. 11334006).
Experimental reconstruction of the Berry curvature in a topological Bloch band
Weitenberg, Christof; Flaeschner, Nick; Rem, Benno; Tarnowski, Matthias; Vogel, Dominik; Luehmann, Dirk-Soeren; Sengstock, Klaus
2016-05-01
Topological properties lie at the heart of many fascinating phenomena in solid state systems such as quantum Hall systems or Chern insulators. The topology can be captured by the distribution of Berry curvature, which describes the geometry of the eigenstates across the Brillouin zone. Employing fermionic ultracold atoms in a hexagonal optical lattice, we engineer the Berry curvature of the Bloch bands using resonant driving and measure it with full momentum resolution. Our results pave the way to explore intriguing phases of matter with interactions in topological band structures.
Hedayatrasa, Saeid; Uddin, Mohammad
2016-01-01
Optimized topology of bi-material acoustic metamaterial lattice plates is studied for maximized locally resonant bandgap of flexural guided waves. Optimized layout of the two relatively stiff and compliant material phases in the design domain is explored, free from any restrictions on the topology and shape of the relevant domains. Multiobjective optimization is performed through which maximized effective stiffness or minimized overall mass of the bandgap topology is additionally ensured. Extreme and selected intermediate optimized topologies of Pareto fronts are presented and their bandgap efficiencies and effective stiffness are compared. The bi-material constitution of selected topologies are further altered and modal band structure of resultant multilateral and porous designs are evaluated. Novel, core-shell like, locally resonant bandgaps are introduced. It is shown that how the bandgap efficiency and structural mass and/or stiffness can be optimized through optimized microstructural design of the matrix...
Majorana Fermions and Topology in Superconductors
Sato, Masatoshi; Fujimoto, Satoshi
2016-01-01
Topological superconductors are novel classes of quantum condensed phases, characterized by topologically nontrivial structures of Cooper pairing states. On the surfaces of samples and in vortex cores of topological superconductors, Majorana fermions, which are particles identified with their own anti-particles, appear as Bogoliubov quasiparticles. The existence and stability of Majorana fermions are ensured by bulk topological invariants constrained by the symmetries of the systems. Majorana...
Topological Properties of Spatial Coherence Function
REN Ji-Rong; ZHU Tao; DUAN Yi-Shi
2008-01-01
The topological properties of the spatial coherence function are investigated rigorously.The phase singular structures(coherence vortices)of coherence function can be naturally deduced from the topological current,which is an abstract mathematical object studied previously.We find that coherence vortices are characterized by the Hopf index and Brouwer degree in topology.The coherence flux quantization and the linking of the closed coherence vortices are also studied from the topological properties of the spatial coherence function.
Berry's phase for a spin 1/2 particle in the presence of topological defects
Carvalho, Josevi S. de; Passos, E.; Furtado, Claudio; Moraes, Fernando [Universidade Federal da Paraiba, Departamento de Fisica, CCEN, Joao Pessoa, PB (Brazil)
2008-10-15
The relativistic quantum dynamics of a spinorial quantum particle in the presence of a chiral conical background is investigated. We study the gravitational Berry geometric quantum phase acquired by a spin 1/2 particle in the chiral cosmic string spacetime. We obtain the result that this phase depends on the global features of this spacetime. We also consider the case that a string possesses an internal magnetic flux and obtain the geometric quantum phase in this case. The spacetime of multiple chiral cosmic strings is considered and the relativistic Berry quantum phase is also obtained. (orig.)
Lunar exploration phase III: Launch window and trajectory design for a lunar lander
Li, Jingyang; Yang, Hongwei; Baoyin, Hexi
2015-09-01
The lunar exploration phase III mission is a part of the China Aerospace Science and Technology Corporation's lunar exploration program that will perform a soft-landing and sample return from the Moon to test the key technologies that are required for human lunar missions. This paper focuses primarily on the trajectory design and orbital launch window generation for a lunar probe that are consistent with the constraints imposed by third phase of lunar exploration. Two categories of trajectories are explored: Earth-to-Moon and Moon-to-Earth. With the patched conic technique, the analytical and modified analytical models of the transfer trajectories are developed. The requirement of high-latitude landing for the return phase trajectory is considered in the modified model. By varying the initial input conditions and with a fast convergence iteration scheme, different characteristics of the transfer trajectory are generated. The orbital launch windows are established to study the mission sensitivities to time and fuel consumption and to provide a launch timetable that is compatible with this mission's requirements. The lunar surface stay time is analyzed for different conditions. The high-fidelity gravitational model is introduced to demonstrate the accuracy and convergence behavior of the analytical solution. The design method can also be used as a basis for the future human lunar missions.
M. R. McGillen
2007-02-01
Full Text Available The reactivity of aromatic compounds is of great relevance to pure and applied chemical disciplines, yet existing methods for estimating gas-phase rate coefficients for their reactions with free radicals lack accuracy and universality. Here a novel approach is taken, whereby strong relationships between rate coefficients of aromatic hydrocarbons and a Randić-type topological index are investigated, optimized and developed into a method which requires no specialist software or computing power.
Measured gas-phase rate coefficients for the reaction of aromatic hydrocarbons with OH radicals were correlated with a calculated Randić-type index, and optimized by including a term for side chain length. Although this method is exclusively for use with hydrocarbons, it is more diverse than any single existing methodology since it incorporates alkenylbenzenes into correlations, and can be extended towards other radical species such as O(^{3}P (and tentatively NO_{3}, H and Cl. A comparison (with species common to both techniques is made between the topological approach advocated here and a popular approach based on electrophilic subsituent constants, where it compares favourably.
A modelling study was carried out to assess the impact of using estimated rate coefficients as opposed to measured data in an atmospheric model. The difference in model output was negligible for a range of NO_{x} concentrations, which implies that this method has utility in complex chemical models.
Strong relationships (e.g.~for OH, R^{2} = 0.96 between seemingly diverse compounds including benzene, multisubstituted benzenes with saturated, unsaturated, aliphatic and cyclic substitutions and the nonbenzenoid aromatic, azulene suggests that the Randić-type index presented here represents a new and effective way of describing aromatic reactivity, based on a quantitative structure-activity relationship (QSAR.
M. R. McGillen
2007-07-01
Full Text Available The reactivity of aromatic compounds is of great relevance to pure and applied chemical disciplines, yet existing methods for estimating gas-phase rate coefficients for their reactions with free radicals lack accuracy and universality. Here a novel approach is taken, whereby strong relationships between rate coefficients of aromatic hydrocarbons and a Randić-type topological index are investigated, optimized and developed into a method which requires no specialist software or computing power.
Measured gas-phase rate coefficients for the reaction of aromatic hydrocarbons with OH radicals were correlated with a calculated Randić-type index, and optimized by including a term for side chain length. Although this method is exclusively for use with hydrocarbons, it is more diverse than any single existing methodology since it incorporates alkenylbenzenes into correlations, and can be extended towards other radical species such as O(^{3}P (and tentatively NO_{3}, H and Cl. A comparison (with species common to both techniques is made between the topological approach advocated here and a popular approach based on electrophilic subsituent constants, where it compares favourably.
A modelling study was carried out to assess the impact of using estimated rate coefficients as opposed to measured data in an atmospheric model. The difference in model output was negligible for a range of NO_{x} concentrations, which implies that this method has utility in complex chemical models.
Strong relationships (e.g. for OH, R^{2}=0.96 between seemingly diverse compounds including benzene, multisubstituted benzenes with saturated, unsaturated, aliphatic and cyclic substitutions and the nonbenzenoid aromatic, azulene suggests that the Randić-type index presented here represents a new and effective way of describing aromatic reactivity, based on a quantitative structure-activity relationship (QSAR.
Spin and topological order in a periodically driven spin chain
Russomanno, Angelo; Friedman, Bat-el; Dalla Torre, Emanuele G.
2017-07-01
The periodically driven quantum Ising chain has recently attracted a large attention in the context of Floquet engineering. In addition to the common paramagnet and ferromagnet, this driven model can give rise to new topological phases. In this work, we systematically explore its quantum phase diagram by examining the properties of its Floquet ground state. We specifically focus on driving protocols with time-reversal invariant points, and demonstrate the existence of an infinite number of distinct phases. These phases are separated by second-order quantum phase transitions, accompanied by continuous changes of local and string order parameters, as well as sudden changes of a topological winding number and of the number of protected edge states. When one of these phase transitions is adiabatically crossed, the correlator associated to the order parameter is nonvanishing over a length scale which shows a Kibble-Zurek scaling. In some phases, the Floquet ground state spontaneously breaks the discrete time-translation symmetry of the Hamiltonian. Our findings provide a better understanding of topological phases in periodically driven clean integrable models.
Franz, M; Tesanović, Z
2001-12-17
Within the phase fluctuation model for the pseudogap state of cuprate superconductors we identify a novel statistical "Berry phase" interaction between the nodal quasiparticles and fluctuating vortex-antivortex excitations. The effective action describing this model assumes the form of an anisotropic Euclidean quantum electrodynamics in (2+1) dimensions (QED (3)) and naturally generates non-Fermi liquid behavior for its fermionic excitations. The doping axis in the x -T phase diagram emerges as a quantum critical line which regulates the low energy fermiology.
Single stage single phase active power factor corrected Ĉuk Topology Based AC-DC Converter
Md. Ismail Hossain
2014-03-01
Full Text Available This paper focuses on the analysis of a power factor correction (PFC converter using close loop Ĉuk topology. Regardless of the input line voltage and output load variations, input current drawn by the buck or buck-boost converter is always discontinuous. The Boost converter suffers from high voltage stresses across the power electronic devices. The input current in Ĉuk converter is comparable to boost converter’s input current. In this paper output voltage is controlled by inner current and outer voltage control loop along with power factor correction (PFC. It shows less input current THD, nearly unity power factor and better output voltage regulation of AC-DC converter under variable input voltage and output load. In this paper the relative performance between normal diode rectifier, open loop Ĉuk rectifier and close loop Ĉuk rectifier is presented. An algorithm for implementing close loop Ĉuk rectifier in digital domain is developed and simulated.
A. Kristensen, Anders Schmidt; Damkilde, Lars
2007-01-01
. A way to solve the initial design problem namely finding a form can be solved by so-called topology optimization. The idea is to define a design region and an amount of material. The loads and supports are also fidefined, and the algorithm finds the optimal material distribution. The objective function...... dictates the form, and the designer can choose e.g. maximum stiness, maximum allowable stresses or maximum lowest eigenfrequency. The result of the topology optimization is a relatively coarse map of material layout. This design can be transferred to a CAD system and given the necessary geometrically...... refinements, and then remeshed and reanalysed in other to secure that the design requirements are met correctly. The output of standard topology optimization has seldom well-defined, sharp contours leaving the designer with a tedious interpretation, which often results in less optimal structures. In the paper...
Nourbakhsh, Z., E-mail: z.nourbakhsh@sci.ui.ac.ir; Faizi-Mohazzab, B.
2015-12-15
The structural, electronic and magnetic properties and existence of topological phase of Gd{sub x}Y{sub 1−x}PtBi (x=0, 0.25, 0.5, 0.75, 1) alloys are studied using density functional theory. The lattice constant and bulk modulus of these alloys in ferromagnetic phase are calculated using the generalized gradient approximation (GGA) in the presence of spin-orbit coupling. To investigate the electronic properties and existence of topological phase, the local density approximation (LDA), GGA and Engel–Vosko generalized gradient approximation (EV-GGA) are used. The electron density of states, band structure and topological band order of these alloys are investigated. Furthermore the variations of magnetic momentum, the linear coefficient of electronic specific heat and the band inversion strength with increase of x are investigated. - Highlights: • The Gd{sub x}Y{sub 1-x}PtBi alloys expect for x=0 have ferromagnetic phases. The lattice constants and bulk modulus are linear and non-linear function of x. • These alloys have an inverted band order and are candidates for topological semimetals. The band inversion strength has non-linear function of x. • The magnetic moment increases with increase of Gd composition and is a linear function of x.
Warner, S
1993-01-01
This text brings the reader to the frontiers of current research in topological rings. The exercises illustrate many results and theorems while a comprehensive bibliography is also included. The book is aimed at those readers acquainted with some very basic point-set topology and algebra, as normally presented in semester courses at the beginning graduate level or even at the advanced undergraduate level. Familiarity with Hausdorff, metric, compact and locally compact spaces and basic properties of continuous functions, also with groups, rings, fields, vector spaces and modules, and with Zorn''s Lemma, is also expected.
Arnold, Vladimir; Zorich, Anton
1999-01-01
This volume offers an account of the present state of the art in pseudoperiodic topology-a young branch of mathematics, born at the boundary between the ergodic theory of dynamical systems, topology, and number theory. Related topics include the theory of algorithms, convex integer polyhedra, Morse inequalities, real algebraic geometry, statistical physics, and algebraic number theory. The book contains many new results. Most of the articles contain brief surveys on the topics, making the volume accessible to a broad audience. From the Preface by V.I. Arnold: "The authors … have done much to s
Milewski, Emil G
2013-01-01
REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Topology includes an overview of elementary set theory, relations and functions, ordinals and cardinals, topological spaces, continuous functions, metric spaces and normed spaces, co
The Kodama state for topological quantum field theory beyond instantons
Cartas-Fuentevilla, R
2005-01-01
Constructing a symplectic structure that preserves the ordinary symmetries and the topological invariance for topological Yang-Mills theory, it is shown that the Kodama (Chern-Simons) state traditionally associated with a topological phase of unbroken diffeomorphism invariance for instantons, exists actually for the complete topological sector of the theory. The case of gravity is briefly discussed.
Exploring fluctuations and phase equilibria in fluid mixtures via Monte Carlo simulation
Denton, Alan R.; Schmidt, Michael P.
2013-03-01
Monte Carlo simulation provides a powerful tool for understanding and exploring thermodynamic phase equilibria in many-particle interacting systems. Among the most physically intuitive simulation methods is Gibbs ensemble Monte Carlo (GEMC), which allows direct computation of phase coexistence curves of model fluids by assigning each phase to its own simulation cell. When one or both of the phases can be modelled virtually via an analytic free energy function (Mehta and Kofke 1993 Mol. Phys. 79 39), the GEMC method takes on new pedagogical significance as an efficient means of analysing fluctuations and illuminating the statistical foundation of phase behaviour in finite systems. Here we extend this virtual GEMC method to binary fluid mixtures and demonstrate its implementation and instructional value with two applications: (1) a lattice model of simple mixtures and polymer blends and (2) a free-volume model of a complex mixture of colloids and polymers. We present algorithms for performing Monte Carlo trial moves in the virtual Gibbs ensemble, validate the method by computing fluid demixing phase diagrams, and analyse the dependence of fluctuations on system size. Our open-source simulation programs, coded in the platform-independent Java language, are suitable for use in classroom, tutorial, or computational laboratory settings.
Sotoodeh, Pedram
This dissertation presents the design of a novel multi-level inverter with FACTS capability for small to mid-size (10-20kW) permanent-magnet wind installations using modular multi-level converter (MMC) topology. The aim of the work is to design a new type of inverter with D-STATCOM option to provide utilities with more control on active and reactive power transfer of distribution lines. The inverter is placed between the renewable energy source, specifically a wind turbine, and the distribution grid in order to fix the power factor of the grid at a target value, regardless of wind speed, by regulating active and reactive power required by the grid. The inverter is capable of controlling active and reactive power by controlling the phase angle and modulation index, respectively. The unique contribution of the proposed work is to combine the two concepts of inverter and D-STATCOM using a novel voltage source converter (VSC) multi-level topology in a single unit without additional cost. Simulations of the proposed inverter, with 5 and 11 levels, have been conducted in MATLAB/Simulink for two systems including 20 kW/kVAR and 250 W/VAR. To validate the simulation results, a scaled version (250 kW/kVAR) of the proposed inverter with 5 and 11 levels has been built and tested in the laboratory. Experimental results show that the reduced-scale 5- and 11-level inverter is able to fix PF of the grid as well as being compatible with IEEE standards. Furthermore, total cost of the prototype models, which is one of the major objectives of this research, is comparable with market prices.
Stoyka, V.
2008-01-01
Full Text Available The relations between regimes of dynamic annealing, state of secondary particles system and the onset temperature of abnormal grain growth are investigated. Two distinguish types of Fe-3%Si grain-oriented steels, after one and two stage cold rolling, were studied. The second phase particles remain unaffected in first type of steel during the heat treatment. Vice versa, the increased density of second phases was observed after annealing in the second type of the investigated materials. It is shown that start/onset of abnormal grain growth strongly depends on both volume fraction of second phase particles and annealing temperature. Texture and magnetic properties of the investigated samples are investigated within the current study.
Theiss, P; Karpas, A; Wise, K S
1996-05-01
Antibodies to P29, a major lipid-modified surface protein of Mycoplasma fermentans, reveal phase variation of surface epitopes occurring with high frequency in clonal lineages of the organism. This occurs despite continuous expression of the entire epitope-bearing P29 product (detected by Western immunoblotting) and contrasts with phase variation of other surface antigens mediated by differential expression of proteins. To understand the structure and antigenic topology of P29, the single-copy p29 gene from strain PG18 was cloned and sequenced. The gene encodes a prolipoprotein containing a signal sequence predicted to be modified with lipid and cleaved at the N-terminal Cys-1 residue of the mature P29 lipoprotein. The remaining 218-residue hydrophilic sequence of P29 is predicted to be located external to the single plasma membrane. Additional Cys residues at positions 91 and 128 in the mature protein were shown to form a 36-residue disulfide loop by selectively labeling sulfhydryl groups that were liberated only after chemical reduction of monomeric P29. Two nearly identical charged amino acid sequences occurred in P29, within the disulfide loop and upstream of this structure. Two distinct epitopes binding different monoclonal antibodies were associated with opposite ends of the P29 protein, by mapping products expressed in Escherichia coli from PCR-generated 3' deletion mutations of the p29 gene. Each monoclonal antibody detected high-frequency and noncoordinate changes in accessibility of the corresponding epitopes in colony immunoblots of clonal variants, yet sequencing of the p29 gene from these variants and analysis of disulfide bonds revealed no associated changes in the primary sequence or disulfide loop structure of P29. These results suggest that P29 surface epitope variation may involve masking of selected regions of P29, possibly by other surface components undergoing phase variation by differential expression. Differential masking may be an important
Oliver, Bob; Pawałowski, Krzystof
1991-01-01
As part of the scientific activity in connection with the 70th birthday of the Adam Mickiewicz University in Poznan, an international conference on algebraic topology was held. In the resulting proceedings volume, the emphasis is on substantial survey papers, some presented at the conference, some written subsequently.
Bendsøe, Martin P.; Sigmund, Ole
2007-01-01
Taking as a starting point a design case for a compliant mechanism (a force inverter), the fundamental elements of topology optimization are described. The basis for the developments is a FEM format for this design problem and emphasis is given to the parameterization of design as a raster image...
Frank-Kamenetskii, Maxim D.
2013-01-01
A new variety on non-coding RNA has been discovered by several groups: circular RNA (circRNA). This discovery raises intriguing questions about the possibility of the existence of knotted RNA molecules and the existence of a new class of enzymes changing RNA topology, RNA topoisomerases.
Zhang, Min, E-mail: zmzmi1987@163.com; Liu, Ligang; Yang, Hui
2016-09-05
We report the observation of ferromagnetism in topological insulator Co{sub 0.08}Bi{sub 1.92}Se{sub 3} single crystal. The structural, magnetic, and microstructure properties of Co{sub 0.08}Bi{sub 1.92}Se{sub 3} are investigated. The existence of complicated ferromagnetic ordering, indicates the anomalous second ferromagnetic phase transition below 30 K. Well-defined ferromagnetic hysteresis in the magnetization was found in the sample. The origin of bulk ferromagnetism in Co{sub 0.08}Bi{sub 1.92}Se{sub 3} is concerned with three aspects: Co cluster, RKKY interactions, and the spin texture of Co impurities. - Highlights: • The bulk ferromagnetism have been found in the C{sub o0.08}Bi{sub 1.92}Se{sub 3} single crystal. • The anomalous second ferromagnetic phase transition is found below 30 K. • The origin of bulk ferromagnetism in Co{sub 0.08}Bi{sub 1.92}Se{sub 3} is concerned with three aspects.
Emergence of magnetic topological states in topological insulators doped with magnetic impurities
Tran, Minh-Tien; Nguyen, Hong-Son; Le, Duc-Anh
2016-04-01
Emergence of the topological invariant and the magnetic moment in topological insulators doped with magnetic impurities is studied based on a mutual cooperation between the spin-orbit coupling of electrons and the spin exchange of these electrons with magnetic impurity moments. The mutual cooperation is realized based on the Kane-Mele model in the presence of magnetic impurities. The topological invariants and the spontaneous magnetization are self-consistently determined within the dynamical mean-field theory. We find different magnetic topological phase transitions, depending on the electron filling. At half filling an antiferromagnetic topological insulator, which exhibits the quantum spin Hall effect, exists in the phase region between the paramagnetic topological insulator and the trivially topological antiferromagnetic insulator. At quarter and three-quarter fillings, a ferromagnetic topological insulator, which exhibits the quantum anomalous Hall effect, occurs in the strong spin-exchange regime.
Phase dependent sign changes of GABAergic synaptic input explored in-silicio and in-vitro.
Stiefel, Klaus M; Wespatat, Valérie; Gutkin, Boris; Tennigkeit, Frank; Singer, Wolf
2005-08-01
Inhibitory interactions play a crucial role in the synchronization of neuronal activity. Here we investigate the effect of GABAergic PSPs on spike timing in cortical neurons that exhibit an oscillatory modulation of their membrane potential. To this end we combined numerical simulations with in-vitro patch-clamp recordings from layer II/III pyramidal cells of the rat visual cortex. Special emphasis was placed on exploring how the reversal potential of the GABAergic synaptic currents (EGABA) and the phase relations of the PSPs relative to the oscillation cycles affect the timing of spikes riding on the depolarizing peaks of the oscillations. The simulations predicted: (1) With EGABA more negative than the oscillation minima PSPs are hyperpolarizing at all phases and thus delay or prevent spikes. (2) With EGABA being more positive than the oscillation maxima PSPs are depolarizing in a phase-independent way and lead to a phase advance of spikes. (3) In the intermediate case where EGABA lies within oscillation maxima and minima PSPs are either hyper- or depolarizing depending on their phase relations to the V(m) oscillations and can therefore either delay or advance spikes. Experiments conducted in this most interesting last configuration with biphasic PSPs agreed with the model predictions. Additional theoretical investigations revealed the effect of these PSP induced shifts in spike timing on synchronization in neuronal circuits. The results suggest that GABAergic mechanisms can assume highly specific timing functions in oscillatory networks.
Fracton topological order, generalized lattice gauge theory, and duality
Vijay, Sagar; Haah, Jeongwan; Fu, Liang
2016-12-01
We introduce a generalization of conventional lattice gauge theory to describe fracton topological phases, which are characterized by immobile, pointlike topological excitations, and subextensive topological degeneracy. We demonstrate a duality between fracton topological order and interacting spin systems with symmetries along extensive, lower-dimensional subsystems, which may be used to systematically search for and characterize fracton topological phases. Commutative algebra and elementary algebraic geometry provide an effective mathematical tool set for our results. Our work paves the way for identifying possible material realizations of fracton topological phases.
Large Chern-number topological superfluids in a coupled-layer system
Huang, Beibing; Chan, Chun Fai; Gong, Ming
2015-04-01
Large Chern-number topological phase is always an important topic in modern physics. Here we investigate the topological superfluids in a coupled-layer system, in which transitions between different topological superfluids can be realized by controlling the binding energy, interlayer tunneling, and layer asymmetry, etc. These topological transitions are characterized by energy gap closing and reopening at the critical points at zero momentum, where the Chern number and sign of Pfaffian undergo a discontinuous change. Topological protected edge modes at the boundaries are ensured by the bulk-edge correspondence. In a trapped potential the edge modes are spatially localized at the interfaces between distinct topological superfluids, where the number of edge modes is equal to the Chern-number difference between the left and right superfluids. These topological transitions can be detected by spin texture at or near zero momentum, which changes discretely across the critical points due to band inversion. The model can be generalized to a multilayer system in which the Chern number can be equal to any positive integer. These large Chern-number topological superfluids provide fertile grounds for exploring exotic quantum matters in the context of ultracold atoms.
Circuit topology of self-interacting chains: implications for folding and unfolding dynamics.
Mugler, Andrew; Tans, Sander J; Mashaghi, Alireza
2014-11-07
Understanding the relationship between molecular structure and folding is a central problem in disciplines ranging from biology to polymer physics and DNA origami. Topology can be a powerful tool to address this question. For a folded linear chain, the arrangement of intra-chain contacts is a topological property because rearranging the contacts requires discontinuous deformations. Conversely, the topology is preserved when continuously stretching the chain while maintaining the contact arrangement. Here we investigate how the folding and unfolding of linear chains with binary contacts is guided by the topology of contact arrangements. We formalize the topology by describing the relations between any two contacts in the structure, which for a linear chain can either be in parallel, in series, or crossing each other. We show that even when other determinants of folding rate such as contact order and size are kept constant, this 'circuit' topology determines folding kinetics. In particular, we find that the folding rate increases with the fractions of parallel and crossed relations. Moreover, we show how circuit topology constrains the conformational phase space explored during folding and unfolding: the number of forbidden unfolding transitions is found to increase with the fraction of parallel relations and to decrease with the fraction of series relations. Finally, we find that circuit topology influences whether distinct intermediate states are present, with crossed contacts being the key factor. The approach presented here can be more generally applied to questions on molecular dynamics, evolutionary biology, molecular engineering, and single-molecule biophysics.
Exploring phase transitions by finite-entanglement scaling of MPS in the 1D ANNNI model
Nagy, Adam
2011-02-01
We use the finite-entanglement scaling of infinite matrix product states (iMPS) to explore supposedly infinite order transitions. This universal method may have lower computational costs than finite-size scaling. To this end, we study possible MPS-based algorithms to find the ground states of the transverse axial next-nearest-neighbor Ising (ANNNI) model in a spin chain with first and second neighbor interactions and frustration. The ground state has four distinct phases with transitions of second order and one of supposedly infinite order, the Kosterlitz-Thouless transition. To explore phase transitions in the model, we study general quantities such as the correlation length, entanglement entropy and the second derivative of the energy with respect to the external field, and test the finite-entanglement scaling. We propose a scaling ansatz for the correlation length of a non-critical system in order to explore infinite order transitions. This method provides considerably less computational costs compared to the finite-size scaling method in [8], and quantities obtained by applying fixed boundary conditions (such as domain wall energy in [8]) are omitted. The results show good agreement with previous studies of finite-size scaling using DMRG.
Rendering the Topological Spines
Nieves-Rivera, D. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2015-05-05
Many tools to analyze and represent high dimensional data already exits yet most of them are not flexible, informative and intuitive enough to help the scientists make the corresponding analysis and predictions, understand the structure and complexity of scientific data, get a complete picture of it and explore a greater number of hypotheses. With this in mind, N-Dimensional Data Analysis and Visualization (ND²AV) is being developed to serve as an interactive visual analysis platform with the purpose of coupling together a number of these existing tools that range from statistics, machine learning, and data mining, with new techniques, in particular with new visualization approaches. My task is to create the rendering and implementation of a new concept called topological spines in order to extend ND²AV's scope. Other existing visualization tools create a representation preserving either the topological properties or the structural (geometric) ones because it is challenging to preserve them both simultaneously. Overcoming such challenge by creating a balance in between them, the topological spines are introduced as a new approach that aims to preserve them both. Its render using OpenGL and C++ and is currently being tested to further on be implemented on ND²AV. In this paper I will present what are the Topological Spines and how they are rendered.
He, Yuan-Yao; Wu, Han-Qing; Meng, Zi Yang; Lu, Zhong-Yi
2016-05-01
Topological phase transitions in free fermion systems can be characterized by the closing of single-particle gap and the change in topological invariants. However, in the presence of electronic interactions, topological phase transitions can be more complicated. In paper I of this series [Phys. Rev. B 93, 195163 (2016), 10.1103/PhysRevB.93.195163], we have proposed an efficient scheme to evaluate the topological invariants based on the single-particle Green's function formalism. Here, in paper II, we demonstrate several interaction-driven topological phase transitions (TPTs) in two-dimensional (2D) interacting topological insulators (TIs) via large-scale quantum Monte Carlo (QMC) simulations, based on the scheme of evaluating topological invariants presented in paper I. Across these transitions, the defining symmetries of the TIs have been neither explicitly nor spontaneously broken. In the first two models, the topological invariants calculated from the Green's function formalism succeed in characterizing the topologically distinct phases and identifying interaction-driven TPTs. However, in the other two models, we find that the single-particle gap does not close and the topological invariants constructed from the single-particle Green's function acquire no change across the TPTs. Unexpected breakdown of the Green's function formalism in constructing the topological invariants is thus discovered. We thence classify the topological phase transitions in interacting TIs into two categories in practical computation: Those that have noninteracting correspondence can be characterized successfully by the topological invariants constructed from the Green's functions, while for the others that do not have noninteracting correspondence, the Green's function formalism experiences a breakdown, but more interesting and exciting phenomena, such as emergent collective critical modes at the transition, arise. Discussion on the success and breakdown of topological invariants
Fomenko, Anatoly
2016-01-01
This classic text of the renowned Moscow mathematical school equips the aspiring mathematician with a solid grounding in the core of topology, from a homotopical perspective. Its comprehensiveness and depth of treatment are unmatched among topology textbooks: in addition to covering the basics—the fundamental notions and constructions of homotopy theory, covering spaces and the fundamental group, CW complexes, homology and cohomology, homological algebra—the book treats essential advanced topics, such as obstruction theory, characteristic classes, Steenrod squares, K-theory and cobordism theory, and, with distinctive thoroughness and lucidity, spectral sequences. The organization of the material around the major achievements of the golden era of topology—the Adams conjecture, Bott periodicity, the Hirzebruch–Riemann–Roch theorem, the Atiyah–Singer index theorem, to name a few—paints a clear picture of the canon of the subject. Grassmannians, loop spaces, and classical groups play a central role ...
Exploring novel phases of Cd-O system at ambient pressure
Zaoui, A.; Ferhat, M.
2017-02-01
First-principles evolutionary searches are used to explore stable Cd-O compounds at ambient pressure. Besides the well-known rock-salt CdO, a new cubic thermodynamically stable phase CdO2 with space group Pa3 and two metastable compounds: zinc-blende and wurtzite phases of CdO have been discovered at ambient pressure. Among these, CdO2 was successfully synthesized with perfect structural agreement to our theoretical predictions. The global stability of the well known rock-salt phase of CdO, our calculations of elastic constants and phonon dispersion curves demonstrate that the Pa3, zinc-blende and wurtzite structures are mechanically and dynamically stable. Finally, the state-of-the-art LDA-1/2 methods reveal that at ambient conditions, zinc-blende and wurtzite phases are semiconducting with a direct band gap (Γ- Γ) of 0.89 eV and 0.97 eV respectively; whereas the semiconducting cubic-Pa3 structure shows direct band gap (Γ- Γ) of ∼2.93 eV and an indirect band gap of ∼2.58 eV agreeing well with the experimental value of ∼2.4 eV.
Williams-Byrd, Julie; Antol, Jeff; Jefferies, Sharon; Goodliff, Kandyce; Williams, Phillip; Ambrose, Rob; Sylvester, Andre; Anderson, Molly; Dinsmore, Craig; Hoffman, Stephen; Lawrence, James; Seibert, Marc; Schier, Jim; Frank, Jeremy; Alexander, Leslie; Ruff, Gary; Soeder, Jim; Guinn, Joseph; Stafford, Matthew
2016-01-01
NASA is transforming human spaceflight. The Agency is shifting from an exploration-based program with human activities in low Earth orbit (LEO) and targeted robotic missions in deep space to a more sustainable and integrated pioneering approach. However, pioneering space involves daunting technical challenges of transportation, maintaining health, and enabling crew productivity for long durations in remote, hostile, and alien environments. Subject matter experts from NASA's Human Exploration and Operations Mission Directorate (HEOMD) are currently studying a human exploration campaign that involves deployment of assets for planetary exploration. This study, called the Evolvable Mars Campaign (EMC) study, explores options with solar electric propulsion as a central component of the transportation architecture. This particular in-space transportation option often results in long duration transit to destinations. The EMC study is also investigating deployed human rated systems like landers, habitats, rovers, power systems and ISRU system to the surface of Mars, which also will involve long dormant periods when these systems are staged on the surface. In order to enable the EMC architecture, campaign and element design leads along with system and capability development experts from HEOMD's System Maturation Team (SMT) have identified additional capabilities, systems and operation modes that will sustain these systems especially during these dormant phases of the mission. Dormancy is defined by the absence of crew and relative inactivity of the systems. For EMC missions, dormant periods could range from several months to several years. Two aspects of uncrewed dormant operations are considered herein: (1) the vehicle systems that are placed in a dormant state and (2) the autonomous vehicle systems and robotic capabilities that monitor, maintain, and repair the vehicle and systems. This paper describes the mission stages of dormancy operations, phases of dormant
Topology in the S U (Nf) chiral symmetry restored phase of unquenched QCD and axion cosmology. II.
Azcoiti, Vicente
2017-07-01
We investigate the physical consequences of the survival of the effects of the U (1 )A anomaly in the chiral symmetric phase of Q C D , and show that the free energy density is a singular function of the quark mass m , in the chiral limit, and that the σ and π ¯ susceptibilities diverge in this limit at any T ≥Tc. We also show that the difference between the π ¯ and δ ¯ susceptibilities diverges in the chiral limit at any T ≥Tc, a result which seems to be excluded by recent results of Tomiya et al. from numerical simulations of two-flavor QCD. We also discuss on the generalization of these results to the Nf≥3 model.
Merli, Marcello; Sciascia, Luciana
2013-06-01
In this work, the Bader's topological analysis of the electron density, coupled with Thom's catastrophe theory, was used to characterize the pressure-induced transformations in α-quartz. In particular, ab initio calculations of the α-quartz structures in the range 0-105 Gpa have been performed at the HF/DFT exchange-correlation terms level, using Hamiltonians based on a WC1LYP hybrid scheme. The electron densities calculated throughout the ab initio wave functions have been analysed by means of the Bader's theory, seeking for some catastrophic mechanism in the sense of Thom's theory. The analysis mainly showed that there is a typical fold catastrophe feature involving an O-O interaction at the quartz-coesite transition pressure, while the amorphization of α-quartz is coincident with an average distribution of the gradient field of the electron density around the oxygen atom which is typically observed in the free atoms. This approach is addressed to depict a phase transition from a novel viewpoint, particularly useful in predicting the stability of a compound at extreme conditions, especially in the absence of experimental data.
Gonnelli, R. S.; Daghero, D.; Tortello, M.; Ummarino, G. A.; Bukowski, Z.; Karpinski, J.; Reuvekamp, P. G.; Kremer, R. K.; Profeta, G.; Suzuki, K.; Kuroki, K.
2016-01-01
Iron-based compounds (IBS) display a surprising variety of superconducting properties that seems to arise from the strong sensitivity of these systems to tiny details of the lattice structure. In this respect, systems that become superconducting under pressure, like CaFe2As2, are of particular interest. Here we report on the first directional point-contact Andreev-reflection spectroscopy (PCARS) measurements on CaFe2As2 crystals under quasi-hydrostatic pressure, and on the interpretation of the results using a 3D model for Andreev reflection combined with ab-initio calculations of the Fermi surface (within the density functional theory) and of the order parameter symmetry (within a random-phase-approximation approach in a ten-orbital model). The almost perfect agreement between PCARS results at different pressures and theoretical predictions highlights the intimate connection between the changes in the lattice structure, a topological transition in the holelike Fermi surface sheet, and the emergence on the same sheet of an order parameter with a horizontal node line. PMID:27216477
Gonnelli, R. S.; Daghero, D.; Tortello, M.; Ummarino, G. A.; Bukowski, Z.; Karpinski, J.; Reuvekamp, P. G.; Kremer, R. K.; Profeta, G.; Suzuki, K.; Kuroki, K.
2016-05-01
Iron-based compounds (IBS) display a surprising variety of superconducting properties that seems to arise from the strong sensitivity of these systems to tiny details of the lattice structure. In this respect, systems that become superconducting under pressure, like CaFe2As2, are of particular interest. Here we report on the first directional point-contact Andreev-reflection spectroscopy (PCARS) measurements on CaFe2As2 crystals under quasi-hydrostatic pressure, and on the interpretation of the results using a 3D model for Andreev reflection combined with ab-initio calculations of the Fermi surface (within the density functional theory) and of the order parameter symmetry (within a random-phase-approximation approach in a ten-orbital model). The almost perfect agreement between PCARS results at different pressures and theoretical predictions highlights the intimate connection between the changes in the lattice structure, a topological transition in the holelike Fermi surface sheet, and the emergence on the same sheet of an order parameter with a horizontal node line.
Two-Phase Flow Technology Developed and Demonstrated for the Vision for Exploration
Sankovic, John M.; McQuillen, John B.; Lekan, Jack F.
2005-01-01
NASA s vision for exploration will once again expand the bounds of human presence in the universe with planned missions to the Moon and Mars. To attain the numerous goals of this vision, NASA will need to develop technologies in several areas, including advanced power-generation and thermal-control systems for spacecraft and life support. The development of these systems will have to be demonstrated prior to implementation to ensure safe and reliable operation in reduced-gravity environments. The Two-Phase Flow Facility (T(PHI) FFy) Project will provide the path to these enabling technologies for critical multiphase fluid products. The safety and reliability of future systems will be enhanced by addressing focused microgravity fluid physics issues associated with flow boiling, condensation, phase separation, and system stability, all of which are essential to exploration technology. The project--a multiyear effort initiated in 2004--will include concept development, normal-gravity testing (laboratories), reduced gravity aircraft flight campaigns (NASA s KC-135 and C-9 aircraft), space-flight experimentation (International Space Station), and model development. This project will be implemented by a team from the NASA Glenn Research Center, QSS Group, Inc., ZIN Technologies, Inc., and the Extramural Strategic Research Team composed of experts from academia.
Self-Organized Topological State with Majorana Fermions
Vazifeh, M. M.; Franz, M.
2013-11-01
Most physical systems known to date tend to resist entering the topological phase and must be fine-tuned to reach that phase. Here, we introduce a system in which a key dynamical parameter adjusts itself in response to the changing external conditions so that the ground state naturally favors the topological phase. The system consists of a quantum wire formed of individual magnetic atoms placed on the surface of an ordinary s-wave superconductor. It realizes the Kitaev paradigm of topological superconductivity when the wave vector characterizing the emergent spin helix dynamically self-tunes to support the topological phase. We call this phenomenon a self-organized topological state.
Analysis of phase space topologies for models of 4D betatronic motion in view of 4D beam splitting
Percival, Benjamin
2015-01-01
The novel technique of multiturn extraction is used to ll the Super Proton Synchrotron (SPS) at CERN with a high-intensity proton beam delivered by the Proton Synchrotron (PS). This technique involves manipulating nonlinear fields of sextupoles and octupoles in the PS to trap the beam into stable islands in the transverse phase space. By varying the tunes slowly and crossing a resonance condition it is possible to trap particles by means of stable structures. This generates a number of well-dened beamlets, which may be extracted over a number of turns proportional to the order of the resonance that is crossed and its stability. In this report, the theoretical background of how to construct the Normal Form of a 4D map incorporating a sextupolar and an octupolar eld contribution that act on a particle in our beam close to a 4th order difference resonance is detailed. A Hamiltonian will be analysed after transforming from a 4D to a 2D system using a canonical transformation, which allows us to visualise the isla...
Blok, Anders
2010-01-01
Climate change is quickly becoming a ubiquitous socionatural reality, mediating extremes of sociospatial scale from the bodily to the planetary. Although environmentalism invites us to ‘think globally and act locally', the meaning of these scalar designations remains ambiguous. This paper explores...... the topological presuppositions of social theory in the context of global climate change, asking how carbon emissions ‘translate' into various sociomaterial forms. Staging a meeting between Tim Ingold's phenomenology of globes and spheres and the social topologies of actor-network theory (ANT), the paper advances...... a ‘relational-scalar' analytics of spatial practices, technoscience, and power. As technoscience gradually constructs a networked global climate, this ‘grey box' comes to circulate within fluid social spaces, taking on new shades as it hybridizes knowledges, symbols, and practices. Global climates thus come...
Exploring the Phase Diagram SiO2-CO2 at High Pressures and Temperatures
Kavner, A.
2015-12-01
CO2 is an important volatile system relevant for planetary sciences and fundamental chemistry. Molecular CO2 has doubly bonded O=C=O units but high pressure-high temperature (HP-HT) studies have recently shown its transformation into a three-dimensional network of corner-linked [CO4] units analogous to the silica mineral polymorphs, through intermediate non-molecular phases. Here, we report P-V-T data on CO2-IV ice from time-of-flight neutron diffraction experiments, which allow determining the compressibility and thermal expansivity of this intermediate molecular-to-non-molecular phase.1 Aditionally, we have explored the SiO2-CO2 phase diagram and the potential formation of silicon carbonate compounds. New data obtained by laser-heating diamond-anvil experiments in CO2-filled microporous silica polymorphs will be shown. In particular, these HP-HT experiments explore the existence of potential CO2/SiO2 compounds with tetrahedrally-coordinated C/Si atoms by oxygens, which are predicted to be stable (or metastable) by state-of-the-art ab initio simulations.2,3 These theoretical predictions were supported by a recent study that reports the formation of a cristobalite-type Si0.4C0.6O2 solid solution at high-pressures and temperatures, which can be retained as a metastable solid down to ambient conditions.4 Entirely new families of structures could exist based on [CO4]4- units in various degrees of polymerisation, giving rise to a range of chain, sheet and framework solids like those found in silicate chemistry. References[1] S. Palaich et al., Am. Mineral. Submitted (2015) [2] A. Morales-Garcia et al., Theor. Chem. Acc. 132, 1308 (2013) [3] R. Zhou et al., Phys. Rev. X, 4, 011030 (2014) [4] M. Santoro et al. Nature Commun. 5, 3761 (2014)
Experimental Realizations of Magnetic Topological Insulator and Topological Crystalline Insulator
Xu, Suyang
2013-03-01
Over the past few years the experimental research on three-dimensional topological insulators have emerged as one of the most rapidly developing fields in condensed matter physics. In this talk, we report on two new developments in the field: The first part is on the dynamic interplay between ferromagnetism and the Z2 topological insulator state (leading to a magnetic topological insulator). We present our spin-resolved photoemission and magnetic dichroic experiments on MBE grown films where a hedgehog-like spin texture is revealed on the magnetically ordered surface of Mn-Bi2Se3 revealing a Berry's phase gradient in energy-momentum space of the crystal. A chemically/electrically tunable Berry's phase switch is further demonstrated via the tuning of the spin groundstate in Mn-Bi2Se3 revealed in our data (Nature Physics 8, 616 (2012)). The second part of this talk describes our experimental observation of a new topological phase of matter, namely a topological crystalline insulator where space group symmetries replace the role of time-reversal symmetry in an otherwise Z2 topological insulator predicted in theory. We experimentally investigate the possibility of a mirror symmetry protected topological phase transition in the Pb1-xSnxTe alloy system, which has long been known to contain an even number of band inversions based on band theory. Our experimental results show that at a composition below the theoretically predicted band inversion, the system is fully gapped, whereas in the band-inverted regime, the surface exhibits even number of spin-polarized Dirac cone states revealing mirror-protected topological order (Nature Communications 3, 1192 (2012)) distinct from that observed in Z2 topological insulators. We discuss future experimental possibilities opened up by these new developments in topological insulators research. This work is in collaboration with M. Neupane, C. Liu, N. Alidoust, I. Belopolski, D. Qian, D.M. Zhang, A. Richardella, A. Marcinkova, Q
Topologically nontrivial magnons at an interface of two kagome ferromagnets
Mook, Alexander; Henk, Jürgen; Mertig, Ingrid
2015-06-01
Magnon band structures of topological magnon insulators exhibit a nontrivial topology due to the Dzyaloshinskii-Moriya interaction, which manifests itself by topologically protected edge magnons. Bringing two topological magnon insulators into contact can lead to nontrivial unidirectional magnons located at their common interface. We study theoretically interfaces of semi-infinite kagome ferromagnets in various topological phases, with a focus on the formation and the confinement of nontrivial interface magnons. We analyze generic magnon dispersions with respect to the number of band gaps and the respective winding numbers. Eventually, we prove that interfaces of topologically identical phases can host nontrivial interface magnons as well.
Ekman, Ulrik
2015-01-01
This article discusses the issue of approaching the design of the ubiquitous city as a matter of topology. The general context here is the design of contemporary global urbanity in the form of u-cities, smart cities, or intelligent cities emerging with the second phase of network societies...... that increasingly develop mixed reality environments with context-aware out-of-the-box computing as well as the soci-ocultural and experiental horizon of a virtually and physically mobile citizenry. Design here must meet an ongoing and exceedingly complex interactivity among environmental, technical, social...... and personal multiplicities of urban nodes on the move. This chapter focuses on the design of a busy traffic intersection in the South Korean u-city Songdo. Hence, the discussion whether and how Songdo may be approached via design as topology primarily considers the situation, event, and experience in which...
Guillemin, Victor
2010-01-01
Differential Topology provides an elementary and intuitive introduction to the study of smooth manifolds. In the years since its first publication, Guillemin and Pollack's book has become a standard text on the subject. It is a jewel of mathematical exposition, judiciously picking exactly the right mixture of detail and generality to display the richness within. The text is mostly self-contained, requiring only undergraduate analysis and linear algebra. By relying on a unifying idea-transversality-the authors are able to avoid the use of big machinery or ad hoc techniques to establish the main
Transport signatures in topological systems coupled to ac fields
Ruocco, Leonard; Gómez-León, Álvaro
2017-02-01
We study the transport properties of a topological system coupled to an ac electric field by means of Floquet-Keldysh formalism. We consider a semi-infinite chain of dimers coupled to a semi-infinite metallic lead and obtain the density of states and current when the system is out of equilibrium. Our formalism is nonperturbative and allows us to explore, in the thermodynamic limit, a wide range of regimes for the ac field, arbitrary values of the coupling strength to the metallic contact and corrections to the wide-band limit (WBL). We find that hybridization with the contact can change the dimerization phase, and that the current dependence on the field amplitude can be used to discriminate between them. We also show the appearance of side bands and nonequilibrium zero-energy modes, characteristic of the Floquet systems. Our results directly apply to the stability of nonequilibrium topological phases, when transport measurements are used for their detection.
Probing topological protection using a designer surface plasmon structure
Gao, Fei; Gao, Zhen; Shi, Xihang; Yang, Zhaoju; Lin, Xiao; Xu, Hongyi; Joannopoulos, John D.; Soljačić, Marin; Chen, Hongsheng; Lu, Ling; Chong, Yidong; Zhang, Baile
2016-01-01
Topological photonic states, inspired by robust chiral edge states in topological insulators, have recently been demonstrated in a few photonic systems, including an array of coupled on-chip ring resonators at communication wavelengths. However, the intrinsic difference between electrons and photons determines that the ‘topological protection' in time-reversal-invariant photonic systems does not share the same robustness as its counterpart in electronic topological insulators. Here in a designer surface plasmon platform consisting of tunable metallic sub-wavelength structures, we construct photonic topological edge states and probe their robustness against a variety of defect classes, including some common time-reversal-invariant photonic defects that can break the topological protection, but do not exist in electronic topological insulators. This is also an experimental realization of anomalous Floquet topological edge states, whose topological phase cannot be predicted by the usual Chern number topological invariants. PMID:27197877
Dinnebier,R.; Vensky, S.; Jensen, M.; Hanson, J.
2005-01-01
The high-temperature phases of the alkali-metal oxalates M{sub 2}[C{sub 2}O{sub 4}] (M=K, Rb, Cs), and their decomposition products M{sub 2}[CO{sub 3}] (M=K, Rb, Cs), were investigated by fast, angle-dispersive X-ray powder diffraction with an image-plate detector, and also by simultaneous differential thermal analysis (DTA)/thermogravimetric analysis (TGA)/mass spectrometry (MS) and differential scanning calorimetry (DSC) techniques. The following phases, in order of decreasing temperature, were observed and crystallographically characterized (an asterisk denotes a previously unknown modification): *{alpha}-K{sub 2}[C{sub 2}O{sub 4}], *{alpha}-Rb{sub 2}[C{sub 2}O{sub 4}], *{alpha}-Cs{sub 2}[C{sub 2}O{sub 4}], {alpha}-K{sub 2}[CO{sub 3}], *{alpha}-Rb{sub 2}[CO{sub 3}], and *{alpha}-Cs{sub 2}[CO{sub 3}] in space group P6{sub 3}/mmc; *{beta}-Rb{sub 2}[C{sub 2}O{sub 4}], *{beta}-Cs{sub 2}[C{sub 2}O{sub 4}], *{beta}-Rb{sub 2}[CO{sub 3}], and *{beta}-Cs{sub 2}[CO{sub 3}] in Pnma; {gamma}-Rb{sub 2}[C{sub 2}O{sub 4}], {gamma}-Cs[C{sub 2}O{sub 4}], {gamma}-Rb{sub 2}[CO{sub 3}], and {gamma}-Cs{sub 2}[CO{sub 3}] in P2{sub 1}/c; and {delta}-K{sub 2}[C{sub 2}O{sub 4}] and {delta}-Rb{sub 2}[C{sub 2}O{sub 4}] in Pbam. With respect to the centers of gravity of the oxalate and carbonate anions, respectively, the crystal structures of all known alkali-metal oxalates and carbonates belong to the AlB{sub 2} family, and adopt either the AlB{sub 2} or the Ni{sub 2}In arrangement depending on the size of the cation and the temperature. Despite the different sizes and constitutions of the carbonate and oxalate anions, the high-temperature phases of the alkali-metal carbonates M{sub 2}[CO{sub 3}] (M=K, Rb, Cs), exhibit the same sequence of basic structures as the corresponding alkali-metal oxalates. The topological aspects and order-disorder phenomena at elevated temperature are discussed.
Topology of nonsymmorphic crystalline insulators and superconductors
Shiozaki, Ken; Sato, Masatoshi; Gomi, Kiyonori
2016-05-01
Topological classification in our previous paper [K. Shiozaki and M. Sato, Phys. Rev. B 90, 165114 (2014), 10.1103/PhysRevB.90.165114] is extended to nonsymmorphic crystalline insulators and superconductors. Using the twisted equivariant K theory, we complete the classification of topological crystalline insulators and superconductors in the presence of additional order-two nonsymmorphic space-group symmetries. The order-two nonsymmorphic space groups include half-lattice translation with Z2 flip, glide, twofold screw, and their magnetic space groups. We find that the topological periodic table shows modulo-2 periodicity in the number of flipped coordinates under the order-two nonsymmorphic space group. It is pointed out that the nonsymmorphic space groups allow Z2 topological phases even in the absence of time-reversal and/or particle-hole symmetries. Furthermore, the coexistence of the nonsymmorphic space group with time-reversal and/or particle-hole symmetries provides novel Z4 topological phases, which have not been realized in ordinary topological insulators and superconductors. We present model Hamiltonians of these new topological phases and analytic expressions of the Z2 and Z4 topological invariants. The half-lattice translation with Z2 spin flip and glide symmetry are compatible with the existence of boundaries, leading to topological surface gapless modes protected by the order-two nonsymmorphic symmetries. We also discuss unique features of these gapless surface modes.
Eid, Sameh; Saleh, Noureldin; Zalewski, Adam; Vedani, Angelo
2014-12-01
Carbohydrates play a key role in a variety of physiological and pathological processes and, hence, represent a rich source for the development of novel therapeutic agents. Being able to predict binding mode and binding affinity is an essential, yet lacking, aspect of the structure-based design of carbohydrate-based ligands. We assembled a diverse data set comprising 273 carbohydrate-protein crystal structures with known binding affinity and evaluated the prediction accuracy of a large collection of well-established scoring and free-energy functions, as well as combinations thereof. Unfortunately, the tested functions were not capable of reproducing binding affinities in the studied complexes. To simplify the complex free-energy surface of carbohydrate-protein systems, we classified the studied proteins according to the topology and solvent exposure of the carbohydrate-binding site into five distinct categories. A free-energy model based on the proposed classification scheme reproduced binding affinities in the carbohydrate data set with an r 2 of 0.71 and root-mean-squared-error of 1.25 kcal/mol ( N = 236). The improvement in model performance underlines the significance of the differences in the local micro-environments of carbohydrate-binding sites and demonstrates the usefulness of calibrating free-energy functions individually according to binding-site topology and solvent exposure.
Emerging Trends in Topological Insulators and Topological Superconductors
A M Jayannavar; Arijit Saha
2017-08-01
Topological insulators are new class of materials which arecharacterized by a bulk band gap like ordinary band insulatorsbut have protected conducting states on their edgesor surfaces. These states emerge due to the combination ofspin-orbit coupling and time reversal symmetry. Also, thesestates are insensitive to scattering by non-magnetic impurities.A two-dimensional topological insulator has one dimensionaledge states in which the spin-momentum locking ofthe electrons give rise to quantum spin Hall effect. A threedimensionaltopological insulator supports novel spin-polarized2D Dirac fermions on its surface. These topological insulatormaterials have been theoretically predicted and experimentallyobserved in a variety of 2D and 3D systems, includingHgTe quantum wells, BiSb alloys, and Bi2Te3, Bi2Se3 crystals.Moreover, proximity induced superconductivity in these systemscan lead to a state that supports zero energy Majoranafermions, and the phase is known as topological superconductors.In this article, the basic idea of topological insulatorsand topological superconductors are presented alongwith their experimental development.
Data Envelopment Analysis as a tool for the exploration phase of mining
Kauppinen, Tommi
2016-08-01
The exploration of mining has often been limited by time-consuming methods of analysis. This paper introduces Data Envelopment Analysis (DEA) as a new tool for the exploration phase of mining. DEA is a non-parametric method for data fusion, and it is used alongside with the on-site Raman analysis. Ten meters of halved rock drillcore from the Kittil mine (Suurikuusikko deposit) were pulverised and homogenised, thus ensuring that each meter had a representative sample. These 10 samples, one for each meter, were subsequently measured with a grid measurement (32×32 measurement each) using the Raman setup. All the data points were analysed using the point-count method. After identifying the frequency at which potentially valuable minerals appear in the samples, this information was analysed using DEA. The study ends by presenting an efficiency score for each meter of drillcore. These efficiency scores enable geologists to judge more rapidly which parts of the drillcore must be logged more carefully. In addition, Principal Component Analysis (PCA) is discussed as an alternative for producing similar results to DEA.
Peng, Chihan
2014-01-01
Here we presented a framework to explore quad mesh topologies. The core of our work is a systematic enumeration algorithm that can generate all possible quadrangular meshes inside a defined boundary with an upper limit of v3-v5 pairs. The algorithm is orders of magnitude more efficient than previous work. The combination of topological enumeration and shape-space exploration demonstrates that mesh topology has a powerful influence on geometry. The Fig. 18. A gallery of different quadrilateral meshes for a Shuriken. The quadrilaterals of the model were colored in a postprocess. Topological variations have distinctive, interesting patterns of mesh lines. © 2014 ACM 0730-0301/2014/01-ART3 15.00.
Margalef-Roig, J
1992-01-01
...there are reasons enough to warrant a coherent treatment of the main body of differential topology in the realm of Banach manifolds, which is at the same time correct and complete. This book fills the gap: whenever possible the manifolds treated are Banach manifolds with corners. Corners add to the complications and the authors have carefully fathomed the validity of all main results at corners. Even in finite dimensions some results at corners are more complete and better thought out here than elsewhere in the literature. The proofs are correct and with all details. I see this book as a reliable monograph of a well-defined subject; the possibility to fall back to it adds to the feeling of security when climbing in the more dangerous realms of infinite dimensional differential geometry. Peter W. Michor
Topological Varma superfluid in optical lattices
Liberto, M. Di; Hemmerich, A.; de Morais Smith, C.
2016-01-01
Topological states of matter are peculiar quantum phases showing different edge and bulk transport properties connected by the bulk-boundary correspondence. While non-interacting fermionic topological insulators are well established by now and have been classified according to a ten-fold scheme, the
Topological Photonics for Continuous Media
Silveirinha, Mario
Photonic crystals have revolutionized light-based technologies during the last three decades. Notably, it was recently discovered that the light propagation in photonic crystals may depend on some topological characteristics determined by the manner how the light states are mutually entangled. The usual topological classification of photonic crystals explores the fact that these structures are periodic. The periodicity is essential to ensure that the underlying wave vector space is a closed surface with no boundary. In this talk, we prove that it is possible calculate Chern invariants for a wide class of continuous bianisotropic electromagnetic media with no intrinsic periodicity. The nontrivial topology of the relevant continuous materials is linked with the emergence of edge states. Moreover, we will demonstrate that continuous photonic media with the time-reversal symmetry can be topologically characterized by a Z2 integer. This novel classification extends for the first time the theory of electronic topological insulators to a wide range of photonic platforms, and is expected to have an impact in the design of novel photonic systems that enable a topologically protected transport of optical energy. This work is supported in part by Fundacao para a Ciencia e a Tecnologia Grant Number PTDC/EEI-TEL/4543/2014.
Basic algebraic topology and its applications
Adhikari, Mahima Ranjan
2016-01-01
This book provides an accessible introduction to algebraic topology, a ﬁeld at the intersection of topology, geometry and algebra, together with its applications. Moreover, it covers several related topics that are in fact important in the overall scheme of algebraic topology. Comprising eighteen chapters and two appendices, the book integrates various concepts of algebraic topology, supported by examples, exercises, applications and historical notes. Primarily intended as a textbook, the book oﬀers a valuable resource for undergraduate, postgraduate and advanced mathematics students alike. Focusing more on the geometric than on algebraic aspects of the subject, as well as its natural development, the book conveys the basic language of modern algebraic topology by exploring homotopy, homology and cohomology theories, and examines a variety of spaces: spheres, projective spaces, classical groups and their quotient spaces, function spaces, polyhedra, topological groups, Lie groups and cell complexes, etc. T...
Saíz-Urra, Liane; Teijeira, Marta; Rivero-Buceta, Virginia; Helguera, Aliuska Morales; Celeiro, Maria; Terán, Ma Carmen; Besada, Pedro; Borges, Fernanda
2016-02-01
Adenosine regulates tissue function by activating four G-protein-coupled adenosine receptors (ARs). Selective agonists and antagonists for A3 ARs have been investigated for the treatment of a variety of immune disorders, cancer, brain, and heart ischemic conditions. We herein present a QSAR study based on a Topological sub-structural molecular design (TOPS-MODE) approach, intended to predict the A3 ARs of a diverse dataset of 124 (94 training set/ 30 prediction set) adenosine derivatives. The final model showed good fit and predictive capability, displaying 85.1 % of the experimental variance. The TOPS-MODE approach afforded a better understanding and interpretation of the developed model based on the useful information extracted from the analysis of the contribution of different molecular fragments to the affinity.
Recovery of Topological Order Induced by Random Perturbations
Tsomokos, D I; Castelnovo, C
2010-01-01
We analyze the toric code model in presence of quenched disorder, which is introduced via different types of random magnetic fields. Remarkably, we find that topological order can be robust against arbitrarily strong disorder. In general, close to a quantum phase transition between a spin polarized phase and a topologically ordered one, increasing the amount of disorder favors the topological phase. For some realizations of disorder, a quantum spin glass phase borders the topological phase, thus leading to a peculiar transition between two quantum spin liquids, which differ purely by nonlocal properties.
Jaksch, Katrin; Giese, Rüdiger; Kopf, Matthias
2010-05-01
In the case of drilling for deep reservoirs previous exploration is indispensable. In recent years the focus shifted more on geological structures like small layers or hydrothermal fault systems. Beside 2D- or 3D-seismics from the surface and seismic measurements like Vertical Seismic Profile (VSP) or Seismic While Drilling (SWD) within a borehole these methods cannot always resolute this structures. The resolution is worsen the deeper and smaller the sought-after structures are. So, potential horizons like small layers in oil exploration or fault zones usable for geothermal energy production could be failed or not identified while drilling. The application of a device to explore the geology with a high resolution ahead of the drill bit in direction of drilling would be of high importance. Such a device would allow adjusting the drilling path according to the real geology and would minimize the risk of discovery and hence the costs for drilling. Within the project SPWD a device for seismic exploration ahead of the drill bit will be developed. This device should allow the seismic exploration to predict areas about 50 to 100 meters ahead of the drill bit with a resolution of one meter. At the GFZ a first prototype consisting of different units for seismic sources, receivers and data loggers has been designed and manufactured. As seismic sources four standard magnetostrictive actuators and as receivers four 3-component-geophones are used. Every unit, actuator or geophone, can be rotated in steps of 15° around the longitudinal axis of the prototype to test different measurement configurations. The SPWD prototype emits signal frequencies of about 500 up to 5000 Hz which are significant higher than in VSP and SWD. An increased radiation of seismic wave energy in the direction of the borehole axis allows the view in areas to be drilled. Therefore, every actuator must be controlled independently of each other regarding to amplitude and phase of the source signal to
Photonic simulation of topological excitations in metamaterials.
Tan, Wei; Sun, Yong; Chen, Hong; Shen, Shun-Qing
2014-01-23
Condensed matter systems with topological order and metamaterials with left-handed chirality have attracted recently extensive interests in the fields of physics and optics. So far the topological order and chirality of electromagnetic wave are two independent concepts, and there is no work to address their connection. Here we propose to establish the relation between the topological order in condensed matter systems and the chirality in metamaterials, by mapping explicitly Maxwell's equations to the Dirac equation in one dimension. We report an experimental implement of the band inversion in the Dirac equation, which accompanies change of chirality of electromagnetic wave in metamaterials, and the first microwave measurement of topological excitations and topological phases in one dimension. Our finding provides a proof-of-principle example that electromagnetic wave in the metamaterials can be used to simulate the topological order in condensed matter systems and quantum phenomena in relativistic quantum mechanics in a controlled laboratory environment.
Iron-Based Superconductors as topological matter
Hu, Jiangping
We show the existence of non-trivial topological properties in Iron-based superconductors. Several examples are provided, including (1) the single layer FeSe grown on SrTiO3 substrate, in which an topological insulator phase exists due to the band inversion at M point; (2) CaFeAs2, a staggered intercalation compound that integrates both quantum spin hall and superconductivity in which the nontrivial topology stems from the chain-like As layers away from FeAs layers; (3) the Fe(Te,Se) thin films in which the nontrivial Z2 topological invariance originates from the parity exchange at Γ point that is controlled by the Te(Se) height; (4 nontrivial topology that is driven by the nematic order in FeSe. These results lay ground for integrating high Tc superconductivity with topological properties to realize new emergent phenomena, such as majorana particles, in iron-based high temperature superconductors
Nuclear Pasta: Topology and Defects
da Silva Schneider, Andre; Horowitz, Charles; Berry, Don; Caplan, Matt; Briggs, Christian
2015-04-01
A layer of complex non-uniform phases of matter known as nuclear pasta is expected to exist at the base of the crust of neutron stars. Using large scale molecular dynamics we study the topology of some pasta shapes, the formation of defects and how these may affect properties of neutron star crusts.
Kraft, S.; Bézy, J.-L.; Del Bello, U.; Berlich, R.; Drusch, M.; Franco, R.; Gabriele, A.; Harnisch, B.; Meynart, R.; Silvestrin, P.
2013-10-01
The Fluorescence Explorer (FLEX) mission is currently subject to feasibility (Phase A) study as one of the two candidates of ESA's 8th Earth Explorer opportunity mission. The FLuORescence Imaging Spectrometer (FLORIS) will be an imaging grating spectrometer onboard of a medium sized satellite flying in tandem with Sentinel-3 in a Sun synchronous orbit at a height of about 815 km. FLORIS will observe vegetation fluorescence and reflectance within a spectral range between 500 nm and 780 nm. It will thereby cover the photochemical reflection features between 500 nm and 600 nm, the Chlorophyll absorption band between 600 and 677 nm, and the red-edge in the region from 697 nm to 755 nm being located between the Oxygen A and B absorption bands. By this measurement approach, it is expected that the full spectrum and amount of the vegetation fluorescence radiance can be retrieved, and that atmospheric corrections can efficiently be applied. FLORIS will measure Earth reflected spectral radiance at a relatively high spectral resolution of ~0.3 nm around the Oxygen absorption bands. Other spectral band areas with less pronounced absorption features will be measured at medium spectral resolution between 0.5 and 2 nm. FLORIS will provide imagery at 300 m resolution on ground with a swath width of 150 km. This will allow achieving global revisit times of less than one month so as to monitor seasonal variations of the vegetation cycles. The mission life time is expected to be at least 4 years. The fluorescence retrieval will make use of information coming from OLCI and SLSTR, which are onboard of Sentinel-3, to monitor temperature, to detect thin clouds and to derive vegetation reflectance and information on the aerosol content also outside the FLORIS spectral range. In order to mitigate the technological and programmatic risk of this Explorer mission candidate, ESA has initiated two comprehensive bread-boarding activities, in which the most critical technologies and instrument