Statistical Mechanics of the Geometric Control of Flow Topology in Two-Dimensional Turbulence

Science.gov (United States)

Nadiga, Balasubramanya; Loxley, Peter

2013-04-01

We apply the principle of maximum entropy to two dimensional turbulence in a new fashion to predict the effect of geometry on flow topology. We consider two prototypical regimes of turbulence that lead to frequently observed self-organized coherent structures. Our theory predicts bistable behavior that exhibits hysteresis and large abrupt changes in flow topology in one regime; the other regime is predicted to exhibit monstable behavior with a continuous change of flow topology. The predictions are confirmed in fully nonlinear numerical simulations of the two-dimensional Navier-Stokes equation. These results suggest an explanation of the low frequency regime transitions that have been observed in the non-equilibrium setting of this problem. Following further development in the non-equilibrium context, we expect that insights developed in this problem should be useful in developing a better understanding of the phenomenon of low frequency regime transitions that is a pervasive feature of the weather and climate systems. Familiar occurrences of this phenomenon---wherein extreme and abrupt qualitative changes occur, seemingly randomly, after very long periods of apparent stability---include blocking in the extra-tropical winter atmosphere, the bimodality of the Kuroshio extension system, the Dansgaard-Oeschger events, and the glacial-interglacial transitions.

Topology optimization for coated structures

DEFF Research Database (Denmark)

Clausen, Anders; Andreassen, Erik; Sigmund, Ole

2015-01-01

This paper presents new results within the design of three-dimensional (3D) coated structures using topology optimization.The work is an extension of a recently published two-dimensional (2D) method for including coatedstructures into the minimum compliance topology optimization problem. The high...... level of control over key parameters demonstrated for the 2D model can likewise be achieved in 3D. The effectiveness of the approach isdemonstrated with numerical examples, which for the 3D problems have been solved using a parallel topology optimization implementation based on the PETSc toolkit....

Topological origin of edge states in two-dimensional inversion-symmetric insulators and semimetals

NARCIS (Netherlands)

Miert, Guido van|info:eu-repo/dai/nl/413490378; Ortix, Carmine|info:eu-repo/dai/nl/413315304; de Morais Smith, C.|info:eu-repo/dai/nl/304836346

2017-01-01

Symmetries play an essential role in identifying and characterizing topological states of matter. Here, we classify topologically two-dimensional (2D) insulators and semimetals with vanishing spin-orbit coupling using time-reversal ($\\mathcal{T}$) and inversion ($\\mathcal{I}$) symmetry. This allows

The topology of large-scale structure. V - Two-dimensional topology of sky maps

Science.gov (United States)

Gott, J. R., III; Mao, Shude; Park, Changbom; Lahav, Ofer

1992-01-01

A 2D algorithm is applied to observed sky maps and numerical simulations. It is found that when topology is studied on smoothing scales larger than the correlation length, the topology is approximately in agreement with the random phase formula for the 2D genus-threshold density relation, G2(nu) varies as nu(e) exp-nu-squared/2. Some samples show small 'meatball shifts' similar to those seen in corresponding 3D observational samples and similar to those produced by biasing in cold dark matter simulations. The observational results are thus consistent with the standard model in which the structure in the universe today has grown from small fluctuations caused by random quantum noise in the early universe.

Topologically protected states in one-dimensional systems

CERN Document Server

Fefferman, C L; Weinstein, M I

2017-01-01

The authors study a class of periodic Schrödinger operators, which in distinguished cases can be proved to have linear band-crossings or "Dirac points". They then show that the introduction of an "edge", via adiabatic modulation of these periodic potentials by a domain wall, results in the bifurcation of spatially localized "edge states". These bound states are associated with the topologically protected zero-energy mode of an asymptotic one-dimensional Dirac operator. The authors' model captures many aspects of the phenomenon of topologically protected edge states for two-dimensional bulk structures such as the honeycomb structure of graphene. The states the authors construct can be realized as highly robust TM-electromagnetic modes for a class of photonic waveguides with a phase-defect.

Two-dimensional ferroelectric topological insulators in functionalized atomically thin bismuth layers

Science.gov (United States)

Kou, Liangzhi; Fu, Huixia; Ma, Yandong; Yan, Binghai; Liao, Ting; Du, Aijun; Chen, Changfeng

2018-02-01

We introduce a class of two-dimensional (2D) materials that possess coexisting ferroelectric and topologically insulating orders. Such ferroelectric topological insulators (FETIs) occur in noncentrosymmetric atomic layer structures with strong spin-orbit coupling (SOC). We showcase a prototype 2D FETI in an atomically thin bismuth layer functionalized by C H2OH , which exhibits a large ferroelectric polarization that is switchable by a ligand molecule rotation mechanism and a strong SOC that drives a band inversion leading to the topologically insulating state. An external electric field that switches the ferroelectric polarization also tunes the spin texture in the underlying atomic lattice. Moreover, the functionalized bismuth layer exhibits an additional quantum order driven by the valley splitting at the K and K' points in the Brillouin zone stemming from the symmetry breaking and strong SOC in the system, resulting in a remarkable state of matter with the simultaneous presence of the quantum spin Hall and quantum valley Hall effect. These phenomena are predicted to exist in other similarly constructed 2D FETIs, thereby offering a unique quantum material platform for discovering novel physics and exploring innovative applications.

Lagrangian statistics and flow topology in forced two-dimensional turbulence.

Science.gov (United States)

Kadoch, B; Del-Castillo-Negrete, D; Bos, W J T; Schneider, K

2011-03-01

A study of the relationship between Lagrangian statistics and flow topology in fluid turbulence is presented. The topology is characterized using the Weiss criterion, which provides a conceptually simple tool to partition the flow into topologically different regions: elliptic (vortex dominated), hyperbolic (deformation dominated), and intermediate (turbulent background). The flow corresponds to forced two-dimensional Navier-Stokes turbulence in doubly periodic and circular bounded domains, the latter with no-slip boundary conditions. In the double periodic domain, the probability density function (pdf) of the Weiss field exhibits a negative skewness consistent with the fact that in periodic domains the flow is dominated by coherent vortex structures. On the other hand, in the circular domain, the elliptic and hyperbolic regions seem to be statistically similar. We follow a Lagrangian approach and obtain the statistics by tracking large ensembles of passively advected tracers. The pdfs of residence time in the topologically different regions are computed introducing the Lagrangian Weiss field, i.e., the Weiss field computed along the particles' trajectories. In elliptic and hyperbolic regions, the pdfs of the residence time have self-similar algebraic decaying tails. In contrast, in the intermediate regions the pdf has exponential decaying tails. The conditional pdfs (with respect to the flow topology) of the Lagrangian velocity exhibit Gaussian-like behavior in the periodic and in the bounded domains. In contrast to the freely decaying turbulence case, the conditional pdfs of the Lagrangian acceleration in forced turbulence show a comparable level of intermittency in both the periodic and the bounded domains. The conditional pdfs of the Lagrangian curvature are characterized, in all cases, by self-similar power-law behavior with a decay exponent of order -2.

Interplay between topology and disorder in a two-dimensional semi-Dirac material

Science.gov (United States)

Sriluckshmy, P. V.; Saha, Kush; Moessner, Roderich

2018-01-01

We investigate the role of disorder in a two-dimensional semi-Dirac material characterized by a linear dispersion in one direction and a parabolic dispersion in the orthogonal direction. Using the self-consistent Born approximation, we show that disorder can drive a topological Lifshitz transition from an insulator to a semimetal, as it generates a momentum-independent off-diagonal contribution to the self-energy. Breaking time-reversal symmetry enriches the topological phase diagram with three distinct regimes—single-node trivial, two-node trivial, and two-node Chern. We find that disorder can drive topological transitions from both the single- and two-node trivial to the two-node Chern regime. We further analyze these transitions in an appropriate tight-binding Hamiltonian of an anisotropic hexagonal lattice by calculating the real-space Chern number. Additionally, we compute the disorder-averaged entanglement entropy which signals both the topological Lifshitz and Chern transition as a function of the anisotropy of the hexagonal lattice. Finally, we discuss experimental aspects of our results.

Unconventional Topological Phase Transition in Two-Dimensional Systems with Space-Time Inversion Symmetry

Science.gov (United States)

Ahn, Junyeong; Yang, Bohm-Jung

2017-04-01

We study a topological phase transition between a normal insulator and a quantum spin Hall insulator in two-dimensional (2D) systems with time-reversal and twofold rotation symmetries. Contrary to the case of ordinary time-reversal invariant systems, where a direct transition between two insulators is generally predicted, we find that the topological phase transition in systems with an additional twofold rotation symmetry is mediated by an emergent stable 2D Weyl semimetal phase between two insulators. Here the central role is played by the so-called space-time inversion symmetry, the combination of time-reversal and twofold rotation symmetries, which guarantees the quantization of the Berry phase around a 2D Weyl point even in the presence of strong spin-orbit coupling. Pair creation and pair annihilation of Weyl points accompanying partner exchange between different pairs induces a jump of a 2D Z2 topological invariant leading to a topological phase transition. According to our theory, the topological phase transition in HgTe /CdTe quantum well structure is mediated by a stable 2D Weyl semimetal phase because the quantum well, lacking inversion symmetry intrinsically, has twofold rotation about the growth direction. Namely, the HgTe /CdTe quantum well can show 2D Weyl semimetallic behavior within a small but finite interval in the thickness of HgTe layers between a normal insulator and a quantum spin Hall insulator. We also propose that few-layer black phosphorus under perpendicular electric field is another candidate system to observe the unconventional topological phase transition mechanism accompanied by the emerging 2D Weyl semimetal phase protected by space-time inversion symmetry.

Two dimensional topological insulator in quantizing magnetic fields

Science.gov (United States)

Olshanetsky, E. B.; Kvon, Z. D.; Gusev, G. M.; Mikhailov, N. N.; Dvoretsky, S. A.

2018-05-01

The effect of quantizing magnetic field on the electron transport is investigated in a two dimensional topological insulator (2D TI) based on a 8 nm (013) HgTe quantum well (QW). The local resistance behavior is indicative of a metal-insulator transition at B ≈ 6 T. On the whole the experimental data agrees with the theory according to which the helical edge states transport in a 2D TI persists from zero up to a critical magnetic field Bc after which a gap opens up in the 2D TI spectrum.

Electrically controlled band gap and topological phase transition in two-dimensional multilayer germanane

International Nuclear Information System (INIS)

Qi, Jingshan; Li, Xiao; Qian, Xiaofeng

2016-01-01

Electrically controlled band gap and topological electronic states are important for the next-generation topological quantum devices. In this letter, we study the electric field control of band gap and topological phase transitions in multilayer germanane. We find that although the monolayer and multilayer germananes are normal insulators, a vertical electric field can significantly reduce the band gap of multilayer germananes owing to the giant Stark effect. The decrease of band gap eventually leads to band inversion, transforming them into topological insulators with nontrivial Z_2 invariant. The electrically controlled topological phase transition in multilayer germananes provides a potential route to manipulate topologically protected edge states and design topological quantum devices. This strategy should be generally applicable to a broad range of materials, including other two-dimensional materials and ultrathin films with controlled growth.

Effect of static charge fluctuations on the conduction along the edge of two-dimensional topological insulator

Science.gov (United States)

Vayrynen, Jukka; Goldstein, Moshe; Glazman, Leonid

2013-03-01

Static charge disorder may create electron puddles in the bulk of a material which nominally is in the insulating state. A single puddle - quantum dot - coupled to the helical edge of a two-dimensional topological insulator enhances the electron backscattering within the edge. The backscattering rate increases with the electron dwelling time in the dot. While remaining inelastic, the backscattering off a dot may be far more effective than the proposed earlier inelastic processes involving a local scatterer with no internal structure. We find the temperature dependence of the dot-induced correction to the universal conductance of the edge. In addition to the single-dot effect, we calculate the classical temperature-independent conductance correction caused by a weakly conducting bulk. We use our theory to assess the effect of static charge fluctuations in a heterostructure on the edge electron transport in a two-dimensional topological insulator. The work at Yale University is supported by NSF DMR Grant No. 1206612 and the Simons Foundation.

Interplay between topology and disorder in a two-dimensional semi-Dirac material

OpenAIRE

Sriluckshmy, P. V.; Saha, Kush; Moessner, Roderich

2017-01-01

We investigate the role of disorder in a two-dimensional semi-Dirac material characterized by a linear dispersion in one, and a parabolic dispersion in the orthogonal, direction. Using the self-consistent Born approximation, we show that disorder can drive a topological Lifshitz transition from an insulator to a semi-metal, as it generates a momentum independent off-diagonal contribution to the self-energy. Breaking time-reversal symmetry enriches the topological phase diagram with three dist...

All-electric spin modulator based on a two-dimensional topological insulator

Energy Technology Data Exchange (ETDEWEB)

Xiao, Xianbo; Ai, Guoping [School of Computer Science, Jiangxi University of Traditional Chinese Medicine, Nanchang 330004 (China); Liu, Ying; Yang, Shengyuan A., E-mail: shengyuan-yang@sutd.edu.sg [Research Laboratory for Quantum Materials, Singapore University of Technology and Design, Singapore 487372 (Singapore); Liu, Zhengfang [School of Science, East China Jiaotong University, Nanchang 330013 (China); Zhou, Guanghui, E-mail: ghzhou@hunnu.edu.cn [Key Laboratory for Low-Dimensional Structures and Quantum Manipulation (Ministry of Education), and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha 410081 (China)

2016-01-18

We propose and investigate a spin modulator device consisting of two ferromagnetic leads connected by a two-dimensional topological insulator as the channel material. It exploits the unique features of the topological spin-helical edge states, such that the injected carriers with a non-collinear spin-polarization direction would travel through both edges and show interference effect. The conductance of the device can be controlled in a simple and all-electric manner by a side-gate voltage, which effectively rotates the spin-polarization of the carrier. At low voltages, the rotation angle is linear in the gate voltage, and the device can function as a good spin-polarization rotator by replacing the drain electrode with a non-magnetic material.

Pseudogap and Fermi-Surface Topology in the Two-Dimensional Hubbard Model

Science.gov (United States)

Wu, Wei; Scheurer, Mathias S.; Chatterjee, Shubhayu; Sachdev, Subir; Georges, Antoine; Ferrero, Michel

2018-04-01

One of the distinctive features of hole-doped cuprate superconductors is the onset of a "pseudogap" below a temperature T* . Recent experiments suggest that there may be a connection between the existence of the pseudogap and the topology of the Fermi surface. Here, we address this issue by studying the two-dimensional Hubbard model with two distinct numerical methods. We find that the pseudogap only exists when the Fermi surface is holelike and that, for a broad range of parameters, its opening is concomitant with a Fermi-surface topology change from electronlike to holelike. We identify a common link between these observations: The polelike feature of the electronic self-energy associated with the formation of the pseudogap is found to also control the degree of particle-hole asymmetry, and hence the Fermi-surface topology transition. We interpret our results in the framework of an SU(2) gauge theory of fluctuating antiferromagnetism. We show that a mean-field treatment of this theory in a metallic state with U(1) topological order provides an explanation of this polelike feature and a good description of our numerical results. We discuss the relevance of our results to experiments on cuprates.

The non-commutative topology of two-dimensional dirty superconductors

Science.gov (United States)

De Nittis, Giuseppe; Schulz-Baldes, Hermann

2018-01-01

Non-commutative analysis tools have successfully been applied to the integer quantum Hall effect, in particular for a proof of the stability of the Hall conductance in an Anderson localization regime and of the bulk-boundary correspondence. In this work, these techniques are implemented to study two-dimensional dirty superconductors described by Bogoliubov-de Gennes Hamiltonians. After a thorough presentation of the basic framework and the topological invariants, Kubo formulas for the thermal, thermoelectric and spin Hall conductance are analyzed together with the corresponding edge currents.

Pseudo-time-reversal symmetry and topological edge states in two-dimensional acoustic crystals

KAUST Repository

Mei, Jun

2016-09-02

We propose a simple two-dimensional acoustic crystal to realize topologically protected edge states for acoustic waves. The acoustic crystal is composed of a triangular array of core-shell cylinders embedded in a water host. By utilizing the point group symmetry of two doubly degenerate eigenstates at the Î

Pseudo-time-reversal symmetry and topological edge states in two-dimensional acoustic crystals

KAUST Repository

Mei, Jun; Chen, Zeguo; Wu, Ying

2016-01-01

We propose a simple two-dimensional acoustic crystal to realize topologically protected edge states for acoustic waves. The acoustic crystal is composed of a triangular array of core-shell cylinders embedded in a water host. By utilizing the point group symmetry of two doubly degenerate eigenstates at the Î

Predicting a new phase (T'') of two-dimensional transition metal di-chalcogenides and strain-controlled topological phase transition

Science.gov (United States)

Ma, Fengxian; Gao, Guoping; Jiao, Yalong; Gu, Yuantong; Bilic, Ante; Zhang, Haijun; Chen, Zhongfang; Du, Aijun

2016-02-01

Single layered transition metal dichalcogenides have attracted tremendous research interest due to their structural phase diversities. By using a global optimization approach, we have discovered a new phase of transition metal dichalcogenides (labelled as T''), which is confirmed to be energetically, dynamically and kinetically stable by our first-principles calculations. The new T'' MoS2 phase exhibits an intrinsic quantum spin Hall (QSH) effect with a nontrivial gap as large as 0.42 eV, suggesting that a two-dimensional (2D) topological insulator can be achieved at room temperature. Most interestingly, there is a topological phase transition simply driven by a small tensile strain of up to 2%. Furthermore, all the known MX2 (M = Mo or W; X = S, Se or Te) monolayers in the new T'' phase unambiguously display similar band topologies and strain controlled topological phase transitions. Our findings greatly enrich the 2D families of transition metal dichalcogenides and offer a feasible way to control the electronic states of 2D topological insulators for the fabrication of high-speed spintronics devices.Single layered transition metal dichalcogenides have attracted tremendous research interest due to their structural phase diversities. By using a global optimization approach, we have discovered a new phase of transition metal dichalcogenides (labelled as T''), which is confirmed to be energetically, dynamically and kinetically stable by our first-principles calculations. The new T'' MoS2 phase exhibits an intrinsic quantum spin Hall (QSH) effect with a nontrivial gap as large as 0.42 eV, suggesting that a two-dimensional (2D) topological insulator can be achieved at room temperature. Most interestingly, there is a topological phase transition simply driven by a small tensile strain of up to 2%. Furthermore, all the known MX2 (M = Mo or W; X = S, Se or Te) monolayers in the new T'' phase unambiguously display similar band topologies and strain controlled topological

Efficient Reanalysis Procedures in Structural Topology Optimization

DEFF Research Database (Denmark)

Amir, Oded

This thesis examines efficient solution procedures for the structural analysis problem within topology optimization. The research is motivated by the observation that when the nested approach to structural optimization is applied, most of the computational effort is invested in repeated solutions...... on approximate reanalysis. For cases where memory limitations require the utilization of iterative equation solvers, we suggest efficient procedures based on alternative termination criteria for such solvers. These approaches are tested on two- and three-dimensional topology optimization problems including...

Global Anomaly Detection in Two-Dimensional Symmetry-Protected Topological Phases

Science.gov (United States)

Bultinck, Nick; Vanhove, Robijn; Haegeman, Jutho; Verstraete, Frank

2018-04-01

Edge theories of symmetry-protected topological phases are well known to possess global symmetry anomalies. In this Letter we focus on two-dimensional bosonic phases protected by an on-site symmetry and analyze the corresponding edge anomalies in more detail. Physical interpretations of the anomaly in terms of an obstruction to orbifolding and constructing symmetry-preserving boundaries are connected to the cohomology classification of symmetry-protected phases in two dimensions. Using the tensor network and matrix product state formalism we numerically illustrate our arguments and discuss computational detection schemes to identify symmetry-protected order in a ground state wave function.

Two-dimensional Topology of the Two-Degree Field Galaxy Redshift Survey

Science.gov (United States)

Hoyle, Fiona; Vogeley, Michael S.; Gott, J. Richard, III

2002-05-01

We study the topology of the publicly available data released by the Two Degree Field Galaxy Redshift Survey team (2dF GRS). The 2dF GRS data contain over 100,000 galaxy redshifts with a magnitude limit of bJ=19.45 and is the largest such survey to date. The data lie over a wide range of right ascension (75° strips) but only within a narrow range of declination (10° and 15° strips). This allows measurements of the two-dimensional genus to be made. We find that the genus curves of the north Galactic pole (NGP) and south Galactic pole (SGP) are slightly different. The NGP displays a slight meatball shift topology, whereas the SGP displays a bubble-like topology. The current SGP data also have a slightly higher genus amplitude. In both cases, a slight excess of overdense regions is found over underdense regions. We assess the significance of these features using mock catalogs drawn from the Virgo Consortium's Hubble volume ΛCDM z=0 simulation. We find that differences between the NGP and SGP genus curves are only significant at the 1 σ level. The average genus curve of the 2dF GRS agrees well with that extracted from the ΛCDM mock catalogs. We also use the simulations to assess how the current incompleteness of the survey (the strips are not completely filled in) affects the measurement of the genus and find that we are not sensitive to the geometry; there are enough data in the current sample to trace the isolated high- and low-density regions. We compare the amplitude of the 2dF GRS genus curve to the amplitude of the genus curve of a Gaussian random field that we construct to have the same power spectrum as the 2dF GRS. In previous three-dimensional analyses, it was found that the genus curve of observed samples was lower than the Gaussian random field curve, presumably because of high-order correlations present in the data. However, we find that the 2dF GRS genus curve has an amplitude that is slightly higher than that of the power-spectrum-matched Gaussian

Measurement of the quantum capacitance from two-dimensional surface state of a topological insulator at room temperature

Energy Technology Data Exchange (ETDEWEB)

Choi, Hyunwoo, E-mail: chw0089@gmail.com [Department of Electrical and Computer Engineering, University of Seoul, Seoul 02504 (Korea, Republic of); Kim, Tae Geun, E-mail: tgkim1@korea.ac.kr [School of Electrical Engineering, Korea University, Seoul 02841 (Korea, Republic of); Shin, Changhwan, E-mail: cshin@uos.ac.kr [Department of Electrical and Computer Engineering, University of Seoul, Seoul 02504 (Korea, Republic of)

2017-06-15

Highlights: • The quantum capacitance in topological insulator (TI) at room temperature is directly revealed. • The physical origin of quantum capacitance, the two dimensional surface state of TI, is experimentally validated. • Theoretically calculated results of ideal quantum capacitance can well predict the experimental data. - Abstract: A topological insulator (TI) is a new kind of material that exhibits unique electronic properties owing to its topological surface state (TSS). Previous studies focused on the transport properties of the TSS, since it can be used as the active channel layer in metal-oxide-semiconductor field-effect transistors (MOSFETs). However, a TI with a negative quantum capacitance (QC) effect can be used in the gate stack of MOSFETs, thereby facilitating the creation of ultra-low power electronics. Therefore, it is important to study the physics behind the QC in TIs in the absence of any external magnetic field, at room temperature. We fabricated a simple capacitor structure using a TI (TI-capacitor: Au-TI-SiO{sub 2}-Si), which shows clear evidence of QC at room temperature. In the capacitance-voltage (C-V) measurement, the total capacitance of the TI-capacitor increases in the accumulation regime, since QC is the dominant capacitive component in the series capacitor model (i.e., C{sub T}{sup −1} = C{sub Q}{sup −1} + C{sub SiO2}{sup −1}). Based on the QC model of the two-dimensional electron systems, we quantitatively calculated the QC, and observed that the simulated C-V curve theoretically supports the conclusion that the QC of the TI-capacitor is originated from electron–electron interaction in the two-dimensional surface state of the TI.

One-Dimensional Mass-Spring Chains Supporting Elastic Waves with Non-Conventional Topology

Directory of Open Access Journals (Sweden)

2016-04-01

Full Text Available There are two classes of phononic structures that can support elastic waves with non-conventional topology, namely intrinsic and extrinsic systems. The non-conventional topology of elastic wave results from breaking time reversal symmetry (T-symmetry of wave propagation. In extrinsic systems, energy is injected into the phononic structure to break T-symmetry. In intrinsic systems symmetry is broken through the medium microstructure that may lead to internal resonances. Mass-spring composite structures are introduced as metaphors for more complex phononic crystals with non-conventional topology. The elastic wave equation of motion of an intrinsic phononic structure composed of two coupled one-dimensional (1D harmonic chains can be factored into a Dirac-like equation, leading to antisymmetric modes that have spinor character and therefore non-conventional topology in wave number space. The topology of the elastic waves can be further modified by subjecting phononic structures to externally-induced spatio-temporal modulation of their elastic properties. Such modulations can be actuated through photo-elastic effects, magneto-elastic effects, piezo-electric effects or external mechanical effects. We also uncover an analogy between a combined intrinsic-extrinsic systems composed of a simple one-dimensional harmonic chain coupled to a rigid substrate subjected to a spatio-temporal modulation of the side spring stiffness and the Dirac equation in the presence of an electromagnetic field. The modulation is shown to be able to tune the spinor part of the elastic wave function and therefore its topology. This analogy between classical mechanics and quantum phenomena offers new modalities for developing more complex functions of phononic crystals and acoustic metamaterials.

Supergravity and the knitting of the Kalb-Ramond two-form in eight-dimensional topological gravity

Energy Technology Data Exchange (ETDEWEB)

Baulieu, Laurent; Bellon, Marc; Tanzini, Alessandro

2003-07-17

Topological Euclidean gravity is built in eight dimensions for manifolds with Spin(7) subset of SO(8) holonomy. In a previous work, we considered the construction of an eight-dimensional topological theory describing the graviton and one graviphoton. Here we solve the question of determining a topological model for the combined system of a metric and a Kalb-Ramond two-form gauge field. We then recover the complete N=1, D=8 supergravity theory in a twisted form. We observe that the generalized self-duality conditions of our model correspond to the octonionic string equations.

Lattice formulation of a two-dimensional topological field theory

International Nuclear Information System (INIS)

Ohta, Kazutoshi; Takimi, Tomohisa

2007-01-01

We investigate an integrable property and the observables of 2-dimensional N=(4,4) topological field theory defined on a discrete lattice by using the 'orbifolding' and 'deconstruction' methods. We show that our lattice model is integrable and, for this reason, the partition function reduces to matrix integrals of scalar fields on the lattice sites. We elucidate meaningful differences between a discrete lattice and a differentiable manifold. This is important for studying topological quantities on a lattice. We also propose a new construction of N=(2,2) supersymmetric lattice theory, which is realized through a suitable truncation of scalar fields from the N=(4,4) theory. (author)

Coupling effect of topological states and Chern insulators in two-dimensional triangular lattices

Science.gov (United States)

Zhang, Jiayong; Zhao, Bao; Xue, Yang; Zhou, Tong; Yang, Zhongqin

2018-03-01

We investigate topological states of two-dimensional (2D) triangular lattices with multiorbitals. Tight-binding model calculations of a 2D triangular lattice based on px and py orbitals exhibit very interesting doubly degenerate energy points at different positions (Γ and K /K' ) in momentum space, with quadratic non-Dirac and linear Dirac band dispersions, respectively. Counterintuitively, the system shows a global topologically trivial rather than nontrivial state with consideration of spin-orbit coupling due to the "destructive interference effect" between the topological states at the Γ and K /K' points. The topologically nontrivial state can emerge by introducing another set of triangular lattices to the system (bitriangular lattices) due to the breakdown of the interference effect. With first-principles calculations, we predict an intrinsic Chern insulating behavior (quantum anomalous Hall effect) in a family of the 2D triangular lattice metal-organic framework of Co(C21N3H15) (TPyB-Co) from this scheme. Our results provide a different path and theoretical guidance for the search for and design of new 2D topological quantum materials.

Streamline topologies near simple degenerate critical points in two-dimensional flow away from boundaries

DEFF Research Database (Denmark)

Brøns, Morten; Hartnack, Johan Nicolai

1998-01-01

Streamline patterns and their bifurcations in two-dimensional incompressible flow are investigated from a topological point of view. The velocity field is expanded at a point in the fluid, and the expansion coefficients are considered as bifurcation parameters. A series of non-linear coordinate c...

Streamline topologies near simple degenerate critical points in two-dimensional flow away from boundaries

DEFF Research Database (Denmark)

Brøns, Morten; Hartnack, Johan Nicolai

1999-01-01

Streamline patterns and their bifurcations in two-dimensional incompressible flow are investigated from a topological point of view. The velocity field is expanded at a point in the fluid, and the expansion coefficients are considered as bifurcation parameters. A series of nonlinear coordinate ch...

Engineering topological phases with a three-dimensional nodal-loop semimetal

Science.gov (United States)

Li, Linhu; Yap, Han Hoe; Araújo, Miguel A. N.; Gong, Jiangbin

2017-12-01

A three-dimensional (3D) nodal-loop semimetal phase is exploited to engineer a number of intriguing phases featuring different peculiar topological surface states. In particular, by introducing various two-dimensional gap terms to a 3D tight-binding model of a nodal-loop semimetal, we obtain a rich variety of topological phases of great interest to ongoing theoretical and experimental studies, including a chiral insulator, degenerate-surface-loop insulator, and second-order topological insulator, as well as a Weyl semimetal with tunable Fermi arc profiles. The unique concept underlying our approach is to engineer topological surface states that inherit their dispersion relations from a gap term. The results provide one rather unified principle for the creation of novel topological phases and can guide the search for new topological materials. Two-terminal transport studies are also carried out to distinguish the engineered topological phases.

Two-dimensional Topology of the Sloan Digital Sky Survey

Science.gov (United States)

Hoyle, Fiona; Vogeley, Michael S.; Gott, J. Richard, III; Blanton, Michael; Tegmark, Max; Weinberg, David H.; Bahcall, N.; Brinkmann, J.; York, D.

2002-12-01

We present the topology of a volume-limited sample of 11,884 galaxies, selected from an apparent magnitude limited sample of over 100,000 galaxies observed as part of the Sloan Digital Sky Survey (SDSS). The data currently cover three main regions on the sky: one in the Galactic north and one in the south, both at zero degrees declination, and one area in the north at higher declination. Each of these areas covers a wide range of survey longitude but a narrow range of survey latitude, allowing the two-dimensional genus to be measured. The genus curves of the SDSS subsamples are similar, after appropriately normalizing these measurements for the different areas. We sum the genus curves from the three areas to obtain the total genus curve of the SDSS. The total curve has a shape similar to the genus curve derived from mock catalogs drawn from the Hubble volume ΛCDM simulation and is similar to that of a Gaussian random field. Likewise, comparison with the genus of the Two-Degree Field Galaxy Redshift Survey, after normalization for the difference in area, reveals remarkable similarity in the topology of these samples. We test for the effects of galaxy-type segregation by splitting the SDSS data into thirds, based on the u*-r* colors of the galaxies, and measure the genus of the reddest and bluest subsamples. This red/blue split in u*-r* is essentially a split by morphology, as explained by Strateva and coworkers. We find that the genus curve for the reddest galaxies exhibits a ``meatball'' shift of the topology-reflecting the concentration of red galaxies in high-density regions-compared to the bluest galaxies and the full sample, in agreement with predictions from simulations.

Tunable Majorana corner states in a two-dimensional second-order topological superconductor induced by magnetic fields

Science.gov (United States)

Zhu, Xiaoyu

2018-05-01

A two-dimensional second-order topological superconductor exhibits a finite gap in both bulk and edges, with the nontrivial topology manifesting itself through Majorana zero modes localized at the corners, i.e., Majorana corner states. We investigate a time-reversal-invariant topological superconductor in two dimensions and demonstrate that an in-plane magnetic field could transform it into a second-order topological superconductor. A detailed analysis reveals that the magnetic field gives rise to mass terms which take distinct values among the edges, and Majorana corner states naturally emerge at the intersection of two adjacent edges with opposite masses. With the rotation of the magnetic field, Majorana corner states localized around the boundary may hop from one corner to a neighboring one and eventually make a full circle around the system when the field rotates by 2 π . In the end, we briefly discuss physical realizations of this system.

Pair creation, motion, and annihilation of topological defects in two-dimensional nematic liquid crystals

Science.gov (United States)

Cortese, Dario; Eggers, Jens; Liverpool, Tanniemola B.

2018-02-01

We present a framework for the study of disclinations in two-dimensional active nematic liquid crystals and topological defects in general. The order tensor formalism is used to calculate exact multiparticle solutions of the linearized static equations inside a planar uniformly aligned state so that the total charge has to vanish. Topological charge conservation then requires that there is always an equal number of q =1 /2 and q =-1 /2 charges. Starting from a set of hydrodynamic equations, we derive a low-dimensional dynamical system for the parameters of the static solutions, which describes the motion of a half-disclination pair or of several pairs. Within this formalism, we model defect production and annihilation, as observed in experiments. Our dynamics also provide an estimate for the critical density at which production and annihilation rates are balanced.

Quantum transport in new two-dimensional heterostructures: Thin films of topological insulators, phosphorene

Science.gov (United States)

Majidi, Leyla; Zare, Moslem; Asgari, Reza

2018-06-01

The unusual features of the charge and spin transport characteristics are investigated in new two-dimensional heterostructures. Intraband specular Andreev reflection is realized in a topological insulator thin film normal/superconducting junction in the presence of a gate electric field. Perfect specular electron-hole conversion is shown for different excitation energy values in a wide experimentally available range of the electric field and also for all angles of incidence when the excitation energy has a particular value. It is further demonstrated that the transmission probabilities of the incoming electrons from different spin subbands to the monolayer phosphorene ferromagnetic/normal/ferromagnetic (F/N/F) hybrid structure have different behavior with the angle of incidence and perfect transmission occurs at defined angles of incidence to the proposed structure with different length of the N region, and different alignments of magnetization vectors. Moreover, the sign change of the spin-current density is demonstrated by tuning the chemical potential and exchange field of the F region.

Vacuum state structure and the screening mechanism of a charge in two-dimensional massless electrodynamics

International Nuclear Information System (INIS)

Danilov, G.S.; Dyatlov, I.T.; Petrov, V.Yu.

1982-01-01

In two-dimensional electrodynamics (QED 2 ) of massless fermions (quarks) the screening and confinement of a charge is due to the transition of local charges into vacuum of the system under the action of the field changing the topological number. An exact solution of the problem of the quark structure of vacuum for two variants of QED 2 shows that it is consistent with the phenomenon. The structure of vacuum is therefore related directly to the Adler anomaly and to the character of variation of the field topological numbers in dynamic processes. The solutions obtained permit one to investigate in an explicit form the properties of a chiral condensate, the existence of which is also a direct consequence of the Adler anomaly

Ripple-modulated electronic structure of a 3D topological insulator.

Science.gov (United States)

Okada, Yoshinori; Zhou, Wenwen; Walkup, D; Dhital, Chetan; Wilson, Stephen D; Madhavan, V

2012-01-01

Three-dimensional topological insulators host linearly dispersing states with unique properties and a strong potential for applications. An important ingredient in realizing some of the more exotic states in topological insulators is the ability to manipulate local electronic properties. Direct analogy to the Dirac material graphene suggests that a possible avenue for controlling local properties is via a controlled structural deformation such as the formation of ripples. However, the influence of such ripples on topological insulators is yet to be explored. Here we use scanning tunnelling microscopy to determine the effects of one-dimensional buckling on the electronic properties of Bi(2)Te(3.) By tracking spatial variations of the interference patterns generated by the Dirac electrons we show that buckling imposes a periodic potential, which locally modulates the surface-state dispersion. This suggests that forming one- and two-dimensional ripples is a viable method for creating nanoscale potential landscapes that can be used to control the properties of Dirac electrons in topological insulators.

Integrated topology and shape optimization in structural design

Science.gov (United States)

Bremicker, M.; Chirehdast, M.; Kikuchi, N.; Papalambros, P. Y.

1990-01-01

Structural optimization procedures usually start from a given design topology and vary its proportions or boundary shapes to achieve optimality under various constraints. Two different categories of structural optimization are distinguished in the literature, namely sizing and shape optimization. A major restriction in both cases is that the design topology is considered fixed and given. Questions concerning the general layout of a design (such as whether a truss or a solid structure should be used) as well as more detailed topology features (e.g., the number and connectivities of bars in a truss or the number of holes in a solid) have to be resolved by design experience before formulating the structural optimization model. Design quality of an optimized structure still depends strongly on engineering intuition. This article presents a novel approach for initiating formal structural optimization at an earlier stage, where the design topology is rigorously generated in addition to selecting shape and size dimensions. A three-phase design process is discussed: an optimal initial topology is created by a homogenization method as a gray level image, which is then transformed to a realizable design using computer vision techniques; this design is then parameterized and treated in detail by sizing and shape optimization. A fully automated process is described for trusses. Optimization of two dimensional solid structures is also discussed. Several application-oriented examples illustrate the usefulness of the proposed methodology.

On the background independence of two-dimensional topological gravity

Science.gov (United States)

Imbimbo, Camillo

1995-04-01

We formulate two-dimensional topological gravity in a background covariant Lagrangian framework. We derive the Ward identities which characterize the dependence of physical correlators on the background world-sheet metric defining the gauge-slice. We point out the existence of an "anomaly" in Ward identitites involving correlators of observables with higher ghost number. This "anomaly" represents an obstruction for physical correlators to be globally defined forms on moduli space which could be integrated in a background independent way. Starting from the anomalous Ward identities, we derive "descent" equations whose solutions are cocycles of the Lie algebra of the diffeomorphism group with values in the space of local forms on the moduli space. We solve the descent equations and provide explicit formulas for the cocycles, which allow for the definition of background independent integrals of physical correlators on the moduli space.

Dimensional crossover and cold-atom realization of topological Mott insulators

Science.gov (United States)

Scheurer, Mathias S.; Rachel, Stephan; Orth, Peter P.

2015-02-01

Interacting cold-atomic gases in optical lattices offer an experimental approach to outstanding problems of many body physics. One important example is the interplay of interaction and topology which promises to generate a variety of exotic phases such as the fractionalized Chern insulator or the topological Mott insulator. Both theoretically understanding these states of matter and finding suitable systems that host them have proven to be challenging problems. Here we propose a cold-atom setup where Hubbard on-site interactions give rise to spin liquid-like phases: weak and strong topological Mott insulators. They represent the celebrated paradigm of an interacting and topological quantum state with fractionalized spinon excitations that inherit the topology of the non-interacting system. Our proposal shall help to pave the way for a controlled experimental investigation of this exotic state of matter in optical lattices. Furthermore, it allows for the investigation of a dimensional crossover from a two-dimensional quantum spin Hall insulating phase to a three-dimensional strong topological insulator by tuning the hopping between the layers.

Optical conductivity of three and two dimensional topological nodal-line semimetals

Science.gov (United States)

Barati, Shahin; Abedinpour, Saeed H.

2017-10-01

The peculiar shape of the Fermi surface of topological nodal-line semimetals at low carrier concentrations results in their unusual optical and transport properties. We analytically investigate the linear optical responses of three- and two-dimensional nodal-line semimetals using the Kubo formula. The optical conductivity of a three-dimensional nodal-line semimetal is anisotropic. Along the axial direction (i.e., the direction perpendicular to the nodal-ring plane), the Drude weight has a linear dependence on the chemical potential at both low and high carrier dopings. For the radial direction (i.e., the direction parallel to the nodal-ring plane), this dependence changes from linear into quadratic in the transition from low into high carrier concentration. The interband contribution into optical conductivity is also anisotropic. In particular, at large frequencies, it saturates to a constant value for the axial direction and linearly increases with frequency along the radial direction. In two-dimensional nodal-line semimetals, no interband optical transition could be induced and the only contribution to the optical conductivity arises from the intraband excitations. The corresponding Drude weight is independent of the carrier density at low carrier concentrations and linearly increases with chemical potential at high carrier doping.

Two-dimensional epitaxial superconductor-semiconductor heterostructures: A platform for topological superconducting networks

OpenAIRE

Shabani, J.; Kjaergaard, M.; Suominen, H. J.; Kim, Younghyun; Nichele, F.; Pakrouski, K.; Stankevic, T.; Lutchyn, R. M.; Krogstrup, P.; Feidenhans'l, R.; Kraemer, S.; Nayak, C.; Troyer, M.; Marcus, C. M.; Palmstrøm, C. J.

2015-01-01

Progress in the emergent field of topological superconductivity relies on synthesis of new material combinations, combining superconductivity, low density, and spin-orbit coupling (SOC). For example, theory [1-4] indicates that the interface between a one-dimensional (1D) semiconductor (Sm) with strong SOC and a superconductor (S) hosts Majorana modes with nontrivial topological properties [5-8]. Recently, epitaxial growth of Al on InAs nanowires was shown to yield a high quality S-Sm system ...

Topology of Flow Separation on Three-Dimensional Bodies

Science.gov (United States)

Chapman, Gary T.; Yates, Leslie A.

1991-01-01

In recent years there has been extensive research on three-dimensional flow separation. There are two different approaches: the phenomenological approach and a mathematical approach using topology. These two approaches are reviewed briefly and the shortcomings of some of the past works are discussed. A comprehensive approach applicable to incompressible and compressible steady-state flows as well as incompressible unsteady flow is then presented. The approach is similar to earlier topological approaches to separation but is more complete and in some cases adds more emphasis to certain points than in the past. To assist in the classification of various types of flow, nomenclature is introduced to describe the skin-friction portraits on the surface. This method of classification is then demonstrated on several categories of flow to illustrate particular points as well as the diversity of flow separation. The categories include attached, two-dimensional separation and three different types of simple, three-dimensional primary separation, secondary separation, and compound separation. Hypothetical experiments are utilized to illustrate the topological terminology and its role in characterizing these flows. These hypothetical experiments use colored oil injected onto the surface at singular points in the skin-friction portrait. Actual flow-visualization information, if available, is used to corroborate the hypothetical examples.

Traditional Semiconductors in the Two-Dimensional Limit.

Science.gov (United States)

Lucking, Michael C; Xie, Weiyu; Choe, Duk-Hyun; West, Damien; Lu, Toh-Ming; Zhang, S B

2018-02-23

Interest in two-dimensional materials has exploded in recent years. Not only are they studied due to their novel electronic properties, such as the emergent Dirac fermion in graphene, but also as a new paradigm in which stacking layers of distinct two-dimensional materials may enable different functionality or devices. Here, through first-principles theory, we reveal a large new class of two-dimensional materials which are derived from traditional III-V, II-VI, and I-VII semiconductors. It is found that in the ultrathin limit the great majority of traditional binary semiconductors studied (a series of 28 semiconductors) are not only kinetically stable in a two-dimensional double layer honeycomb structure, but more energetically stable than the truncated wurtzite or zinc-blende structures associated with three dimensional bulk. These findings both greatly increase the landscape of two-dimensional materials and also demonstrate that in the double layer honeycomb form, even ordinary semiconductors, such as GaAs, can exhibit exotic topological properties.

A short course on topological insulators band structure and edge states in one and two dimensions

CERN Document Server

Asbóth, János K; Pályi, András

2016-01-01

This course-based primer provides newcomers to the field with a concise introduction to some of the core topics in the emerging field of topological insulators. The aim is to provide a basic understanding of edge states, bulk topological invariants, and of the bulk--boundary correspondence with as simple mathematical tools as possible. The present approach uses noninteracting lattice models of topological insulators, building gradually on these to arrive from the simplest one-dimensional case (the Su-Schrieffer-Heeger model for polyacetylene) to two-dimensional time-reversal invariant topological insulators (the Bernevig-Hughes-Zhang model for HgTe). In each case the discussion of simple toy models is followed by the formulation of the general arguments regarding topological insulators. The only prerequisite for the reader is a working knowledge in quantum mechanics, the relevant solid state physics background is provided as part of this self-contained text, which is complemented by end-of-chapter problems.

Higher dimensional quantum Hall effect as A-class topological insulator

Energy Technology Data Exchange (ETDEWEB)

Hasebe, Kazuki, E-mail: khasebe@stanford.edu

2014-09-15

We perform a detail study of higher dimensional quantum Hall effects and A-class topological insulators with emphasis on their relations to non-commutative geometry. There are two different formulations of non-commutative geometry for higher dimensional fuzzy spheres: the ordinary commutator formulation and quantum Nambu bracket formulation. Corresponding to these formulations, we introduce two kinds of monopole gauge fields: non-abelian gauge field and antisymmetric tensor gauge field, which respectively realize the non-commutative geometry of fuzzy sphere in the lowest Landau level. We establish connection between the two types of monopole gauge fields through Chern–Simons term, and derive explicit form of tensor monopole gauge fields with higher string-like singularity. The connection between two types of monopole is applied to generalize the concept of flux attachment in quantum Hall effect to A-class topological insulator. We propose tensor type Chern–Simons theory as the effective field theory for membranes in A-class topological insulators. Membranes turn out to be fractionally charged objects and the phase entanglement mediated by tensor gauge field transforms the membrane statistics to be anyonic. The index theorem supports the dimensional hierarchy of A-class topological insulator. Analogies to D-brane physics of string theory are discussed too.

The Topological Structure of the SU(2) Chern–Simons Topological Current in the Four-Dimensional Quantum Hall Effect

International Nuclear Information System (INIS)

Xiu-Ming, Zhang; Yi-Shi, Duan

2010-01-01

In the light of the decomposition of the SU(2) gauge potential for I = 1/2, we obtain the SU(2) Chern-Simons current over S 4 , i.e. the vortex current in the effective field for the four-dimensional quantum Hall effect. Similar to the vortex excitations in the two-dimensional quantum Hall effect (2D FQH) which are generated from the zero points of the complex scalar field, in the 4D FQH, we show that the SU(2) Chern–Simons vortices are generated from the zero points of the two-component wave functions Ψ, and their topological charges are quantized in terms of the Hopf indices and Brouwer degrees of φ-mapping under the condition that the zero points of field Ψ are regular points. (condensed matter: electronicstructure, electrical, magnetic, and opticalproperties)

Wind load modeling for topology optimization of continuum structures

NARCIS (Netherlands)

Zakhama, R.; Abdalla, M.M.; Gürdal, Z.; Smaoui, H.

2010-01-01

Topology optimization of two and three dimensional structures subject to dead and wind loading is considered. The wind loading is introduced into the formulation by using standard expressions for the drag force, and a strategy is devised so that wind pressure is ignored where there is no surface

D-branes and coherent topological charge structure in QCD

Science.gov (United States)

Thacker, Hank

2006-12-01

Monte Carlo studies of pure glue SU(3) gauge theory using the overlap-based topological charge operator have revealed a laminar structure in the QCD vacuum consisting of extended, thin, co- herent, locally 3-dimensional sheets of topological charge embedded in 4D space, with opposite sign sheets interleaved. Studies of localization properties of Dirac eigenmodes have also shown evidence for the delocalization of low-lying modes on effectively 3-dimensional surfaces. In this talk, I review some theoretical ideas which suggest the possibility of 3-dimensionally coherent topological charge structure in 4-dimensional gauge theory and provide a possible interpretation of the observed structure. I begin with Luscher's "Wilson bag" integral over the 3-index Chern- Simons tensor. The analogy with a Wilson loop as a charged world line in 2-dimensional CP N-1 sigma models suggests that the Wilson bag surface represents the world volume of a physical membrane. The large-N chiral Lagrangian arguments of Witten also indicate the existence of multiple "k-vacuum" states with discontinuous transitions between k-vacua at θ = odd multi- ples of π. The domain walls between these vacua have the properties of a Wilson bag surface. Finally, I review the AdS/CFT duality view of θ dependence in QCD. The dual realtionship be- tween topological charge in gauge theory and Ramond-Ramond charge in type IIA string theory suggests that the coherent topological charge sheets observed on the lattice are the holographic image of wrapped D6 branes.

Topology Optimization of Lightweight Lattice Structural Composites Inspired by Cuttlefish Bone

Science.gov (United States)

Hu, Zhong; Gadipudi, Varun Kumar; Salem, David R.

2018-03-01

Lattice structural composites are of great interest to various industries where lightweight multifunctionality is important, especially aerospace. However, strong coupling among the composition, microstructure, porous topology, and fabrication of such materials impedes conventional trial-and-error experimental development. In this work, a discontinuous carbon fiber reinforced polymer matrix composite was adopted for structural design. A reliable and robust design approach for developing lightweight multifunctional lattice structural composites was proposed, inspired by biomimetics and based on topology optimization. Three-dimensional periodic lattice blocks were initially designed, inspired by the cuttlefish bone microstructure. The topologies of the three-dimensional periodic blocks were further optimized by computer modeling, and the mechanical properties of the topology optimized lightweight lattice structures were characterized by computer modeling. The lattice structures with optimal performance were identified.

Self-ordering of nontrivial topological polarization structures in nanoporous ferroelectrics.

Science.gov (United States)

Van Lich, Le; Shimada, Takahiro; Wang, Jie; Kitamura, Takayuki

2017-10-19

Topological field structures, such as skyrmions, merons, and vortices, are important features found in ordered systems with spontaneously broken symmetry. A plethora of topological field structures have been discovered in magnetic and ordered soft matter systems due to the presence of inherent chiral interactions, and this has provided a fruitful platform for unearthing additional groundbreaking functionalities. However, despite being one of the most important classes of ordered systems, ferroelectrics scarcely form topological polarization structures due to their lack of intrinsic chiral interactions. In the present study, we demonstrate using multiphysics phase-field modelling based on the Ginzburg-Landau theory that a rich assortment of nontrivial topological polarization structures, including hedgehogs, antivortices, multidirectional vortices, and vortex arrays, can be spontaneously formed in three-dimensional nanoporous ferroelectric structures. We realize that confining ferroelectrics to trivial geometries that are incompatible with the orientation symmetry may impose extrinsic frustration to the polarization field through the enhancement of depolarization fields at free porous surfaces. This frustration gives rise to symmetry breaking, resulting in the formation of nontrivial topological polarization structures as the ground state. We further topologically characterize the local accommodation of polarization structures by viewing them in a new perspective, in which polarization ordering can be mapped on the order parameter space, according to the topological theory of defects and homotopy theory. The results indicate that the nanoporous structures contain composite topological objects composed of two or more elementary topological polarization structures. The present study therefore offers a playground for exploring novel physical phenomena in ferroelectric systems as well as a novel nanoelectronics characterization platform for future topology

Entanglement entropy for (3+1)-dimensional topological order with excitations

Science.gov (United States)

Wen, Xueda; He, Huan; Tiwari, Apoorv; Zheng, Yunqin; Ye, Peng

2018-02-01

Excitations in (3+1)-dimensional [(3+1)D] topologically ordered phases have very rich structures. (3+1)D topological phases support both pointlike and stringlike excitations, and in particular the loop (closed string) excitations may admit knotted and linked structures. In this work, we ask the following question: How do different types of topological excitations contribute to the entanglement entropy or, alternatively, can we use the entanglement entropy to detect the structure of excitations, and further obtain the information of the underlying topological order? We are mainly interested in (3+1)D topological order that can be realized in Dijkgraaf-Witten (DW) gauge theories, which are labeled by a finite group G and its group 4-cocycle ω ∈H4[G ;U(1 ) ] up to group automorphisms. We find that each topological excitation contributes a universal constant lndi to the entanglement entropy, where di is the quantum dimension that depends on both the structure of the excitation and the data (G ,ω ) . The entanglement entropy of the excitations of the linked/unlinked topology can capture different information of the DW theory (G ,ω ) . In particular, the entanglement entropy introduced by Hopf-link loop excitations can distinguish certain group 4-cocycles ω from the others.

Two-dimensional manifolds with metrics of revolution

International Nuclear Information System (INIS)

Sabitov, I Kh

2000-01-01

This is a study of the topological and metric structure of two-dimensional manifolds with a metric that is locally a metric of revolution. In the case of compact manifolds this problem can be thoroughly investigated, and in particular it is explained why there are no closed analytic surfaces of revolution in R 3 other than a sphere and a torus (moreover, in the smoothness class C ∞ such surfaces, understood in a certain generalized sense, exist in any topological class)

Structures of two-dimensional three-body systems

International Nuclear Information System (INIS)

Ruan, W.Y.; Liu, Y.Y.; Bao, C.G.

1996-01-01

Features of the structure of L = 0 states of a two-dimensional three-body model system have been investigated. Three types of permutation symmetry of the spatial part, namely symmetric, antisymmetric, and mixed, have been considered. A comparison has been made between the two-dimensional system and the corresponding three-dimensional one. The effect of symmetry on microscopic structures is emphasized. (author)

Even-dimensional topological gravity from Chern-Simons gravity

International Nuclear Information System (INIS)

Merino, N.; Perez, A.; Salgado, P.

2009-01-01

It is shown that the topological action for gravity in 2n-dimensions can be obtained from the (2n+1)-dimensional Chern-Simons gravity genuinely invariant under the Poincare group. The 2n-dimensional topological gravity is described by the dynamics of the boundary of a (2n+1)-dimensional Chern-Simons gravity theory with suitable boundary conditions. The field φ a , which is necessary to construct this type of topological gravity in even dimensions, is identified with the coset field associated with the non-linear realizations of the Poincare group ISO(d-1,1).

Two new Zn(II) and Cd(II) coordinastion polymers based on amino-tetrazole and phenylcarboxylate: Syntheses, topological structures and photoluminescent properties

International Nuclear Information System (INIS)

Liu, Dong-Sheng; Sui, Yan; Chen, Weng-Tong; Huang, Jian-Gen; Chen, Jian-Zhong; Huang, Chang-Cang

2012-01-01

Two Zn(II) and Cd(II) compounds with the in-situ generated ligand of 5-amino-tetrazolate (atz − ) were prepared from the hydrothermal reactions of the corresponding Cd or Zn(II) salts with phenylcarboxylate, and characterized by elemental analysis, IR spectroscopy, and TGA. The results of X-ray crystallographic analysis reveal that compound [Zn 2 (BZA)(atz) 2 (OH)] n (1) (BZA=benzoic acid) presents a two-dimensional (2D) “hcb” topological network constructed from the ZnN 2 O 2 tetrahedra. In compound [Cd 6 (atz) 6 (PTA) 3 ] n (2) (PTA=terephthalic acid), the identical [Cd 3 (atz) 3 )] 3+ n clusters are connected by atz ligands to generate a 2D cationic layer, and the neighboring cationic layers are pillared by PTA giving birth to 3D network. After simplifying, the complicated 3D network of 2 can be presented as an unprecedented (4, 4, 10)-connected trinodal topology. The formations of the structures show a good example that using the combination of the in-situ generated ligand and other coligand synthetic strategy can construct interesting topological structures. The thermal stabilities and fluorescent properties of the complexes have also been studied. - Graphical abstract: Two d 10 metal complexes have been synthesized by employing mixed-ligand synthetic approach. Complex 1 presents a 2D “hcb” topological network. Complex 2 shows an unprecedented (4, 4, 10)-connected trinodal topology. Highlights: ► Coligand synthetic strategy was applied to obtain new MOFs with useful properties. ► Two new Zn(II) and Cd(II) complexes were constructed from the mixed-ligand. ► Topologically, compound 2 presented an unprecedented (4, 4, 10)-connected trinodal topology. ► The two compounds may be excellent candidates for potential photoactive material.

On topological RNA interaction structures.

Science.gov (United States)

Qin, Jing; Reidys, Christian M

2013-07-01

Recently a folding algorithm of topological RNA pseudoknot structures was presented in Reidys et al. (2011). This algorithm folds single-stranded γ-structures, that is, RNA structures composed by distinct motifs of bounded topological genus. In this article, we set the theoretical foundations for the folding of the two backbone analogues of γ structures: the RNA γ-interaction structures. These are RNA-RNA interaction structures that are constructed by a finite number of building blocks over two backbones having genus at most γ. Combinatorial properties of γ-interaction structures are of practical interest since they have direct implications for the folding of topological interaction structures. We compute the generating function of γ-interaction structures and show that it is algebraic, which implies that the numbers of interaction structures can be computed recursively. We obtain simple asymptotic formulas for 0- and 1-interaction structures. The simplest class of interaction structures are the 0-interaction structures, which represent the two backbone analogues of secondary structures.

Modification of electronic structure, magnetic structure, and topological phase of bismuthene by point defects

Science.gov (United States)

Kadioglu, Yelda; Kilic, Sevket Berkay; Demirci, Salih; Aktürk, O. Üzengi; Aktürk, Ethem; Ciraci, Salim

2017-12-01

This paper reveals how the electronic structure, magnetic structure, and topological phase of two-dimensional (2D), single-layer structures of bismuth are modified by point defects. We first showed that a free-standing, single-layer, hexagonal structure of bismuth, named h-bismuthene, exhibits nontrivial band topology. We then investigated interactions between single foreign adatoms and bismuthene structures, which comprise stability, bonding, electronic structure, and magnetic structures. Localized states in diverse locations of the band gap and resonant states in band continua of bismuthene are induced upon the adsorption of different adatoms, which modify electronic and magnetic properties. Specific adatoms result in reconstruction around the adsorption site. Single vacancies and divacancies can form readily in bismuthene structures and remain stable at high temperatures. Through rebondings, Stone-Whales-type defects are constructed by divacancies, which transform into a large hole at high temperature. Like adsorbed adatoms, vacancies induce also localized gap states, which can be eliminated through rebondings in divacancies. We also showed that not only the optical and magnetic properties, but also the topological features of pristine h-bismuthene can be modified by point defects. The modification of the topological features depends on the energies of localized states and also on the strength of coupling between point defects.

Three-dimensional topological insulators and bosonization

Energy Technology Data Exchange (ETDEWEB)

Cappelli, Andrea [INFN, Sezione di Firenze,Via G. Sansone 1, 50019 Sesto Fiorentino - Firenze (Italy); Randellini, Enrico [INFN, Sezione di Firenze,Via G. Sansone 1, 50019 Sesto Fiorentino - Firenze (Italy); Dipartimento di Fisica e Astronomia, Università di Firenze,Via G. Sansone 1, 50019 Sesto Fiorentino - Firenze (Italy); Sisti, Jacopo [Scuola Internazionale Superiore di Studi Avanzati (SISSA),Via Bonomea 265, 34136 Trieste (Italy)

2017-05-25

Massless excitations at the surface of three-dimensional time-reversal invariant topological insulators possess both fermionic and bosonic descriptions, originating from band theory and hydrodynamic BF theory, respectively. We analyze the corresponding field theories of the Dirac fermion and compactified boson and compute their partition functions on the three-dimensional torus geometry. We then find some non-dynamic exact properties of bosonization in (2+1) dimensions, regarding fermion parity and spin sectors. Using these results, we extend the Fu-Kane-Mele stability argument to fractional topological insulators in three dimensions.

Structural and Topology Optimization of Complex Civil Engineering Structures

DEFF Research Database (Denmark)

Hald, Frederik; Kirkegaard, Poul Henning; Andersen, Lars Vabbersgaard

2013-01-01

This paper shows the use of topology optimization for finding an optimized form for civil engineering structures. Today topology optimization and shape optimization have been integrated in several commercial finite element codes. Here, the topology of two complex civil engineering structures...

Two Topologically Distinct Dirac-Line Semimetal Phases and Topological Phase Transitions in Rhombohedrally Stacked Honeycomb Lattices

Science.gov (United States)

Hyart, T.; Ojajärvi, R.; Heikkilä, T. T.

2018-04-01

Three-dimensional topological semimetals can support band crossings along one-dimensional curves in the momentum space (nodal lines or Dirac lines) protected by structural symmetries and topology. We consider rhombohedrally (ABC) stacked honeycomb lattices supporting Dirac lines protected by time-reversal, inversion and spin rotation symmetries. For typical band structure parameters there exists a pair of nodal lines in the momentum space extending through the whole Brillouin zone in the stacking direction. We show that these Dirac lines are topologically distinct from the usual Dirac lines which form closed loops inside the Brillouin zone. In particular, an energy gap can be opened only by first merging the Dirac lines going through the Brillouin zone in a pairwise manner so that they turn into closed loops inside the Brillouin zone, and then by shrinking these loops into points. We show that this kind of topological phase transition can occur in rhombohedrally stacked honeycomb lattices by tuning the ratio of the tunneling amplitudes in the directions perpendicular and parallel to the layers. We also discuss the properties of the surface states in the different phases of the model.

Structure of six-dimensional microstate geometries

International Nuclear Information System (INIS)

Lange, Paul de; Mayerson, Daniel R.; Vercnocke, Bert

2015-01-01

We investigate the structure of smooth and horizonless microstate geometries in six dimensions, in the spirit of the five-dimensional analysis of Gibbons and Warner http://arxiv.org/abs/1305.0957 . In six dimensions, which is the natural setting for horizonless geometries with the charges of the D1-D5-P black hole, the natural black objects are strings and there are no Chern-Simons terms for the tensor gauge fields. However, we still find that the same reasoning applies: in absence of horizons, there can be no smooth stationary solutions without non-trivial topology. We use topological arguments to describe the Smarr formula in various examples: the uplift of the five-dimensional minimal supergravity microstates to six dimensions, the two-charge D1-D5 microstates, and the non-extremal JMaRT solution. We also discuss D1-D5-P superstrata and confirm that the Smarr formula gives the same result as for the D1-D5 supertubes which are topologically equivalent.

Structure of six-dimensional microstate geometries

Energy Technology Data Exchange (ETDEWEB)

Lange, Paul de; Mayerson, Daniel R.; Vercnocke, Bert [Institute for Theoretical Physics, University of Amsterdam,Science Park 904, Postbus 94485, 1090 GL Amsterdam (Netherlands)

2015-09-14

We investigate the structure of smooth and horizonless microstate geometries in six dimensions, in the spirit of the five-dimensional analysis of Gibbons and Warner http://arxiv.org/abs/1305.0957 . In six dimensions, which is the natural setting for horizonless geometries with the charges of the D1-D5-P black hole, the natural black objects are strings and there are no Chern-Simons terms for the tensor gauge fields. However, we still find that the same reasoning applies: in absence of horizons, there can be no smooth stationary solutions without non-trivial topology. We use topological arguments to describe the Smarr formula in various examples: the uplift of the five-dimensional minimal supergravity microstates to six dimensions, the two-charge D1-D5 microstates, and the non-extremal JMaRT solution. We also discuss D1-D5-P superstrata and confirm that the Smarr formula gives the same result as for the D1-D5 supertubes which are topologically equivalent.

Quantum anomalous Hall effect and topological phase transition in two-dimensional antiferromagnetic Chern insulator NiOsCl6

Science.gov (United States)

Yang, Wei-Wei; Li, Lei; Zhao, Jing-Sheng; Liu, Xiao-Xiong; Deng, Jian-Bo; Tao, Xiao-Ma; Hu, Xian-Ru

2018-05-01

By doing calculations based on density functional theory, we predict that the two-dimensional anti-ferromagnetic (AFM) NiOsCl6 as a Chern insulator can realize the quantum anomalous Hall (QAH) effect. We investigate the magnetocrystalline anisotropy energies in different magnetic configurations and the Néel AFM configuration is proved to be ground state. When considering spin–orbit coupling (SOC), this layered material with spins perpendicular to the plane shows properties as a Chern insulator characterized by an inversion band structure and a nonzero Chern number. The nontrivial band gap is 37 meV and the Chern number C  =  ‑1, which are induced by a strong SOC and AFM order. With strong SOC, the NiOsCl6 system performs a continuous topological phase transition from the Chern insulator to the trivial insulator upon the increasing Coulomb repulsion U. The critical U c is indicated as 0.23 eV, at which the system is in a metallic phase with . Upon increasing U, the E g reduces linearly with C  =  ‑1 for 0    U c . At last we analysis the QAH properties and this continuous topological phase transition theoretically in a two-band model. This AFM Chern insulator NiOsCl6 proposes not only a promising way to realize the QAH effect, but also a new material to study the continuous topological phase transition.

(d -2 ) -Dimensional Edge States of Rotation Symmetry Protected Topological States

Science.gov (United States)

Song, Zhida; Fang, Zhong; Fang, Chen

2017-12-01

We study fourfold rotation-invariant gapped topological systems with time-reversal symmetry in two and three dimensions (d =2 , 3). We show that in both cases nontrivial topology is manifested by the presence of the (d -2 )-dimensional edge states, existing at a point in 2D or along a line in 3D. For fermion systems without interaction, the bulk topological invariants are given in terms of the Wannier centers of filled bands and can be readily calculated using a Fu-Kane-like formula when inversion symmetry is also present. The theory is extended to strongly interacting systems through the explicit construction of microscopic models having robust (d -2 )-dimensional edge states.

Topological phases of interacting fermions in one-dimensional superconductor - normal metal geometry

Energy Technology Data Exchange (ETDEWEB)

Meidan, Dganit [Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva 84105 (Israel); Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universitaet Berlin, 14195 Berlin (Germany); Romito, Alessandro; Brouwer, Piet W. [Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva 84105 (Israel)

2015-07-01

One-dimensional superconductors can be in non-trivial topological phases harboring Majorana end-states, which possess non-abelian statistics. It has been recently established that in the presence of interactions the classification of topological superconducting phases can be significantly altered. Specifically, for one-dimensional superconductors possessing a time reversal symmetry (BDI class), interactions reduce the infinitely many non-interacting phases (Z topological index) to eight distinct ones (Z{sub 8} topological index). In this talk I will consider multi-mode superconducting wires in such BDI class when probed by an external contact, and discuss their low temperature and voltage bias transport properties. I will first show that the Andreev reflection component of the scattering matrix of the probing lead provides a topological index, r=-4,.., 4, which distinguish the eight topological phases. The two topologically equivalent phases with r= 4,-4 support emergent many-body end states, which are identified to be a topologically protected Kondo-like resonance. The path in phase space that connects these equivalent phases crosses a non-fermi liquid fixed point where a multiple channel Kondo effect develops.

Spin-orbit coupling, electron transport and pairing instabilities in two-dimensional square structures

Energy Technology Data Exchange (ETDEWEB)

Kocharian, Armen N. [Department of Physics, California State University, Los Angeles, CA 90032 (United States); Fernando, Gayanath W.; Fang, Kun [Department of Physics, University of Connecticut, Storrs, Connecticut 06269 (United States); Palandage, Kalum [Department of Physics, Trinity College, Hartford, Connecticut 06106 (United States); Balatsky, Alexander V. [AlbaNova University Center Nordita, SE-106 91 Stockholm (Sweden)

2016-05-15

Rashba spin-orbit effects and electron correlations in the two-dimensional cylindrical lattices of square geometries are assessed using mesoscopic two-, three- and four-leg ladder structures. Here the electron transport properties are systematically calculated by including the spin-orbit coupling in tight binding and Hubbard models threaded by a magnetic flux. These results highlight important aspects of possible symmetry breaking mechanisms in square ladder geometries driven by the combined effect of a magnetic gauge field spin-orbit interaction and temperature. The observed persistent current, spin and charge polarizations in the presence of spin-orbit coupling are driven by separation of electron and hole charges and opposite spins in real-space. The modeled spin-flip processes on the pairing mechanism induced by the spin-orbit coupling in assembled nanostructures (as arrays of clusters) engineered in various two-dimensional multi-leg structures provide an ideal playground for understanding spatial charge and spin density inhomogeneities leading to electron pairing and spontaneous phase separation instabilities in unconventional superconductors. Such studies also fall under the scope of current challenging problems in superconductivity and magnetism, topological insulators and spin dependent transport associated with numerous interfaces and heterostructures.

Spin-orbit coupling, electron transport and pairing instabilities in two-dimensional square structures

Directory of Open Access Journals (Sweden)

Armen N. Kocharian

2016-05-01

Full Text Available Rashba spin-orbit effects and electron correlations in the two-dimensional cylindrical lattices of square geometries are assessed using mesoscopic two-, three- and four-leg ladder structures. Here the electron transport properties are systematically calculated by including the spin-orbit coupling in tight binding and Hubbard models threaded by a magnetic flux. These results highlight important aspects of possible symmetry breaking mechanisms in square ladder geometries driven by the combined effect of a magnetic gauge field spin-orbit interaction and temperature. The observed persistent current, spin and charge polarizations in the presence of spin-orbit coupling are driven by separation of electron and hole charges and opposite spins in real-space. The modeled spin-flip processes on the pairing mechanism induced by the spin-orbit coupling in assembled nanostructures (as arrays of clusters engineered in various two-dimensional multi-leg structures provide an ideal playground for understanding spatial charge and spin density inhomogeneities leading to electron pairing and spontaneous phase separation instabilities in unconventional superconductors. Such studies also fall under the scope of current challenging problems in superconductivity and magnetism, topological insulators and spin dependent transport associated with numerous interfaces and heterostructures.

A new Pb{sup II}(ethylenediaminetetraacetate) coordination polymer with a two-dimensional layer structure

Energy Technology Data Exchange (ETDEWEB)

Zhao, D., E-mail: iamzd@hpu.edu.cn; Zhang, R. H.; Li, F. F. [Henan Polytechnic University, Department of Physics and Chemistry (China)

2016-12-15

A new Pb{sup II}−edta{sup 4–} coordination polymer, Pb{sub 2}(edta)(H{sub 2}O){sub 0.76} (edta{sup 4–} = ethylenediaminetetraacetate) was synthesized under hydrothermal condition. Single crystal X-ray analysis reveals that it represents a novel two-dimensional (2D) Pb{sup 2+}–edta{sup 4–} layer structure with a (4,8{sup 2})-topology. Each edta{sup 4–} ligand employs its four carboxylate O and two N atoms to chelate one Pb{sup II} atom (hexa-coordinated) and connects five Pb{sup II} atoms (ennea-coordinated) via its four carboxylate groups to form 2D layer framework. Adjacent layers are packed into the overall structure through vander Waals interactions.

Topological insulators and superconductors: tenfold way and dimensional hierarchy

International Nuclear Information System (INIS)

Ryu, Shinsei; Schnyder, Andreas P; Furusaki, Akira; Ludwig, Andreas W W

2010-01-01

It has recently been shown that in every spatial dimension there exist precisely five distinct classes of topological insulators or superconductors. Within a given class, the different topological sectors can be distinguished, depending on the case, by a Z or a Z 2 topological invariant. This is an exhaustive classification. Here we construct representatives of topological insulators and superconductors for all five classes and in arbitrary spatial dimension d, in terms of Dirac Hamiltonians. Using these representatives we demonstrate how topological insulators (superconductors) in different dimensions and different classes can be related via 'dimensional reduction' by compactifying one or more spatial dimensions (in 'Kaluza-Klein'-like fashion). For Z-topological insulators (superconductors) this proceeds by descending by one dimension at a time into a different class. The Z 2 -topological insulators (superconductors), on the other hand, are shown to be lower-dimensional descendants of parent Z-topological insulators in the same class, from which they inherit their topological properties. The eightfold periodicity in dimension d that exists for topological insulators (superconductors) with Hamiltonians satisfying at least one reality condition (arising from time-reversal or charge-conjugation/particle-hole symmetries) is a reflection of the eightfold periodicity of the spinor representations of the orthogonal groups SO(N) (a form of Bott periodicity). Furthermore, we derive for general spatial dimensions a relation between the topological invariant that characterizes topological insulators and superconductors with chiral symmetry (i.e., the winding number) and the Chern-Simons invariant. For lower-dimensional cases, this formula relates the winding number to the electric polarization (d=1 spatial dimensions) or to the magnetoelectric polarizability (d=3 spatial dimensions). Finally, we also discuss topological field theories describing the spacetime theory of

Accidental degeneracy in photonic bands and topological phase transitions in two-dimensional core-shell dielectric photonic crystals.

Science.gov (United States)

Xu, Lin; Wang, Hai-Xiao; Xu, Ya-Dong; Chen, Huan-Yang; Jiang, Jian-Hua

2016-08-08

A simple core-shell two-dimensional photonic crystal is studied where the triangular lattice symmetry and the C6 point group symmetry give rich physics in accidental touching points of photonic bands. We systematically evaluate different types of accidental nodal points at the Brillouin zone center for transverse-magnetic harmonic modes when the geometry and permittivity of the core-shell material are continuously tuned. The accidental nodal points can have different dispersions and topological properties (i.e., Berry phases). These accidental nodal points can be the critical states lying between a topological phase and a normal phase of the photonic crystal. They are thus very important for the study of topological photonic states. We show that, without breaking time-reversal symmetry, by tuning the geometry of the core-shell material, a phase transition into the photonic quantum spin Hall insulator can be achieved. Here the "spin" is defined as the orbital angular momentum of a photon. We study the topological phase transition as well as the properties of the edge and bulk states and their application potentials in optics.

Topologically protected bound states in one-dimensional Floquet acoustic waveguide systems

Science.gov (United States)

Peng, Yu-Gui; Geng, Zhi-Guo; Zhu, Xue-Feng

2018-03-01

Topological manipulation of sound has recently been a hot spot in acoustics due to the fascinating property of defect immune transport. To the best of our knowledge, the studies on one-dimensional (1D) topological acoustic systems hitherto mainly focus on the case of the Su-Schrieffer-Heeger model. Here, we show that topologically protected bound states may also exist in 1D periodically modulated acoustic waveguide systems, viz., 1D Floquet topological insulators. The results show that tuning the coupling strength in a waveguide lattice could trigger topological phase transition, which gives rise to topologically protected interface states as we put together two waveguide lattices featured with different topological phases or winding numbers. However, for the combined lattice, input at the waveguides other than the interfacial ones will excite bulk states. We have further verified the robustness of interface bound states against the variation of coupling strengths between the two distinct waveguide lattices. This work extends the scope of topological acoustics and may promote potential applications for acoustic devices with topological functionalities.

Topological states in a two-dimensional metal alloy in Si surface: BiAg/Si(111)-4 ×4 surface

Science.gov (United States)

Zhang, Xiaoming; Cui, Bin; Zhao, Mingwen; Liu, Feng

2018-02-01

A bridging topological state with a conventional semiconductor platform offers an attractive route towards future spintronics and quantum device applications. Here, based on first-principles and tight-binding calculations, we demonstrate the existence of topological states hosted by a two-dimensional (2D) metal alloy in a Si surface, the BiAg/Si(111)-4 ×4 surface, which has already been synthesized experimentally. It exhibits a topological insulating state with an energy gap of 71 meV (˜819 K ) above the Fermi level and a topological metallic state with quasiquantized conductance below the Fermi level. The underlying mechanism leading to the formation of such nontrivial states is revealed by analysis of the "charge-transfer" and "orbital-filtering" effect of the Si substrate. A minimal effective tight-binding model is employed to reveal the formation mechanism of the topological states. Our finding opens opportunities to detect topological states and measure its quantized conductance in a large family of 2D surface metal alloys, which have been or are to be grown on semiconductor substrates.

Localization and diagonalization. A review of functional integral techniques for low-dimensional gauge theories and topological field theories

International Nuclear Information System (INIS)

Blau, M.; Thompson, G.

1995-01-01

We review localization techniques for functional integrals which have recently been used to perform calculations in and gain insight into the structure of certain topological field theories and low-dimensional gauge theories. These are the functional integral counterparts of the Mathai-Quillen formalism, the Duistermaat-Heckman theorem, and the Weyl integral formula respectively. In each case, we first introduce the necessary mathematical background (Euler classes of vector bundles, equivariant cohomology, topology of Lie groups), and describe the finite dimensional integration formulae. We then discuss some applications to path integrals and give an overview of the relevant literature. The applications we deal with include supersymmetric quantum mechanics, cohomological field theories, phase space path integrals, and two-dimensional Yang-Mills theory. (author). 83 refs

A topologically twisted index for three-dimensional supersymmetric theories

International Nuclear Information System (INIS)

Benini, Francesco; Zaffaroni, Alberto

2015-01-01

We provide a general formula for the partition function of three-dimensional N=2 gauge theories placed on S 2 ×S 1 with a topological twist along S 2 , which can be interpreted as an index for chiral states of the theories immersed in background magnetic fields. The result is expressed as a sum over magnetic fluxes of the residues of a meromorphic form which is a function of the scalar zero-modes. The partition function depends on a collection of background magnetic fluxes and fugacities for the global symmetries. We illustrate our formula in many examples of 3d Yang-Mills-Chern-Simons theories with matter, including Aharony and Giveon-Kutasov dualities. Finally, our formula generalizes to Ω-backgrounds, as well as two-dimensional theories on S 2 and four-dimensional theories on S 2 ×T 2 . In particular this provides an alternative way to compute genus-zero A-model topological amplitudes and Gromov-Witten invariants.

Charge order-superfluidity transition in a two-dimensional system of hard-core bosons and emerging domain structures

Science.gov (United States)

Moskvin, A. S.; Panov, Yu. D.; Rybakov, F. N.; Borisov, A. B.

2017-11-01

We have used high-performance parallel computations by NVIDIA graphics cards applying the method of nonlinear conjugate gradients and Monte Carlo method to observe directly the developing ground state configuration of a two-dimensional hard-core boson system with decrease in temperature, and its evolution with deviation from a half-filling. This has allowed us to explore unconventional features of a charge order—superfluidity phase transition, specifically, formation of an irregular domain structure, emergence of a filamentary superfluid structure that condenses within of the charge-ordered phase domain antiphase boundaries, and formation and evolution of various topological structures.

Topological supersymmetric structure of hadron cross sections

International Nuclear Information System (INIS)

Gauron, P.; Nicolescu, B.; Ouvry, S.

1980-12-01

Recently a way of fully implementing unitarity in the framework of a Dual Topological Unitarization theory, including not only mesons but also baryons, was found. This theory consists in the topological description of hadron interactions involving confined quarks in terms of two 2-dimensional surfaces (a closed 'quantum' surface and a bounded 'classical' surface). We show that this description directly leads, at the zeroth order of the topological expansion, to certain relations between hadron cross-sections, in nice agreement with experimental data. A new topological suppression mechanism is shown to play an important dynamical role. We also point out a new topological supersymmetry property, which leads to realistic experimental consequences. A possible topological origin of the rho and ω universality relations emerges as a by-product of our study

The Topology Optimization of Three-dimensional Cooling Fins by the Internal Element Connectivity Parameterization Method

International Nuclear Information System (INIS)

Yoo, Sung Min; Kim, Yoon Young

2007-01-01

This work is concerned with the topology optimization of three-dimensional cooling fins or heat sinks. Motivated by earlier success of the Internal Element Connectivity Method (I-ECP) method in two dimensional problems, the extension of I-ECP to three-dimensional problems is carried out. The main efforts were made to maintain the numerical trouble-free characteristics of I-ECP for full three-dimensional problems; a serious numerical problem appearing in thermal topology optimization is erroneous temperature undershooting. The effectiveness of the present implementation was checked through the design optimization of three-dimensional fins

Three-dimensional low-energy topological invariants

International Nuclear Information System (INIS)

Bakalarska, M.; Broda, B.

2000-01-01

A description of the one-loop approximation formula for the partition function of a three-dimensional abelian version of the Donaldson-Witten theory is proposed. The one-loop expression is shown to contain such topological invariants of a three-dimensional manifold M like the Reidemeister-Ray-Singer torsion τ R and Betti numbers. (orig.)

Topology and incompleteness for 2+1-dimensional cosmological spacetimes

Science.gov (United States)

Fajman, David

2017-06-01

We study the long-time behavior of the Einstein flow coupled to matter on 2-dimensional surfaces. We consider massless matter models such as collisionless matter composed of massless particles, massless scalar fields and radiation fluids and show that the maximal globally hyperbolic development of homogeneous and isotropic initial data on the 2-sphere is geodesically incomplete in both time directions, i.e. the spacetime recollapses. This behavior also holds for open sets of initial data. In particular, we construct classes of recollapsing 2+1-dimensional spacetimes with spherical spatial topology which provide evidence for a closed universe recollapse conjecture for massless matter models in 2+1 dimensions. Furthermore, we construct solutions with toroidal and higher genus topology for the massless matter fields, which in both cases are future complete. The spacetimes with toroidal topology are 2+1-dimensional analogies of the Einstein-de Sitter model. In addition, we point out a general relation between the energy-momentum tensor and the Kretschmann scalar in 2+1 dimensions and use it to infer strong cosmic censorship for all these models. In view of this relation, we also recall corresponding models containing massive particles, constructed in a previous work and determine the nature of their initial singularities. We conclude that the global structure of non-vacuum cosmological spacetimes in 2+1 dimensions is determined by the mass of particles and—in the homogeneous and isotropic setting studied here—verifies strong cosmic censorship.

The Topology of Three-Dimensional Symmetric Tensor Fields

Science.gov (United States)

Lavin, Yingmei; Levy, Yuval; Hesselink, Lambertus

1994-01-01

We study the topology of 3-D symmetric tensor fields. The goal is to represent their complex structure by a simple set of carefully chosen points and lines analogous to vector field topology. The basic constituents of tensor topology are the degenerate points, or points where eigenvalues are equal to each other. First, we introduce a new method for locating 3-D degenerate points. We then extract the topological skeletons of the eigenvector fields and use them for a compact, comprehensive description of the tensor field. Finally, we demonstrate the use of tensor field topology for the interpretation of the two-force Boussinesq problem.

Topology of high-dimensional manifolds

Energy Technology Data Exchange (ETDEWEB)

Farrell, F T [State University of New York, Binghamton (United States); Goettshe, L [Abdus Salam ICTP, Trieste (Italy); Lueck, W [Westfaelische Wilhelms-Universitaet Muenster, Muenster (Germany)

2002-08-15

The School on High-Dimensional Manifold Topology took place at the Abdus Salam ICTP, Trieste from 21 May 2001 to 8 June 2001. The focus of the school was on the classification of manifolds and related aspects of K-theory, geometry, and operator theory. The topics covered included: surgery theory, algebraic K- and L-theory, controlled topology, homology manifolds, exotic aspherical manifolds, homeomorphism and diffeomorphism groups, and scalar curvature. The school consisted of 2 weeks of lecture courses and one week of conference. Thwo-part lecture notes volume contains the notes of most of the lecture courses.

Algebraic definition of topological W gravity

International Nuclear Information System (INIS)

Hosono, S.

1992-01-01

In this paper, the authors propose a definition of the topological W gravity using some properties of the principal three-dimensional subalgebra of a simple Lie algebra due to Kostant. In the authors' definition, structures of the two-dimensional topological gravity are naturally embedded in the extended theories. In accordance with the definition, the authors will present some explicit calculations for the W 3 gravity

Topics in two dimensional conformal field theory and three dimensional topological lattice field theory

International Nuclear Information System (INIS)

Chung, Stephen-wei.

1993-01-01

The authors first construct new parafermions in two-dimensional conformal field theory, generalizing the Z L parafermion theories from integer L to rational L. These non-unitary parafermions have some novel features: an infinite number of currents with negative conformal dimensions for most (if not all) of them. String functions of these new parafermion theories are calculated. They also construct new representations of N = 2 superconformal field theories, whose characters are obtained in terms of these new string functions. They then generalize Felder's BRST cohomology method to construct the characters and branching functions of the SU(2) L x SU(2) K /SU(2) K+L coset theories, where one of the (K,L) is an integer. This method of obtaining the branching functions also serves as a check of their new Z L parafermion theories. The next topic is the Lagrangian formulation of conformal field theory. They construct a chiral gauged WZW theory where the gauge fields are chiral and belong to the subgroups H L and H R , which can be different groups. This new construction is beyond the ordinary vector gauged WZW theory, whose gauge group H is a subgroup of both G L and G R . In the special case where H L = H R , the quantum theory of chiral gauged WZW theory is equivalent to that of the vector gauged WZW theory. It can be further shown that the chiral gauged WZW theory is equivalent to [G L /H L ](z) direct-product [G R /H R ](bar z) coset models in conformal field theory. In the second half of this thesis, they construct topological lattice field theories in three dimensions. After defining a general class of local lattice field theories, they impose invariance under arbitrary topology-preserving deformations of the underlying lattice, which are generated by two local lattice moves. Invariant solutions are in one-to-one correspondence with Hopf algebras satisfying a certain constraint

Spin-polarized currents in the tunnel contact of a normal conductor and a two-dimensional topological insulator

International Nuclear Information System (INIS)

Sukhanov, A. A.; Sablikov, V. A.

2013-01-01

The spin filtering of electrons tunneling from the edge states of a two-dimensional topological insulator into a normal conductor under a magnetic field (external or induced due to proximity to a magnetic insulator) is studied. Calculations are performed for a tunnel contact of finite length between the topological insulator and an electronic multimode quantum strip. It is shown that the flow of tunneling electrons is split in the strip, so that spin-polarized currents arise in its left and right branches. These currents can be effectively controlled by the contact voltage and the chemical potential of the system. The presence of a magnetic field, which splits the spin subbands of the electron spectrum in the strip, gives rise to switching of the spin current between the strip branches

Spacetime representation of topological phononics

Science.gov (United States)

Deymier, Pierre A.; Runge, Keith; Lucas, Pierre; Vasseur, Jérôme O.

2018-05-01

Non-conventional topology of elastic waves arises from breaking symmetry of phononic structures either intrinsically through internal resonances or extrinsically via application of external stimuli. We develop a spacetime representation based on twistor theory of an intrinsic topological elastic structure composed of a harmonic chain attached to a rigid substrate. Elastic waves in this structure obey the Klein–Gordon and Dirac equations and possesses spinorial character. We demonstrate the mapping between straight line trajectories of these elastic waves in spacetime and the twistor complex space. The twistor representation of these Dirac phonons is related to their topological and fermion-like properties. The second topological phononic structure is an extrinsic structure composed of a one-dimensional elastic medium subjected to a moving superlattice. We report an analogy between the elastic behavior of this time-dependent superlattice, the scalar quantum field theory and general relativity of two types of exotic particle excitations, namely temporal Dirac phonons and temporal ghost (tachyonic) phonons. These phonons live on separate sides of a two-dimensional frequency space and are delimited by ghost lines reminiscent of the conventional light cone. Both phonon types exhibit spinorial amplitudes that can be measured by mapping the particle behavior to the band structure of elastic waves.

Topology of Large-Scale Structures of Galaxies in two Dimensions—Systematic Effects

Science.gov (United States)

Appleby, Stephen; Park, Changbom; Hong, Sungwook E.; Kim, Juhan

2017-02-01

We study the two-dimensional topology of galactic distribution when projected onto two-dimensional spherical shells. Using the latest Horizon Run 4 simulation data, we construct the genus of the two-dimensional field and consider how this statistic is affected by late-time nonlinear effects—principally gravitational collapse and redshift space distortion (RSD). We also consider systematic and numerical artifacts, such as shot noise, galaxy bias, and finite pixel effects. We model the systematics using a Hermite polynomial expansion and perform a comprehensive analysis of known effects on the two-dimensional genus, with a view toward using the statistic for cosmological parameter estimation. We find that the finite pixel effect is dominated by an amplitude drop and can be made less than 1% by adopting pixels smaller than 1/3 of the angular smoothing length. Nonlinear gravitational evolution introduces time-dependent coefficients of the zeroth, first, and second Hermite polynomials, but the genus amplitude changes by less than 1% between z = 1 and z = 0 for smoothing scales {R}{{G}}> 9 {Mpc}/{{h}}. Non-zero terms are measured up to third order in the Hermite polynomial expansion when studying RSD. Differences in the shapes of the genus curves in real and redshift space are small when we adopt thick redshift shells, but the amplitude change remains a significant ˜ { O }(10 % ) effect. The combined effects of galaxy biasing and shot noise produce systematic effects up to the second Hermite polynomial. It is shown that, when sampling, the use of galaxy mass cuts significantly reduces the effect of shot noise relative to random sampling.

A Three-dimensional Topological Model of Ternary Phase Diagram

International Nuclear Information System (INIS)

Mu, Yingxue; Bao, Hong

2017-01-01

In order to obtain a visualization of the complex internal structure of ternary phase diagram, the paper realized a three-dimensional topology model of ternary phase diagram with the designed data structure and improved algorithm, under the guidance of relevant theories of computer graphics. The purpose of the model is mainly to analyze the relationship between each phase region of a ternary phase diagram. The model not only obtain isothermal section graph at any temperature, but also extract a particular phase region in which users are interested. (paper)

Topological Insulators Dirac Equation in Condensed Matters

CERN Document Server

Shen, Shun-Qing

2012-01-01

Topological insulators are insulating in the bulk, but process metallic states around its boundary owing to the topological origin of the band structure. The metallic edge or surface states are immune to weak disorder or impurities, and robust against the deformation of the system geometry. This book, Topological insulators, presents a unified description of topological insulators from one to three dimensions based on the modified Dirac equation. A series of solutions of the bound states near the boundary are derived, and the existing conditions of these solutions are described. Topological invariants and their applications to a variety of systems from one-dimensional polyacetalene, to two-dimensional quantum spin Hall effect and p-wave superconductors, and three-dimensional topological insulators and superconductors or superfluids are introduced, helping readers to better understand this fascinating new field. This book is intended for researchers and graduate students working in the field of topological in...

Third sound in one and two dimensional modulated structures

International Nuclear Information System (INIS)

Komuro, T.; Kawashima, H., Shirahama, K.; Kono, K.

1996-01-01

An experimental technique is developed to study acoustic transmission in one and two dimensional modulated structures by employing third sound of a superfluid helium film. In particular, the Penrose lattice, which is a two dimensional quasiperiodic structure, is studied. In two dimensions, the scattering of third sound is weaker than in one dimension. Nevertheless, the authors find that the transmission spectrum in the Penrose lattice, which is a two dimensional prototype of the quasicrystal, is observable if the helium film thickness is chosen around 5 atomic layers. The transmission spectra in the Penrose lattice are explained in terms of dynamical theory of diffraction

Discrete elastic model for two-dimensional melting.

Science.gov (United States)

Lansac, Yves; Glaser, Matthew A; Clark, Noel A

2006-04-01

We present a network model for the study of melting and liquid structure in two dimensions, the first in which the presence and energy of topological defects (dislocations and disclinations) and of geometrical defects (elemental voids) can be independently controlled. Interparticle interaction is via harmonic springs and control is achieved by Monte Carlo moves which springs can either be orientationally "flipped" between particles to generate topological defects, or can be "popped" in force-free shape, to generate geometrical defects. With the geometrical defects suppressed the transition to the liquid phase occurs via disclination unbinding, as described by the Kosterlitz-Thouless-Halperin-Nelson-Young model and found in soft potential two-dimensional (2D) systems, such as the dipole-dipole potential [H. H. von Grünberg, Phys. Rev. Lett. 93, 255703 (2004)]. By contrast, with topological defects suppressed, a disordering transition, the Glaser-Clark condensation of geometrical defects [M. A. Glaser and N. A. Clark, Adv. Chem. Phys. 83, 543 (1993); M. A. Glaser, (Springer-Verlag, Berlin, 1990), Vol. 52, p. 141], produces a state that accurately characterizes the local liquid structure and first-order melting observed in hard-potential 2D systems, such as hard disk and the Weeks-Chandler-Andersen (WCA) potentials (M. A. Glaser and co-workers, see above). Thus both the geometrical and topological defect systems play a role in melting. The present work introduces a system in which the relative roles of topological and geometrical defects and their interactions can be explored. We perform Monte Carlo simulations of this model in the isobaric-isothermal ensemble, and present the phase diagram as well as various thermodynamic, statistical, and structural quantities as a function of the relative populations of geometrical and topological defects. The model exhibits a rich phase behavior including hexagonal and square crystals, expanded crystal, dodecagonal quasicrystal

Monolayer group-III monochalcogenides by oxygen functionalization: a promising class of two-dimensional topological insulators

Science.gov (United States)

Zhou, Si; Liu, Cheng-Cheng; Zhao, Jijun; Yao, Yugui

2018-03-01

Monolayer group-III monochalcogenides (MX, M = Ga, In; X = S, Se, Te), an emerging category of two-dimensional (2D) semiconductors, hold great promise for electronics, optoelectronics and catalysts. By first-principles calculations, we show that the phonon dispersion and Raman spectra, as well as the electronic and topological properties of monolayer MX can be tuned by oxygen functionalization. Chemisorption of oxygen atoms on one side or both sides of the MX sheet narrows or even closes the band gap, enlarges work function, and significantly reduces the carrier effective mass. More excitingly, InS, InSe, and InTe monolayers with double-side oxygen functionalization are 2D topological insulators with sizeable bulk gap up to 0.21 eV. Their low-energy bands near the Fermi level are dominated by the px and py orbitals of atoms, allowing band engineering via in-plane strains. Our studies provide viable strategy for realizing quantum spin Hall effect in monolayer group-III monochalcogenides at room temperature, and utilizing these novel 2D materials for high-speed and dissipationless transport devices.

Sensitivity of quantum walks to a boundary of two-dimensional lattices: approaches based on the CGMV method and topological phases

International Nuclear Information System (INIS)

Endo, Takako; Konno, Norio; Obuse, Hideaki; Segawa, Etsuo

2017-01-01

In this paper, we treat quantum walks in a two-dimensional lattice with cutting edges along a straight boundary introduced by Asboth and Edge (2015 Phys. Rev . A 91 022324) in order to study one-dimensional edge states originating from topological phases of matter and to obtain collateral evidence of how a quantum walker reacts to the boundary. Firstly, we connect this model to the CMV matrix, which provides a 5-term recursion relation of the Laurent polynomial associated with spectral measure on the unit circle. Secondly, we explicitly derive the spectra of bulk and edge states of the quantum walk with the boundary using spectral analysis of the CMV matrix. Thirdly, while topological numbers of the model studied so far are well-defined only when gaps in the bulk spectrum exist, we find a new topological number defined only when there are no gaps in the bulk spectrum. We confirm that the existence of the spectrum for edge states derived from the CMV matrix is consistent with the prediction from a bulk-edge correspondence using topological numbers calculated in the cases where gaps in the bulk spectrum do or do not exist. Finally, we show how the edge states contribute to the asymptotic behavior of the quantum walk through limit theorems of the finding probability. Conversely, we also propose a differential equation using this limit distribution whose solution is the underlying edge state. (paper)

Magnetotransport and induced superconductivity in Bi based three-dimensional topological insulators

International Nuclear Information System (INIS)

Veldhorst, M.; Snelder, M.; Hoek, M.; Molenaar, C.G.; Leusink, D.P.; Golubov, A.A.; Hilgenkamp, H.; Brinkman, A.

2013-01-01

The surface of a three-dimensional (3D) topological insulator is conducting and the topologically nontrivial nature of the surface states is observed in experiments. It is the aim of this paper to review and analyze experimental observations with respect to the magnetotransport in Bi-based 3D topological insulators, as well as the superconducting transport properties of hybrid structures consisting of superconductors and these topological insulators. The helical spin-momentum coupling of the surface state electrons becomes visible in quantum corrections to the conductivity and magnetoresistance oscillations. An analysis will be provided of the reported magnetoresistance, also in the presence of bulk conductivity shunts. Special attention is given to the large and linear magnetoresistance. Superconductivity can be induced in topological superconductors by means of the proximity effect. The induced supercurrents, Josephson effects and current-phase relations will be reviewed. These materials hold great potential in the field of spintronics and the route towards Majorana devices. (copyright 2013 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)

Magnetotransport and induced superconductivity in Bi based three-dimensional topological insulators

Energy Technology Data Exchange (ETDEWEB)

Veldhorst, M.; Snelder, M.; Hoek, M.; Molenaar, C.G.; Leusink, D.P.; Golubov, A.A.; Hilgenkamp, H.; Brinkman, A. [MESA + Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500 AE Enschede (Netherlands)

2013-02-15

The surface of a three-dimensional (3D) topological insulator is conducting and the topologically nontrivial nature of the surface states is observed in experiments. It is the aim of this paper to review and analyze experimental observations with respect to the magnetotransport in Bi-based 3D topological insulators, as well as the superconducting transport properties of hybrid structures consisting of superconductors and these topological insulators. The helical spin-momentum coupling of the surface state electrons becomes visible in quantum corrections to the conductivity and magnetoresistance oscillations. An analysis will be provided of the reported magnetoresistance, also in the presence of bulk conductivity shunts. Special attention is given to the large and linear magnetoresistance. Superconductivity can be induced in topological superconductors by means of the proximity effect. The induced supercurrents, Josephson effects and current-phase relations will be reviewed. These materials hold great potential in the field of spintronics and the route towards Majorana devices. (copyright 2013 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)

Reality of the fundamental topological structure in the QCD vacuum

International Nuclear Information System (INIS)

Alexandru, Andrei; Horvath, Ivan; Zhang Jianbo

2005-01-01

Long-range order of a specific kind has recently been found directly in configurations dominating the regularized QCD path integral. In particular, a low-dimensional global structure was identified in typical space-time distributions of topological charge defined via the overlap Dirac matrix. The presence of the order has been concluded from the fact that the structure disappears after random permutation of position coordinates in measured densities. Here we complete the argument for the reality of this structure (namely the conjecture that its existence is a consequence of QCD dynamics and not an artifact of the overlap-based definition of lattice topological field) by showing that the structure ceases to exist after randomizing the space-time coordinates of the underlying gauge field. This implies that the long-range order present in the overlap-based topological density is indeed a manifestation of the QCD vacuum, and that the notion of the fundamental structure (structure involving relevant features at all scales) is viable

Buckled two-dimensional Xene sheets.

Science.gov (United States)

Molle, Alessandro; Goldberger, Joshua; Houssa, Michel; Xu, Yong; Zhang, Shou-Cheng; Akinwande, Deji

2017-02-01

Silicene, germanene and stanene are part of a monoelemental class of two-dimensional (2D) crystals termed 2D-Xenes (X = Si, Ge, Sn and so on) which, together with their ligand-functionalized derivatives referred to as Xanes, are comprised of group IVA atoms arranged in a honeycomb lattice - similar to graphene but with varying degrees of buckling. Their electronic structure ranges from trivial insulators, to semiconductors with tunable gaps, to semi-metallic, depending on the substrate, chemical functionalization and strain. More than a dozen different topological insulator states are predicted to emerge, including the quantum spin Hall state at room temperature, which, if realized, would enable new classes of nanoelectronic and spintronic devices, such as the topological field-effect transistor. The electronic structure can be tuned, for example, by changing the group IVA element, the degree of spin-orbit coupling, the functionalization chemistry or the substrate, making the 2D-Xene systems promising multifunctional 2D materials for nanotechnology. This Perspective highlights the current state of the art and future opportunities in the manipulation and stability of these materials, their functions and applications, and novel device concepts.

Minkowski space structure of the Higgs potential in the two-Higgs-doublet model. II. Minima, symmetries, and topology

International Nuclear Information System (INIS)

Ivanov, I. P.

2008-01-01

We continue to explore the consequences of the recently discovered Minkowski space structure of the Higgs potential in the two-Higgs-doublet model. Here, we focus on the vacuum properties. The search for extrema of the Higgs potential is reformulated in terms of 3-quadrics in the 3+1-dimensional Minkowski space. We prove that 2HDM cannot have more than two local minima in the orbit space and that a twice-degenerate minimum can arise only via spontaneous violation of a discrete symmetry of the Higgs potential. Investigating topology of the 3-quadrics, we give concise criteria for existence of noncontractible paths in the Higgs orbit space. We also study explicit symmetries of the Higgs potential/Lagrangian and their spontaneous violation from a wider perspective than usual

Bifurcations of edge states—topologically protected and non-protected—in continuous 2D honeycomb structures

International Nuclear Information System (INIS)

Fefferman, C L; Lee-Thorp, J P; Weinstein, M I

2016-01-01

Edge states are time-harmonic solutions to energy-conserving wave equations, which are propagating parallel to a line-defect or ‘edge’ and are localized transverse to it. This paper summarizes and extends the authors’ work on the bifurcation of topologically protected edge states in continuous two-dimensional (2D) honeycomb structures. We consider a family of Schrödinger Hamiltonians consisting of a bulk honeycomb potential and a perturbing edge potential. The edge potential interpolates between two different periodic structures via a domain wall. We begin by reviewing our recent bifurcation theory of edge states for continuous 2D honeycomb structures (http://arxiv.org/abs/1506.06111). The topologically protected edge state bifurcation is seeded by the zero-energy eigenstate of a one-dimensional Dirac operator. We contrast these protected bifurcations with (more common) non-protected bifurcations from spectral band edges, which are induced by bound states of an effective Schrödinger operator. Numerical simulations for honeycomb structures of varying contrasts and ‘rational edges’ (zigzag, armchair and others), support the following scenario: (a) for low contrast, under a sign condition on a distinguished Fourier coefficient of the bulk honeycomb potential, there exist topologically protected edge states localized transverse to zigzag edges. Otherwise, and for general edges, we expect long lived edge quasi-modes which slowly leak energy into the bulk. (b) For an arbitrary rational edge, there is a threshold in the medium-contrast (depending on the choice of edge) above which there exist topologically protected edge states. In the special case of the armchair edge, there are two families of protected edge states; for each parallel quasimomentum (the quantum number associated with translation invariance) there are edge states which propagate in opposite directions along the armchair edge. (paper)

Bifurcations of edge states—topologically protected and non-protected—in continuous 2D honeycomb structures

Science.gov (United States)

Fefferman, C. L.; Lee-Thorp, J. P.; Weinstein, M. I.

2016-03-01

Edge states are time-harmonic solutions to energy-conserving wave equations, which are propagating parallel to a line-defect or ‘edge’ and are localized transverse to it. This paper summarizes and extends the authors’ work on the bifurcation of topologically protected edge states in continuous two-dimensional (2D) honeycomb structures. We consider a family of Schrödinger Hamiltonians consisting of a bulk honeycomb potential and a perturbing edge potential. The edge potential interpolates between two different periodic structures via a domain wall. We begin by reviewing our recent bifurcation theory of edge states for continuous 2D honeycomb structures (http://arxiv.org/abs/1506.06111). The topologically protected edge state bifurcation is seeded by the zero-energy eigenstate of a one-dimensional Dirac operator. We contrast these protected bifurcations with (more common) non-protected bifurcations from spectral band edges, which are induced by bound states of an effective Schrödinger operator. Numerical simulations for honeycomb structures of varying contrasts and ‘rational edges’ (zigzag, armchair and others), support the following scenario: (a) for low contrast, under a sign condition on a distinguished Fourier coefficient of the bulk honeycomb potential, there exist topologically protected edge states localized transverse to zigzag edges. Otherwise, and for general edges, we expect long lived edge quasi-modes which slowly leak energy into the bulk. (b) For an arbitrary rational edge, there is a threshold in the medium-contrast (depending on the choice of edge) above which there exist topologically protected edge states. In the special case of the armchair edge, there are two families of protected edge states; for each parallel quasimomentum (the quantum number associated with translation invariance) there are edge states which propagate in opposite directions along the armchair edge.

A Lagrangian analysis of a two-dimensional airfoil with vortex shedding

Energy Technology Data Exchange (ETDEWEB)

Lipinski, Doug; Cardwell, Blake; Mohseni, Kamran [Department of Aerospace Engineering Sciences, University of Colorado, Boulder, CO 80309-0429 (United States)], E-mail: Mohseni@colorado.edu

2008-08-29

Using invariant material manifolds and flow topology, the flow behavior and structure of flow around a two-dimensional Eppler 387 airfoil is examined with an emphasis on vortex shedding and the time-dependent reattachment profile. The examination focuses on low Reynolds number (Re = 60 000) flow at several angles of attack. Using specialized software, we identify invariant manifolds in the flow and use these structures to illuminate the process of vortex formation and the periodic behavior of the reattachment profile. Our analysis concludes with a topological view of the flow, including fixed points and a discussion of phase plots and the frequency spectrum of several key points in the flow. The behavior of invariant manifolds directly relates to the flow topology and illuminates some aspects seen in phase space during vortex shedding. Furthermore, it highlights the reattachment behavior in ways not seen before.

A Lagrangian analysis of a two-dimensional airfoil with vortex shedding

International Nuclear Information System (INIS)

Lipinski, Doug; Cardwell, Blake; Mohseni, Kamran

2008-01-01

Using invariant material manifolds and flow topology, the flow behavior and structure of flow around a two-dimensional Eppler 387 airfoil is examined with an emphasis on vortex shedding and the time-dependent reattachment profile. The examination focuses on low Reynolds number (Re = 60 000) flow at several angles of attack. Using specialized software, we identify invariant manifolds in the flow and use these structures to illuminate the process of vortex formation and the periodic behavior of the reattachment profile. Our analysis concludes with a topological view of the flow, including fixed points and a discussion of phase plots and the frequency spectrum of several key points in the flow. The behavior of invariant manifolds directly relates to the flow topology and illuminates some aspects seen in phase space during vortex shedding. Furthermore, it highlights the reattachment behavior in ways not seen before

Dirac Cones, Topological Edge States, and Nontrivial Flat Bands in Two-Dimensional Semiconductors with a Honeycomb Nanogeometry

Directory of Open Access Journals (Sweden)

E. Kalesaki

2014-01-01

Full Text Available We study theoretically two-dimensional single-crystalline sheets of semiconductors that form a honeycomb lattice with a period below 10 nm. These systems could combine the usual semiconductor properties with Dirac bands. Using atomistic tight-binding calculations, we show that both the atomic lattice and the overall geometry influence the band structure, revealing materials with unusual electronic properties. In rocksalt Pb chalcogenides, the expected Dirac-type features are clouded by a complex band structure. However, in the case of zinc-blende Cd-chalcogenide semiconductors, the honeycomb nanogeometry leads to rich band structures, including, in the conduction band, Dirac cones at two distinct energies and nontrivial flat bands and, in the valence band, topological edge states. These edge states are present in several electronic gaps opened in the valence band by the spin-orbit coupling and the quantum confinement in the honeycomb geometry. The lowest Dirac conduction band has S-orbital character and is equivalent to the π-π^{⋆} band of graphene but with renormalized couplings. The conduction bands higher in energy have no counterpart in graphene; they combine a Dirac cone and flat bands because of their P-orbital character. We show that the width of the Dirac bands varies between tens and hundreds of meV. These systems emerge as remarkable platforms for studying complex electronic phases starting from conventional semiconductors. Recent advancements in colloidal chemistry indicate that these materials can be synthesized from semiconductor nanocrystals.

Positional isomerism-driven two 3D pillar-layered metal-organic frameworks: Syntheses, topological structures and photoluminescence properties

Energy Technology Data Exchange (ETDEWEB)

Sun, Yayong; Zhao, Siwei; Ma, Haoran; Han, Yi; Liu, Kang; Wang, Lei, E-mail: inorchemwl@126.com

2016-06-15

Two novel three-dimensional (3D) pillar-layered metal-organic frameworks (MOFs), namely [Zn{sub 2}(μ{sub 2}-OH)(boaba)(1,4-bmimb)]{sub n} (1) and {[Zn_5K_2(μ_2-H_2O)_2(boaba)_4(1,2-bmimb)_2(H_2O)_2]·H_2O}{sub n} (2), were prepared by hydrothermal reactions (H{sub 3}boaba=3,5-bis-oxyacetate-benzoic acid; 1,4-bmimb=1,4-bis((2-methyl-1H-imidazol-1-yl)methyl)benzene; 1,2-bmimb =1,2-bis((2-methyl-1H-imidazol-1-yl)methyl)benzene). Notably, 1 exhibits a (3,5)-connected binodal (6{sup 3})(6{sup 9}·8)-gra net with binuclear [Zn{sub 2}(μ{sub 2}-OH)(COO)]{sup 2+} clusters, while 2 shows a novel (4,4,5,9)-connected 4-nodal net constructed from the unique Zn(II)-K(I) heterometal rod-like substructures. The results indicate that the disposition of the 2-methylimidazolyl groups of bis(imidazole) ligands have a significant effect on structural diversity. Moreover, the photoluminescence properties of 1 and 2 have been investigated. - Graphical abstract: Two novel 3D pillar-layered metal-organic coordination networks with aromatic multicarboxylate anion and bis(imidazole) ligands have been synthesized and structurally characterized. Display Omitted - Highlights: • It is rarely reported that metal-organic frameworks prepared with 3,5-bis-oxyacetate-benzoic acid. • Two metal-organic frameworks based on positional isomeric ligands were synthesized and structurally characterized. • Compond 1 displays unique (3,5)-connected binodal gra topology. • Compound 2 exhibits (4,4,5,9)-connected 4-nodal topology based on the Zn(II)-K(I) heterometal rod-like substructures. • The photoluminescence properties of compound 1 and 2 have been investigated.

Charge-spin Transport in Surface-disordered Three-dimensional Topological Insulators

Science.gov (United States)

Peng, Xingyue

As one of the most promising candidates for the building block of the novel spintronic circuit, the topological insulator (TI) has attracted world-wide interest of study. Robust topological order protected by time-reversal symmetry (TRS) makes charge transport and spin generation in TIs significantly different from traditional three-dimensional (3D) or two-dimensional (2D) electronic systems. However, to date, charge transport and spin generation in 3D TIs are still primarily modeled as single-surface phenomena, happening independently on top and bottom surfaces. In this dissertation, I will demonstrate via both experimental findings and theoretical modeling that this "single surface'' theory neither correctly describes a realistic 3D TI-based device nor reveals the amazingly distinct physical picture of spin transport dynamics in 3D TIs. Instead, I present a new viewpoint of the spin transport dynamics where the role of the insulating yet topologically non-trivial bulk of a 3D TI becomes explicit. Within this new theory, many mysterious transport and magneto-transport anomalies can be naturally explained. The 3D TI system turns out to be more similar to its low dimensional sibling--2D TI rather than some other systems sharing the Dirac dispersion, such as graphene. This work not only provides valuable fundamental physical insights on charge-spin transport in 3D TIs, but also offers important guidance to the design of 3D TI-based spintronic devices.

Fracton topological order from nearest-neighbor two-spin interactions and dualities

Science.gov (United States)

Slagle, Kevin; Kim, Yong Baek

2017-10-01

Fracton topological order describes a remarkable phase of matter, which can be characterized by fracton excitations with constrained dynamics and a ground-state degeneracy that increases exponentially with the length of the system on a three-dimensional torus. However, previous models exhibiting this order require many-spin interactions, which may be very difficult to realize in a real material or cold atom system. In this work, we present a more physically realistic model which has the so-called X-cube fracton topological order [Vijay, Haah, and Fu, Phys. Rev. B 94, 235157 (2016), 10.1103/PhysRevB.94.235157] but only requires nearest-neighbor two-spin interactions. The model lives on a three-dimensional honeycomb-based lattice with one to two spin-1/2 degrees of freedom on each site and a unit cell of six sites. The model is constructed from two orthogonal stacks of Z2 topologically ordered Kitaev honeycomb layers [Kitaev, Ann. Phys. 321, 2 (2006), 10.1016/j.aop.2005.10.005], which are coupled together by a two-spin interaction. It is also shown that a four-spin interaction can be included to instead stabilize 3+1D Z2 topological order. We also find dual descriptions of four quantum phase transitions in our model, all of which appear to be discontinuous first-order transitions.

Topological organization of (low-dimensional) chaos

International Nuclear Information System (INIS)

Tufillaro, N.B.

1992-01-01

Recent progress toward classifying low-dimensional chaos measured from time series data is described. This classification theory assigns a template to the time series once the time series is embedded in three dimensions. The template describes the primary folding and stretching mechanisms of phase space responsible for the chaotic motion. Topological invariants of the unstable periodic orbits in the closure of the strange set are calculated from the (reconstructed) template. These topological invariants must be consistent with ampersand ny model put forth to describe the time series data, and are useful in invalidating (or gaining confidence in) any model intended to describe the dynamical system generating the time series

Yang Monopoles and Emergent Three-Dimensional Topological Defects in Interacting Bosons

Science.gov (United States)

Yan, Yangqian; Zhou, Qi

2018-06-01

The Yang monopole as a zero-dimensional topological defect has been well established in multiple fields in physics. However, it remains an intriguing question to understand the interaction effects on Yang monopoles. Here, we show that the collective motion of many interacting bosons gives rise to exotic topological defects that are distinct from Yang monopoles seen by a single particle. Whereas interactions may distribute Yang monopoles in the parameter space or glue them to a single giant one of multiple charges, three-dimensional topological defects also arise from continuous manifolds of degenerate many-body eigenstates. Their projections in lower dimensions lead to knotted nodal lines and nodal rings. Our results suggest that ultracold bosonic atoms can be used to create emergent topological defects and directly measure topological invariants that are not easy to access in solids.

Electrically tunable robust edge states in graphene-based topological photonic crystal slabs

Science.gov (United States)

Song, Zidong; Liu, HongJun; Huang, Nan; Wang, ZhaoLu

2018-03-01

Topological photonic crystals are optical structures supporting topologically protected unidirectional edge states that exhibit robustness against defects. Here, we propose a graphene-based all-dielectric photonic crystal slab structure that supports two-dimensionally confined topological edge states. These topological edge states can be confined in the out-of-plane direction by two parallel graphene sheets. In the structure, the excitation frequency range of topological edge states can be dynamically and continuously tuned by varying bias voltage across the two parallel graphene sheets. Utilizing this kind of architecture, we construct Z-shaped channels to realize topological edge transmission with diffrerent frequencies. The proposal provides a new degree of freedom to dynamically control topological edge states and potential applications for robust integrated photonic devices and optical communication systems.

Topological and trivial magnetic oscillations in nodal loop semimetals

Science.gov (United States)

Oroszlány, László; Dóra, Balázs; Cserti, József; Cortijo, Alberto

2018-05-01

Nodal loop semimetals are close descendants of Weyl semimetals and possess a topologically dressed band structure. We argue by combining the conventional theory of magnetic oscillation with topological arguments that nodal loop semimetals host coexisting topological and trivial magnetic oscillations. These originate from mapping the topological properties of the extremal Fermi surface cross sections onto the physics of two dimensional semi-Dirac systems, stemming from merging two massless Dirac cones. By tuning the chemical potential and the direction of magnetic field, a sharp transition is identified from purely trivial oscillations, arising from the Landau levels of a normal two dimensional (2D) electron gas, to a phase where oscillations of topological and trivial origin coexist, originating from 2D massless Dirac and semi-Dirac points, respectively. These could in principle be directly identified in current experiments.

Few remarks on chiral theories with sophisticated topology

International Nuclear Information System (INIS)

Golo, V.L.; Perelomov, A.M.

1978-01-01

Two classes of the two-dimensional Euclidean chiral field theoreties are singled out: 1) the field phi(x) takes the values in the compact Hermitiam symmetric space 2) the field phi(x) takes the values in an orbit of the adjoint representation of the comcompact Lie group. The theories have sophisticated topological and rich analytical structures. They are considered with the help of topological invariants (topological charges). Explicit formulae for the topological charges are indicated, and the lower bound extimate for the action is given

Three-dimensional fractional topological insulators in coupled Rashba layers

Science.gov (United States)

Volpez, Yanick; Loss, Daniel; Klinovaja, Jelena

2017-08-01

We propose a model of three-dimensional topological insulators consisting of weakly coupled electron- and hole-gas layers with Rashba spin-orbit interaction stacked along a given axis. We show that in the presence of strong electron-electron interactions the system realizes a fractional strong topological insulator, where the rotational symmetry and condensation energy arguments still allow us to treat the problem as quasi-one-dimensional with bosonization techniques. We also show that if Rashba and Dresselhaus spin-orbit interaction terms are equally strong, by doping the system with magnetic impurities, one can bring it into the Weyl semimetal phase.

Aspects of Dzyaloshinskii-Moriya Interaction in Two Dimensional Magnetic Structures

Science.gov (United States)

Kundu, Anirban

Research on topologically protected chiral magnetic structures such as magnetic domain walls (DWs) and skyrmions, have gained extensive interest because of their possible applications in magnetic data storage industries. The recently observed chiral DW structures in ultrathin ferromagnetic lms with perpendicular magnetic anisotropy has been attributed to the presence of a strong Dzyaloshinskii-Moriya interaction (DMI). In this thesis, the DMI mediated by the conduction electrons in two dimensional magnetic systems such as magnetic thin lms or at the interfaces between two magnetic materials has been studied. I calculate the Ruderman-Kittel- Kasuya-Yosida (RKKY) type indirect exchange coupling between two magnetic moments at nite temperature using the free electron band. At high temperature, the coupling strength decays with distance faster than the coupling at zero temperature but the period of oscillation remains same. However, the free electron band alone could not produce DMI. In the next step, I show addition of Rashba spin-orbit coupling (RSOC) with the spin-polarized conduction electron band produces the DMI between two magnetic ions. The essential feature of this DMI is: the coupling strength increases with the strength of RSOC, but decreases signi cantly with the Heisenberg exchange coupling. The DMI calculated with this model well explains the possibility of preferred Neel or Bloch DW structures with specifc chirality. In addition: I study switching of magnetization with ultrafast laser pulse by inverse Faraday e ect (IFE) where an optically induced non-equilibrium orbital momentum generates an e ective magnetic eld via spin-orbit coupling for magnetization switching. I calculate the magnitude of induced orbital moment for the generic itinerant band and show that magnitude is not large enough to make the switching by a single pulse, however, switching could be possible if multiple pulses are applied to the material.

Quantification of topological changes of vorticity contours in two-dimensional Navier-Stokes flow.

Science.gov (United States)

Ohkitani, Koji; Al Sulti, Fayeza

2010-06-01

A characterization of reconnection of vorticity contours is made by direct numerical simulations of the two-dimensional Navier-Stokes flow at a relatively low Reynolds number. We identify all the critical points of the vorticity field and classify them by solving an eigenvalue problem of its Hessian matrix on the basis of critical-point theory. The numbers of hyperbolic (saddles) and elliptic (minima and maxima) points are confirmed to satisfy Euler's index theorem numerically. Time evolution of these indices is studied for a simple initial condition. Generally speaking, we have found that the indices are found to decrease in number with time. This result is discussed in connection with related works on streamline topology, in particular, the relationship between stagnation points and the dissipation. Associated elementary procedures in physical space, the merging of vortices, are studied in detail for a number of snapshots. A similar analysis is also done using the stream function.

Topology optimization for acoustic-structure interaction problems

DEFF Research Database (Denmark)

Yoon, Gil Ho; Jensen, Jakob Søndergaard; Sigmund, Ole

2006-01-01

We propose a gradient based topology optimization algorithm for acoustic-structure (vibro-acoustic) interaction problems without an explicit interfacing boundary representation. In acoustic-structure interaction problems, the pressure field and the displacement field are governed by the Helmholtz...... to subdomain interfaces evolving during the optimization process. In this paper, we propose to use a mixed finite element formulation with displacements and pressure as primary variables (u/p formulation) which eliminates the need for explicit boundary representation. In order to describe the Helmholtz......-dimensional acoustic-structure interaction problems are optimized to show the validity of the proposed method....

Topology optimization for three-dimensional electromagnetic waves using an edge element-based finite-element method.

Science.gov (United States)

Deng, Yongbo; Korvink, Jan G

2016-05-01

This paper develops a topology optimization procedure for three-dimensional electromagnetic waves with an edge element-based finite-element method. In contrast to the two-dimensional case, three-dimensional electromagnetic waves must include an additional divergence-free condition for the field variables. The edge element-based finite-element method is used to both discretize the wave equations and enforce the divergence-free condition. For wave propagation described in terms of the magnetic field in the widely used class of non-magnetic materials, the divergence-free condition is imposed on the magnetic field. This naturally leads to a nodal topology optimization method. When wave propagation is described using the electric field, the divergence-free condition must be imposed on the electric displacement. In this case, the material in the design domain is assumed to be piecewise homogeneous to impose the divergence-free condition on the electric field. This results in an element-wise topology optimization algorithm. The topology optimization problems are regularized using a Helmholtz filter and a threshold projection method and are analysed using a continuous adjoint method. In order to ensure the applicability of the filter in the element-wise topology optimization version, a regularization method is presented to project the nodal into an element-wise physical density variable.

An Algebro-Topological Description of Protein Domain Structure

Science.gov (United States)

Penner, Robert Clark; Knudsen, Michael; Wiuf, Carsten; Andersen, Jørgen Ellegaard

2011-01-01

The space of possible protein structures appears vast and continuous, and the relationship between primary, secondary and tertiary structure levels is complex. Protein structure comparison and classification is therefore a difficult but important task since structure is a determinant for molecular interaction and function. We introduce a novel mathematical abstraction based on geometric topology to describe protein domain structure. Using the locations of the backbone atoms and the hydrogen bonds, we build a combinatorial object – a so-called fatgraph. The description is discrete yet gives rise to a 2-dimensional mathematical surface. Thus, each protein domain corresponds to a particular mathematical surface with characteristic topological invariants, such as the genus (number of holes) and the number of boundary components. Both invariants are global fatgraph features reflecting the interconnectivity of the domain by hydrogen bonds. We introduce the notion of robust variables, that is variables that are robust towards minor changes in the structure/fatgraph, and show that the genus and the number of boundary components are robust. Further, we invesigate the distribution of different fatgraph variables and show how only four variables are capable of distinguishing different folds. We use local (secondary) and global (tertiary) fatgraph features to describe domain structures and illustrate that they are useful for classification of domains in CATH. In addition, we combine our method with two other methods thereby using primary, secondary, and tertiary structure information, and show that we can identify a large percentage of new and unclassified structures in CATH. PMID:21629687

Devaney chaos, Li-Yorke chaos, and multi-dimensional Li-Yorke chaos for topological dynamics

Science.gov (United States)

Dai, Xiongping; Tang, Xinjia

2017-11-01

Let π : T × X → X, written T↷π X, be a topological semiflow/flow on a uniform space X with T a multiplicative topological semigroup/group not necessarily discrete. We then prove: If T↷π X is non-minimal topologically transitive with dense almost periodic points, then it is sensitive to initial conditions. As a result of this, Devaney chaos ⇒ Sensitivity to initial conditions, for this very general setting. Let R+↷π X be a C0-semiflow on a Polish space; then we show: If R+↷π X is topologically transitive with at least one periodic point p and there is a dense orbit with no nonempty interior, then it is multi-dimensional Li-Yorke chaotic; that is, there is a uncountable set Θ ⊆ X such that for any k ≥ 2 and any distinct points x1 , … ,xk ∈ Θ, one can find two time sequences sn → ∞ ,tn → ∞ with Moreover, let X be a non-singleton Polish space; then we prove: Any weakly-mixing C0-semiflow R+↷π X is densely multi-dimensional Li-Yorke chaotic. Any minimal weakly-mixing topological flow T↷π X with T abelian is densely multi-dimensional Li-Yorke chaotic. Any weakly-mixing topological flow T↷π X is densely Li-Yorke chaotic. We in addition construct a completely Li-Yorke chaotic minimal SL (2 , R)-acting flow on the compact metric space R ∪ { ∞ }. Our various chaotic dynamics are sensitive to the choices of the topology of the phase semigroup/group T.

Synthesis, structure and topological analysis of glycine templated highly stable cadmium sulfate framework: A New Lewis Acid catalyst

Science.gov (United States)

Paul, Avijit Kumar

2018-04-01

One new open-framework two-dimensional layer, [Cd(NH3CH2COO)(SO4)], I, has been synthesized using amino acid as templating agent. Single crystal structural analysis shows that the compound crystallizes in monoclinic cell with non-centrosymmetric space group P21, a = 4.9513(1) Å, b = 7.9763(2) Å, c = 8.0967(2) Å, β = 105.917(1)° and V = 307.504(12) Å3. The compound has connectivity between the Cd-centers and the sulfate units forming a two-dimensional layer structure. Sulfate unit is coordinated to metal center with η3, μ4 mode possessing a coordination free oxygen atom. The zwitterionic form of glycine molecule is present in the structure bridging with two metal centers through μ2-mode by carboxylate oxygens. The topological analysis reveals that the two-dimensional network is formed with a novel 4- and 6-connected binodal net of (32,42,52)(34,44,54,63) topology. Although one end of the glycine molecule is free from coordination, the structure is highly stable up to 350 °C. Strong N-H⋯ O hydrogen bonding interactions play an important role in the stabilization and formation of three-dimensional supramolecular structure. The cyanosilylation of imines using the present compounds as heterogeneous catalyst indicates good catalytic behavior. The present study illustrates the usefulness of the amino acid for the structure building in less studied sulfate based framework materials as well as designing of new heterogeneous catalysts for the broad application. The compound has also been characterized through elemental analysis, PXRD, IR, SEM and TG-DT studies.

Backscattering from width variations in quasi-one-dimensional strips of topological insulators

International Nuclear Information System (INIS)

Takagaki, Y

2012-01-01

Conductance modulations in wide-narrow-wide electron waveguides constructed from a two-dimensional topological insulator are investigated numerically. The conductance exhibits the Fabry-Perot oscillation at the opening of the helical edge states in the narrow segment when the potential offset imposed in the segment is varied. The quantum multiple reflections between the two ends of the narrow segment manifested by the oscillation demonstrate that the topological states are not protected from the scattering caused by an abrupt change in the channel width. The bulk states do not affect the vulnerability against the geometry scattering but they give rise to resonant transmission in an unconventional fashion.

Signatures of Majorana bound states in one-dimensional topological superconductors

International Nuclear Information System (INIS)

Pientka, Falko

2014-01-01

Topological states of matter have fascinated condensed matter physicists for the past three decades. Famous examples include the integer and fractional quantum Hall states exhibiting a spectacular conductance quantization as well as topological insulators in two and three dimensions featuring gapless Dirac fermions at the boundary. Very recently, novel topological phases in superconductors have been subject of intense experimental and theoretical investigation. One-dimensional topological superconductors are particularly intriguing as they host exotic Majorana end states. These are zero-energy bound states with nonabelian exchange statistics potentially useful for topologically protected quantum computing. Recent theoretical and experimental advances have put the realization of Majorana states within reach of current measurement techniques. In this thesis we investigate signatures of Majorana bound states in realistic experiments aiming to improve the theoretical understanding of ongoing experimental efforts and to design novel measurement schemes, which exhibit convincing signatures of Majoranas. In particular we account for nonideal experimental conditions which can lead to qualitatively new features. Possible signatures of Majoranas can be accessed in the Josephson current through a weak link between two topological superconductors although the signatures in the dc Josephson effect are typically obscured by inevitable quasiparticle relaxation in the superconductor. Here we propose a measurement scheme in mesoscopic superconducting rings, where Majorana signatures persist even for infinitely fast relaxation. In a separate project we outline an alternative to the standard Josephson experiment in topological superconductors based on quantum wires. We delineate how Majoranas can be detected, when the Josephson current is induced by noncollinear magnetic fields applied to the two banks of the junction instead of a superconducting phase difference. Another important

Electrically controlled crossing of energy levels in quantum dots in two-dimensional topological insulators

Energy Technology Data Exchange (ETDEWEB)

Sukhanov, Aleksei A.

2017-05-15

We study the energy spectra of bound states in quantum dots (QDs) formed by an electrostatic potential in two-dimensional topological insulator (TI) and their transformation with changes in QD depth and radius. It is found that, unlike a trivial insulator, the energy difference between the levels of the ground state and first excited state can decrease with decreasing the radius and increasing the depth of the QD so that these levels intersect under some critical condition. The crossing of the levels results in unusual features of optical properties caused by intraceneter electron transitions. In particular, it leads to significant changes of light absorption due to electron transitions between such levels and to the transient electroluminescence induced by electrical tuning of QD and TI parameters. In the case of magnetic TIs, the polarization direction of the absorbed or emitted circularly polarized light is changed due to the level crossing.

Electrically controlled crossing of energy levels in quantum dots in two-dimensional topological insulators

Science.gov (United States)

Sukhanov, Aleksei A.

2017-05-01

We study the energy spectra of bound states in quantum dots (QDs) formed by an electrostatic potential in two-dimensional topological insulator (TI) and their transformation with changes in QD depth and radius. It is found that, unlike a trivial insulator, the energy difference between the levels of the ground state and first excited state can decrease with decreasing the radius and increasing the depth of the QD so that these levels intersect under some critical condition. The crossing of the levels results in unusual features of optical properties caused by intraceneter electron transitions. In particular, it leads to significant changes of light absorption due to electron transitions between such levels and to the transient electroluminescence induced by electrical tuning of QD and TI parameters. In the case of magnetic TIs, the polarization direction of the absorbed or emitted circularly polarized light is changed due to the level crossing.

Geometry and topology of wild translation surfaces

OpenAIRE

Randecker, Anja

2016-01-01

A translation surface is a two-dimensional manifold, equipped with a translation structure. It can be obtained by considering Euclidean polygons and identifying their edges via translations. The vertices of the polygons form singularities if the translation structure can not be extended to them. We study translation surfaces with wild singularities, regarding the topology (genus and space of ends), the geometry (behavior of the singularities), and how the topology and the geometry are related.

Hysteresis and avalanches in two-dimensional foam rheology simulations

International Nuclear Information System (INIS)

Jiang, Y.; Swart, P.J.; Saxena, A.; Asipauskas, M.; Glazier, J.A.

1999-01-01

Foams have unique rheological properties that range from solidlike to fluidlike. We study two-dimensional noncoarsening foams of different disorder under shear in a Monte Carlo simulation, using a driven large-Q Potts model. Simulations of periodic shear on an ordered foam show several different response regimes. At small strain amplitudes, bubbles deform and recover their shapes elastically, and the macroscopic response is that of a linear elastic cellular material. For increasing strain amplitude, the energy-strain curve starts to exhibit hysteresis before any topological rearrangements occur, indicating a macroscopic viscoelastic response. When the applied strain amplitude exceeds a critical value, the yield strain, topological rearrangements occur, the foam starts to flow, and we observe macroscopic irreversibility. We find that the dynamics of topological rearrangements depend sensitively on the structural disorder. Structural disorder decreases the yield strain; sufficiently high disorder changes the macroscopic response of a foam from a viscoelastic solid to a viscoelastic fluid. This wide-ranging dynamical response and the associated history effects of foams result from avalanchelike rearrangement events. The spatiotemporal statistics of rearrangement events do not display long-range correlations for ordered foams or at low shear rates, consistent with experimental observations. As the shear rate or structural disorder increases, the topological events become more correlated and their power spectra change from that of white noise toward 1/f noise. Intriguingly, the power spectra of the total stored energy also exhibit this 1/f trend. copyright 1999 The American Physical Society

Topology of RNA-RNA interaction structures

DEFF Research Database (Denmark)

Andersen, Jørgen Ellegaard; Huang, Fenix Wenda; Penner, Robert

2012-01-01

Abstract The topological filtration of interacting RNA complexes is studied, and the role is analyzed of certain diagrams called irreducible shadows, which form suitable building blocks for more general structures. We prove that, for two interacting RNAs, called interaction structures, there exist...

Topological phases in a three-dimensional topological insulator with a time-reversal invariant external field

International Nuclear Information System (INIS)

Guo, Xiaoyong; Ren, Xiaobin; Wang, Gangzhi; Peng, Jie

2014-01-01

We investigate the impact of a time-reversal invariant external field on the topological phases of a three-dimensional (3D) topological insulator. By taking the momentum k z as a parameter, we calculate the spin-Chern number analytically. It is shown that both the quantum spin Hall phase and the integer quantum Hall phase can be realized in our system. When the strength of the external field is varied, a series of topological phase transitions occurs with the closing of the energy gap or the spin-spectrum gap. In a tight-binding form, the surface modes are discussed numerically to confirm the analytically results. (paper)

Topology of streamlines and vorticity contours for two - dimensional flows

DEFF Research Database (Denmark)

Andersen, Morten

on the vortex filament by the localised induction approximation the stream function is slightly modified and an extra parameter is introduced. In this setting two new flow topologies arise, but not more than two critical points occur for any combination of the parameters. The analysis of the closed form show...... by a point vortex above a wall in inviscid fluid. There is no reason to a priori expect equivalent results of the three vortex definitions. However, the study is mainly motivated by the findings of Kudela & Malecha (Fluid Dyn. Res. 41, 2009) who find good agreement between the vorticity and streamlines...

Gauge-field topology in two dimensions: θ-vacuum, topological phases and composite fields

International Nuclear Information System (INIS)

Ilieva, N.; Pervushin, V.N.

1990-06-01

In the framework of the minimal quantization method, the residual 'longitudinal' vacuum dynamics of the Abelian gauge field, that is described by a new pair of canonical variables, is revealed. This dynamics is shown to give origin to the θ-vacuum, thus providing a field analogy of the Josephson effect. The destructive interference of the topological phases - that the fermion fields are shown to acquire - is considered as a reason for the charge screening in the two-dimensional massless QED. (author). 11 refs

Topological structures of vortex flow on a flying wing aircraft, controlled by a nanosecond pulse discharge plasma actuator

Science.gov (United States)

Du, Hai; Shi, Zhiwei; Cheng, Keming; Wei, Dechen; Li, Zheng; Zhou, Danjie; He, Haibo; Yao, Junkai; He, Chengjun

2016-06-01

Vortex control is a thriving research area, particularly in relation to flying wing or delta wing aircraft. This paper presents the topological structures of vortex flow on a flying wing aircraft controlled by a nanosecond plasma dielectric barrier discharge actuator. Experiments, including oil flow visualization and two-dimensional particle image velocimetry (PIV), were conducted in a wind tunnel with a Reynolds number of 0.5 × 106. Both oil and PIV results show that the vortex can be controlled. Oil topological structures on the aircraft surface coincide with spatial PIV flow structures. Both indicate vortex convergence and enhancement when the plasma discharge is switched on, leading to a reduced region of separated flow.

Sums of two-dimensional spectral triples

DEFF Research Database (Denmark)

Christensen, Erik; Ivan, Cristina

2007-01-01

construct a sum of two dimensional modules which reflects some aspects of the topological dimensions of the compact metric space, but this will only give the metric back approximately. At the end we make an explicit computation of the last module for the unit interval in. The metric is recovered exactly...

Magnetic structure of two- and three-dimensional supramolecular compounds

Energy Technology Data Exchange (ETDEWEB)

Decurtins, S.; Schmalle, H.W.; Pellaux, R. [Zurich Univ. (Switzerland); Fischer, P.; Fauth, F. [Paul Scherrer Inst. (PSI), Villigen (Switzerland); Ouladdiaf, B. [Institut Max von Laue - Paul Langevin, 75 - Paris (France)

1997-09-01

Supramolecular chiral networks of oxalato-bridged transition metals show either two- or three-dimensional structural features. The magnetic structures of such compounds have been investigated by means of elastic neutron powder diffraction. (author) 2 figs., 2 refs.

Variable dimensionality in the uranium fluoride/2-methyl-piperazine system: Synthesis and structures of UFO-5, -6, and -7; Zero-, one-, and two-dimensional materials with unprecedented topologies

International Nuclear Information System (INIS)

Francis, R.J.; Halasyamani, P.S.; Bee, J.S.; O'Hare, D.

1999-01-01

Recently, low temperature (T < 300 C) hydrothermal reactions of inorganic precursors in the presence of organic cations have proven highly productive for the synthesis of novel solid-state materials. Interest in these materials is driven by the astonishingly diverse range of structures produced, as well as by their many potential materials chemistry applications. This report describes the high yield, phase pure hydrothermal syntheses of three new uranium fluoride phases with unprecedented structure types. Through the systematic control of the synthesis conditions the authors have successfully controlled the architecture and dimensionality of the phase formed and selectively synthesized novel zero-, one-, and two-dimensional materials

Infrared magneto-spectroscopy of two-dimensional and three-dimensional massless fermions: A comparison

Energy Technology Data Exchange (ETDEWEB)

Orlita, M., E-mail: milan.orlita@lncmi.cnrs.fr [Laboratoire National des Champs Magnétiques Intenses, CNRS-UJF-UPS-INSA, 38042 Grenoble (France); Faculty of Mathematics and Physics, Charles University, Ke Karlovu 5, 121 16 Prague 2 (Czech Republic); Faugeras, C.; Barra, A.-L.; Martinez, G.; Potemski, M. [Laboratoire National des Champs Magnétiques Intenses, CNRS-UJF-UPS-INSA, 38042 Grenoble (France); Basko, D. M. [LPMMC UMR 5493, Université Grenoble 1/CNRS, B.P. 166, 38042 Grenoble (France); Zholudev, M. S. [Laboratoire Charles Coulomb (L2C), UMR CNRS 5221, GIS-TERALAB, Université Montpellier II, 34095 Montpellier (France); Institute for Physics of Microstructures, RAS, Nizhny Novgorod GSP-105 603950 (Russian Federation); Teppe, F.; Knap, W. [Laboratoire Charles Coulomb (L2C), UMR CNRS 5221, GIS-TERALAB, Université Montpellier II, 34095 Montpellier (France); Gavrilenko, V. I. [Institute for Physics of Microstructures, RAS, Nizhny Novgorod GSP-105 603950 (Russian Federation); Mikhailov, N. N.; Dvoretskii, S. A. [A.V. Rzhanov Institute of Semiconductor Physics, Siberian Branch, Russian Academy of Sciences, Novosibirsk 630090 (Russian Federation); Neugebauer, P. [Institut für Physikalische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart (Germany); Berger, C. [School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332 (United States); Institut Néel/CNRS-UJF BP 166, F-38042 Grenoble Cedex 9 (France); Heer, W. A. de [School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332 (United States)

2015-03-21

Here, we report on a magneto-optical study of two distinct systems hosting massless fermions—two-dimensional graphene and three-dimensional HgCdTe tuned to the zero band gap condition at the point of the semiconductor-to-semimetal topological transition. Both materials exhibit, in the quantum regime, a fairly rich magneto-optical response, which is composed from a series of intra- and interband inter-Landau level resonances with for massless fermions typical √(B) dependence. The impact of the system's dimensionality and of the strength of the spin-orbit interaction on the optical response is also discussed.

Poly[bis(N,N-dimethylformamidetris(μ4-trans-stilbene-4,4′-dicarboxylatotricadmium(II]: a two-dimensional network with an unusual 36 topology

Directory of Open Access Journals (Sweden)

Gyungse Park

2008-07-01

Full Text Available In the title compound, [Cd3(C16H10O43(C3H7NO2]n or [Cd3(SDA3(DMF2]n (H2SDA is trans-stilbene-4,4′-dicarboxylic acid and DMF is dimethylformamide, the linear dicarboxylate ligand forms a two-dimensionally layered metal–organic network with the relatively uncommon 36 topology. The structure reveals trinuclear secondary building units and has an octahedral geometry at a central metal ion (occupying a overline{3} symmetry site and tetrahedral geometries at two surrounding symmetrically equivalent metal ions lying on a threefold axis. The six-connected planar trinuclear CdII centers, Cd3(O2CR6, play a role as potential nodes in generation of the relatively uncommon 36 topology. The coordinated DMF unit is disordered around the threefold axis.

Visualizing vector field topology in fluid flows

Science.gov (United States)

Helman, James L.; Hesselink, Lambertus

1991-01-01

Methods of automating the analysis and display of vector field topology in general and flow topology in particular are discussed. Two-dimensional vector field topology is reviewed as the basis for the examination of topology in three-dimensional separated flows. The use of tangent surfaces and clipping in visualizing vector field topology in fluid flows is addressed.

Two-stage Framework for a Topology-Based Projection and Visualization of Classified Document Collections

Energy Technology Data Exchange (ETDEWEB)

Oesterling, Patrick; Scheuermann, Gerik; Teresniak, Sven; Heyer, Gerhard; Koch, Steffen; Ertl, Thomas; Weber, Gunther H.

2010-07-19

During the last decades, electronic textual information has become the world's largest and most important information source available. People have added a variety of daily newspapers, books, scientific and governmental publications, blogs and private messages to this wellspring of endless information and knowledge. Since neither the existing nor the new information can be read in its entirety, computers are used to extract and visualize meaningful or interesting topics and documents from this huge information clutter. In this paper, we extend, improve and combine existing individual approaches into an overall framework that supports topological analysis of high dimensional document point clouds given by the well-known tf-idf document-term weighting method. We show that traditional distance-based approaches fail in very high dimensional spaces, and we describe an improved two-stage method for topology-based projections from the original high dimensional information space to both two dimensional (2-D) and three dimensional (3-D) visualizations. To show the accuracy and usability of this framework, we compare it to methods introduced recently and apply it to complex document and patent collections.

Mass relations for two-dimensional classical configurations

International Nuclear Information System (INIS)

Tataru-Mihai, P.

1980-01-01

Using the two-dimensional sigma-nonlinear models as a framework mass relations for classical configurations of instanton/soliton type are derived. Our results suggest an interesting differential-geometric interpretation of the mass of a classical configuration in terms of the topological characteristics of an associated manifold. (orig.)

Two-dimensional electron gas in monolayer InN quantum wells

International Nuclear Information System (INIS)

Pan, W.; Wang, G. T.; Dimakis, E.; Moustakas, T. D.; Tsui, D. C.

2014-01-01

We report in this letter experimental results that confirm the two-dimensional nature of the electron systems in a superlattice structure of 40 InN quantum wells consisting of one monolayer of InN embedded between 10 nm GaN barriers. The electron density and mobility of the two-dimensional electron system (2DES) in these InN quantum wells are 5 × 10 15  cm −2 (or 1.25 × 10 14  cm −2 per InN quantum well, assuming all the quantum wells are connected by diffused indium contacts) and 420 cm 2 /Vs, respectively. Moreover, the diagonal resistance of the 2DES shows virtually no temperature dependence in a wide temperature range, indicating the topological nature of the 2DES

The topological filtration of gamma-structures

DEFF Research Database (Denmark)

Li, Thomas; Reidys, Christian

2013-01-01

In this paper we study gamma-structures filtered by topological genus. gamma-structures are a class of RNA pseudoknot structures that plays a key role in the context of polynomial time folding of RNA pseudoknot structures. A gamma-structure is composed by specific building blocks, that have...... topological genus less than or equal to gamma, where composition means concatenation and nesting of such blocks. Our main results are the derivation of a new bivariate generating function for gamma-structures via symbolic methods, the singularity analysis of the solutions and a central limit theorem...... for the distribution of topological genus in gamma-structures of given length. In our derivation specific bivariate polynomials play a central role. Their coefficients count particular motifs of fixed topological genus and they are of relevance in the context of genus recursion and novel folding algorithms....

High-Harmonic Generation in Solids with and without Topological Edge States

DEFF Research Database (Denmark)

Bauer, Dieter; Hansen, Kenneth Christian Klochmann

2018-01-01

High-harmonic generation in the two topological phases of a finite, one-dimensional, periodic structure is investigated using a self-consistent time-dependent density functional theory approach. For harmonic photon energies smaller than the band gap, the harmonic yield is found to differ by up...... to 14 orders of magnitude for the two topological phases. This giant topological effect is explained by the degree of destructive interference in the harmonic emission of all valence-band (and edge-state) electrons, which strongly depends on whether or not topological edge states are present...

Tunable spin-orbit coupling for ultracold atoms in two-dimensional optical lattices

Science.gov (United States)

Grusdt, Fabian; Li, Tracy; Bloch, Immanuel; Demler, Eugene

2017-06-01

Spin-orbit coupling (SOC) is at the heart of many exotic band structures and can give rise to many-body states with topological order. Here we present a general scheme based on a combination of microwave driving and lattice shaking for the realization of two-dimensional SOC with ultracold atoms in systems with inversion symmetry. We show that the strengths of Rashba and Dresselhaus SOC can be independently tuned in a spin-dependent square lattice. More generally, our method can be used to open gaps between different spin states without breaking time-reversal symmetry. We demonstrate that this allows for the realization of topological insulators with nontrivial spin textures closely related to the Kane-Mele model.

Dirac and Weyl fermion dynamics on two-dimensional surface

International Nuclear Information System (INIS)

Kavalov, A.R.; Sedrakyan, A.G.; Kostov, I.K.

1986-01-01

Fermions on 2-dimensional surface, embedded into a 3-dimensional space are investigated. The determinant of induced Dirac operator for the Dirac and Weyl fermions is calculated. The reparametrization-invariant effective action is determined by conformal anomaly (giving Liouville action) and also by Lorentz anomaly leading to Wess-Zumino term, the structure of which at d=3 is determined by the Hopf topological invariant of the S 3 → S 2 map

Local density of states in two-dimensional topological superconductors under a magnetic field: Signature of an exterior Majorana bound state

Science.gov (United States)

Suzuki, Shu-Ichiro; Kawaguchi, Yuki; Tanaka, Yukio

2018-04-01

We study quasiparticle states on a surface of a topological insulator (TI) with proximity-induced superconductivity under an external magnetic field. An applied magnetic field creates two Majorana bound states: a vortex Majorana state localized inside a vortex core and an exterior Majorana state localized along a circle centered at the vortex core. We calculate the spin-resolved local density of states (LDOS) and demonstrate that the shrinking of the radius of the exterior Majorana state, predicted in R. S. Akzyanov et al., Phys. Rev. B 94, 125428 (2016), 10.1103/PhysRevB.94.125428, under a strong magnetic field can be seen in LDOS without smeared out by nonzero-energy states. The spin-resolved LDOS further reveals that the spin of the exterior Majorana state is strongly spin-polarized. Accordingly, the induced odd-frequency spin-triplet pairs are found to be spin-polarized as well. In order to detect the exterior Majorana states, however, the Fermi energy should be closed to the Dirac point to avoid contributions from continuum levels. We also study a different two-dimensional topological-superconducting system where a two-dimensional electron gas with the spin-orbit coupling is sandwiched between an s -wave superconductor and a ferromagnetic insulator. We show that the radius of an exterior Majorana state can be tuned by an applied magnetic field. However, on the contrary to the results at a TI surface, neither the exterior Majorana state nor the induced odd-frequency spin-triplet pairs are spin-polarized. We conclude that the spin polarization of the Majorana state is attributed to the spin-polarized Landau level, which is characteristic for systems with the Dirac-like dispersion.

Performance Comparison of Two Topologies Double-Fed Brushless Machine with 36 Slots for Low-Speed Applications

Directory of Open Access Journals (Sweden)

Yue Hao

2014-12-01

Full Text Available The performances of two topologies of low-speed double-fed brushless machine (DFBM with fractional slot windings are quantitatively compared and analyzed using two-dimensional (2-D finite element method (FEM. To fairly compare the torque capability and power efficiency of different DFBMs, the investigated DFBMs have the same outer diameter, the same axial stack length and the same iron core materials, and some comparison rules are presented. In order to maximize the torque density, several important structure parameters are optimized. The results of this paper reveal the torque density levels and power density levels of two kinds of DFBMs.

Topology of Event Horizon

OpenAIRE

Siino, Masaru

1997-01-01

The topologies of event horizons are investigated. Considering the existence of the endpoint of the event horizon, it cannot be differentiable. Then there are the new possibilities of the topology of the event horizon though they are excluded in smooth event horizons. The relation between the topology of the event horizon and the endpoint of it is revealed. A torus event horizon is caused by two-dimensional endpoints. One-dimensional endpoints provide the coalescence of spherical event horizo...

Effects of Structural and Electronic Disorder in Topological Insulator Sb2Te3 Thin Films

Science.gov (United States)

Korzhovska, Inna

Topological quantum matter is a unique and potentially transformative protectorate against disorder-induced backscattering. The ultimate disorder limits to the topological state, however, are still not known - understanding these limits is critical to potential applications in the fields of spintronics and information processing. In topological insulators spin-orbit interaction and time-reversal-symmetry invariance guarantees - at least up to a certain disorder strength - that charge transport through 2D gapless Dirac surface states is robust against backscattering by non-magnetic disorder. Strong disorder may destroy topological protection and gap out Dirac surface states, although recent theories predict that under severe electronic disorder a quantized topological conductance might yet reemerge. Very strong electronic disorder, however, is not trivial to install and quantify, and topological matter under such conditions thus far has not been experimentally tested. This thesis addresses the behavior of three-dimensional (3D) topological insulator (TI) films in a wide range of structural and electronic disorder. We establish strong positional disorder in thin (20-50 nm) Sb2Te 3 films, free of extrinsic magnetic dopants. Sb 2Te3 is a known 2nd generation topological insulator in the low-disorder crystalline state. It is also a known phase-change material that undergoes insulator-to-metal transition with the concurrent orders of magnitude resistive drop, where a huge range of disorder could be controllably explored. In this work we show that even in the absence of magnetic dopants, disorder may induce spin correlations detrimental to the topological state. Chapter 1 contains a brief introduction to the topological matter and describes the role played by disorder. This is followed by theory considerations and a survey of prior experimental work. Next we describe the motivation for our experiments and explain the choice of the material. Chapter 2 describes deposition

The theory of critical phenomena in two-dimensional systems

International Nuclear Information System (INIS)

Olvera de la C, M.

1981-01-01

An exposition of the theory of critical phenomena in two-dimensional physical systems is presented. The first six chapters deal with the mean field theory of critical phenomena, scale invariance of the thermodynamic functions, Kadanoff's spin block construction, Wilson's renormalization group treatment of critical phenomena in configuration space, and the two-dimensional Ising model on a triangular lattice. The second part of this work is made of four chapters devoted to the application of the ideas expounded in the first part to the discussion of critical phenomena in superfluid films, two-dimensional crystals and the two-dimensional XY model of magnetic systems. Chapters seven to ten are devoted to the following subjects: analysis of long range order in one, two, and three-dimensional physical systems. Topological defects in the XY model, in superfluid films and in two-dimensional crystals. The Thouless-Kosterlitz iterated mean field theory of the dipole gas. The renormalization group treatment of the XY model, superfluid films and two-dimensional crystal. (author)

New hybrid lead iodides: From one-dimensional chain to two-dimensional layered perovskite structure

International Nuclear Information System (INIS)

Xiong, Kecai; Liu, Wei; Teat, Simon J.; An, Litao; Wang, Hao; Emge, Thomas J.; Li, Jing

2015-01-01

Two new hybrid lead halides (H 2 BDA)[PbI 4 ] (1) (H 2 BDA=1,4-butanediammonium dication) and (HNPEIM)[PbI 3 ] (2) (HNPEIM=N-​phenyl-ethanimidamidine cation) have been synthesized and structurally characterized. X-ray diffraction analyses reveal that compound 1 features a two-dimensional corner-sharing perovskite layer whereas compound 2 contains one-dimensional edge-sharing double chains. The N-​phenyl-ethanimidamidine cation within compound 2 was generated in-situ under solvothermal conditions. The optical absorption spectra collected at room temperature suggest that both compounds are semiconductors having direct band gaps, with estimated values of 2.64 and 2.73 eV for 1 and 2, respectively. Results from the density functional theory (DFT) calculations are consistent with the experimental data. Density of states (DOS) analysis reveals that in both compounds 1 and 2, the energy states in the valence band maximum region are iodine 5p atomic orbitals with a small contribution from lead 6s, while in the region of conduction band minimum, the major contributions are from the inorganic (Pb 6p atomic orbitals) and organic components (C and N 2p atomic orbitals) in compound 1 and 2, respectively. - Graphical abstract: Two new hybrid lead halides built on one-dimensional edge-sharing double chains and two-dimensional corner-sharing perovskite layers are synthesized and their structural and electronic properties are analyzed. - Highlights: • Two new hybrid lead iodides are designed, synthesized, and characterized. • They are closely related to, but different from, perovskite structures. • The electronic properties of both compounds are analyzed by DFT calculations

New hybrid lead iodides: From one-dimensional chain to two-dimensional layered perovskite structure

Energy Technology Data Exchange (ETDEWEB)

Xiong, Kecai; Liu, Wei [Department of Chemistry and Chemical Biology, Rutgers University, 610 Taylor Road, Piscataway, NJ 08854 (United States); Teat, Simon J. [Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); An, Litao; Wang, Hao; Emge, Thomas J. [Department of Chemistry and Chemical Biology, Rutgers University, 610 Taylor Road, Piscataway, NJ 08854 (United States); Li, Jing, E-mail: jingli@rutgers.edu [Department of Chemistry and Chemical Biology, Rutgers University, 610 Taylor Road, Piscataway, NJ 08854 (United States)

2015-10-15

Two new hybrid lead halides (H{sub 2}BDA)[PbI{sub 4}] (1) (H{sub 2}BDA=1,4-butanediammonium dication) and (HNPEIM)[PbI{sub 3}] (2) (HNPEIM=N-​phenyl-ethanimidamidine cation) have been synthesized and structurally characterized. X-ray diffraction analyses reveal that compound 1 features a two-dimensional corner-sharing perovskite layer whereas compound 2 contains one-dimensional edge-sharing double chains. The N-​phenyl-ethanimidamidine cation within compound 2 was generated in-situ under solvothermal conditions. The optical absorption spectra collected at room temperature suggest that both compounds are semiconductors having direct band gaps, with estimated values of 2.64 and 2.73 eV for 1 and 2, respectively. Results from the density functional theory (DFT) calculations are consistent with the experimental data. Density of states (DOS) analysis reveals that in both compounds 1 and 2, the energy states in the valence band maximum region are iodine 5p atomic orbitals with a small contribution from lead 6s, while in the region of conduction band minimum, the major contributions are from the inorganic (Pb 6p atomic orbitals) and organic components (C and N 2p atomic orbitals) in compound 1 and 2, respectively. - Graphical abstract: Two new hybrid lead halides built on one-dimensional edge-sharing double chains and two-dimensional corner-sharing perovskite layers are synthesized and their structural and electronic properties are analyzed. - Highlights: • Two new hybrid lead iodides are designed, synthesized, and characterized. • They are closely related to, but different from, perovskite structures. • The electronic properties of both compounds are analyzed by DFT calculations.

Novel topological invariants and anomalies

International Nuclear Information System (INIS)

Hirayama, M.; Sugimasa, N.

1987-01-01

It is shown that novel topological invariants are associated with a class of Dirac operators. Trace formulas which are similar to but different from Callias's formula are derived. Implications of these topological invariants to anomalies in quantum field theory are discussed. A new class of anomalies are calculated for two models: one is two dimensional and the other four dimensional

Topological gravity with minimal matter

International Nuclear Information System (INIS)

Li Keke

1991-01-01

Topological minimal matter, obtained by twisting the minimal N = 2 supeconformal field theory, is coupled to two-dimensional topological gravity. The free field formulation of the coupled system allows explicit representations of BRST charge, physical operators and their correlation functions. The contact terms of the physical operators may be evaluated by extending the argument used in a recent solution of topological gravity without matter. The consistency of the contact terms in correlation functions implies recursion relations which coincide with the Virasoro constraints derived from the multi-matrix models. Topological gravity with minimal matter thus provides the field theoretic description for the multi-matrix models of two-dimensional quantum gravity. (orig.)

Seismically constrained two-dimensional crustal thermal structure of ...

Indian Academy of Sciences (India)

The temperature field within the crust is closely related to tectonic history as well as many other geological processes inside the earth. Therefore, knowledge of the crustal thermal structure of a region is of great importance for its tectonophysical studies. This work deals with the two-dimensional thermal modelling to ...

Topological insulators and topological superconductors

CERN Document Server

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...

Quantum spin Hall effect in IV-VI topological crystalline insulators

Science.gov (United States)

Safaei, S.; Galicka, M.; Kacman, P.; Buczko, R.

2015-06-01

We envision that the quantum spin Hall effect should be observed in (111)-oriented thin films of SnSe and SnTe topological crystalline insulators. Using a tight-binding approach supported by first-principles calculations of the band structures, we demonstrate that in these films the energy gaps in the two-dimensional band spectrum depend in an oscillatory fashion on the layer thickness. These results as well as the calculated topological invariant indexes and edge state spin polarizations show that for films ˜20-40 monolayers thick a two-dimensional topological insulator phase appears. In this range of thicknesses in both SnSe and SnTe, (111)-oriented films edge states with Dirac cones with opposite spin polarization in their two branches are obtained. While in the SnTe layers a single Dirac cone appears at the projection of the {\\boldsymbol{}}\\bar{Γ } point of the two-dimensional Brillouin zone, in the SnSe (111)-oriented layers three Dirac cones at {\\boldsymbol{}}\\bar{M} points projections are predicted.

A series of three-dimensional lanthanide coordination polymers with rutile and unprecedented rutile-related topologies.

Science.gov (United States)

Qin, Chao; Wang, Xin-Long; Wang, En-Bo; Su, Zhong-Min

2005-10-03

The complexes of formulas Ln(pydc)(Hpydc) (Ln = Sm (1), Eu (2), Gd (3); H2pydc = pyridine-2,5-dicarboxylic acid) and Ln(pydc)(bc)(H2O) (Ln = Sm (4), Gd (5); Hbc = benzenecarboxylic acid) have been synthesized under hydrothermal conditions and characterized by elemental analysis, IR, TG analysis, and single-crystal X-ray diffraction. Compounds 1-3 are isomorphous and crystallize in the orthorhombic system, space group Pbcn. Their final three-dimensional racemic frameworks can be considered as being constructed by helix-linked scalelike sheets. Compounds 4 and 5 are isostructural and crystallize in the monoclinic system, space group P2(1)/c. pydc ligands bridge dinuclear lanthanide centers to form the three-dimensional frameworks featuring hexagonal channels along the a-axis that are occupied by one-end-coordinated bc ligands. From the topological point of view, the five three-dimensional nets are binodal with six- and three-connected nodes, the former of which exhibit a rutile-related (4.6(2))(2)(4(2).6(9).8(4)) topology that is unprecedented within coordination frames, and the latter two species display a distorted rutile (4.6(2))(2)(4(2).6(10).8(3)) topology. Furthermore, the luminescent properties of 2 were studied.

Band structure of a three-dimensional topological insulator quantum wire in the presence of a magnetic field.

Science.gov (United States)

Liu, Zhe; Jiang, Liwei; Zheng, Yisong

2016-07-13

By means of a numerical diagonalization approach, we calculate the electronic structure of a three-dimensional topological insulator (3DTI) quantum wire (QW) in the presence of a magnetic field. The QW can be viewed as a 3DTI film with lateral surfaces, when its rectangular cross section has a large aspect ratio. Our calculation indicates that nonchiral edge states emerge because of the confined states at the lateral surfaces. These states completely cover the valence band region among the Landau levels, which reasonably account for the absence of the [Formula: see text] quantum Hall effect in the relevant experimental works. In an ultrathin 3DTI film, inversion between the electron-type and hole-type bands occurs, which leads to the so-called pseudo-spin Hall effect. In a 3DTI QW with a square cross section, a tilting magnetic field can establish well-defined Landau levels in all four surfaces. In such a case, the quantum Hall edge states are localized at the square corners, characterized by the linearly crossing one-dimensional band profile. And they can be shifted between the adjacent corners by simply rotating the magnetic field.

Observation of a phononic quadrupole topological insulator

Science.gov (United States)

Serra-Garcia, Marc; Peri, Valerio; Süsstrunk, Roman; Bilal, Osama R.; Larsen, Tom; Villanueva, Luis Guillermo; Huber, Sebastian D.

2018-03-01

The modern theory of charge polarization in solids is based on a generalization of Berry’s phase. The possibility of the quantization of this phase arising from parallel transport in momentum space is essential to our understanding of systems with topological band structures. Although based on the concept of charge polarization, this same theory can also be used to characterize the Bloch bands of neutral bosonic systems such as photonic or phononic crystals. The theory of this quantized polarization has recently been extended from the dipole moment to higher multipole moments. In particular, a two-dimensional quantized quadrupole insulator is predicted to have gapped yet topological one-dimensional edge modes, which stabilize zero-dimensional in-gap corner states. However, such a state of matter has not previously been observed experimentally. Here we report measurements of a phononic quadrupole topological insulator. We experimentally characterize the bulk, edge and corner physics of a mechanical metamaterial (a material with tailored mechanical properties) and find the predicted gapped edge and in-gap corner states. We corroborate our findings by comparing the mechanical properties of a topologically non-trivial system to samples in other phases that are predicted by the quadrupole theory. These topological corner states are an important stepping stone to the experimental realization of topologically protected wave guides in higher dimensions, and thereby open up a new path for the design of metamaterials.

The emergence of geometry: a two-dimensional toy model

CERN Document Server

Alfaro, Jorge; Puigdomenech, Daniel

2010-01-01

We review the similarities between the effective chiral lagrangrian, relevant for low-energy strong interactions, and the Einstein-Hilbert action. We use these analogies to suggest a specific mechanism whereby gravitons would emerge as Goldstone bosons of a global SO(D) X GL(D) symmetry broken down to SO(D) by fermion condensation. We propose a two-dimensional toy model where a dynamical zwei-bein is generated from a topological theory without any pre-existing metric structure, the space being endowed only with an affine connection. A metric appears only after the symmetry breaking; thus the notion of distance is an induced effective one. In spite of several non-standard features this simple toy model appears to be renormalizable and at long distances is described by an effective lagrangian that corresponds to that of two-dimensional gravity (Liouville theory). The induced cosmological constant is related to the dynamical mass M acquired by the fermion fields in the breaking, which also acts as an infrared re...

Impact of high-frequency pumping on anomalous finite-size effects in three-dimensional topological insulators

Science.gov (United States)

Pervishko, Anastasiia A.; Yudin, Dmitry; Shelykh, Ivan A.

2018-02-01

Lowering of the thickness of a thin-film three-dimensional topological insulator down to a few nanometers results in the gap opening in the spectrum of topologically protected two-dimensional surface states. This phenomenon, which is referred to as the anomalous finite-size effect, originates from hybridization between the states propagating along the opposite boundaries. In this work, we consider a bismuth-based topological insulator and show how the coupling to an intense high-frequency linearly polarized pumping can further be used to manipulate the value of a gap. We address this effect within recently proposed Brillouin-Wigner perturbation theory that allows us to map a time-dependent problem into a stationary one. Our analysis reveals that both the gap and the components of the group velocity of the surface states can be tuned in a controllable fashion by adjusting the intensity of the driving field within an experimentally accessible range and demonstrate the effect of light-induced band inversion in the spectrum of the surface states for high enough values of the pump.

Topological sigma B model in 4-dimensions

International Nuclear Information System (INIS)

Jun, Hyun-Keun; Park, Jae-Suk

2008-01-01

We propose a 4-dimensional version of topological sigma B-model, governing maps from a smooth compact 4-manifold M to a Calabi-Yau target manifold X. The theory depends on complex structure of X, while is independent of Kaehler metric of X. The theory is also a 4-dimensional topological field theory in the sense that the theory is independent of variation of Riemannian metric of the source 4-manifold M, potentially leading to new smooth invariant of 4-manifolds. We argue that the theory also comes with a topological family parametrized by the extended moduli space of complex structures.

Influence of magnetic disorders on quantum anomalous Hall effect in magnetic topological insulator films beyond the two-dimensional limit

Science.gov (United States)

Xing, Yanxia; Xu, Fuming; Cheung, King Tai; Sun, Qing-feng; Wang, Jian; Yao, Yugui

2018-04-01

Quantum anomalous Hall effect (QAHE) has been experimentally realized in magnetic topological insulator (MTI) thin films fabricated on magnetically doped {({{Bi}},{{Sb}})}2{{{Te}}}3. In an MTI thin film with the magnetic easy axis along the normal direction (z-direction), orientations of magnetic dopants are randomly distributed around the magnetic easy axis, acting as magnetic disorders. With the aid of the non-equilibrium Green's function and Landauer–Büttiker formalism, we numerically study the influence of magnetic disorders on QAHE in an MTI thin film modeled by a three-dimensional tight-binding Hamiltonian. It is found that, due to the existence of gapless side surface states, QAHE is protected even in the presence of magnetic disorders as long as the z-component of magnetic moment of all magnetic dopants are positive. More importantly, such magnetic disorders also suppress the dissipation of the chiral edge states and enhance the quality of QAHE in MTI films. In addition, the effect of magnetic disorders depends very much on the film thickness, and the optimal influence is achieved at certain thickness. These findings are new features for QAHE in three-dimensional systems, not present in two-dimensional systems.

Two-dimensional Dirac fermions in thin films of C d3A s2

Science.gov (United States)

Galletti, Luca; Schumann, Timo; Shoron, Omor F.; Goyal, Manik; Kealhofer, David A.; Kim, Honggyu; Stemmer, Susanne

2018-03-01

Two-dimensional states in confined thin films of the three-dimensional Dirac semimetal C d3A s2 are probed by transport and capacitance measurements under applied magnetic and electric fields. The results establish the two-dimensional Dirac electronic spectrum of these states. We observe signatures of p -type conduction in the two-dimensional states as the Fermi level is tuned across their charge neutrality point and the presence of a zero-energy Landau level, all of which indicate topologically nontrivial states. The resistance at the charge neutrality point is approximately h /e2 and increases rapidly under the application of a magnetic field. The results open many possibilities for gate-tunable topological devices and for the exploration of novel physics in the zero-energy Landau level.

Topological microfluidic structures for rapid mixing of emulsions

CSIR Research Space (South Africa)

Land, KJ

2013-10-01

Full Text Available A novel use for topological structures inside microfluidic channels is presented. These structures have been successfully utilised to aid in mixing of two water-in-oil emulsions in order to force coalescence, thereby introducing a cross linker...

Concomitant Hamiltonian and topological structures of extended magnetohydrodynamics

Energy Technology Data Exchange (ETDEWEB)

Lingam, Manasvi, E-mail: mlingam@princeton.edu [Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544 (United States); Department of Physics and Institute for Fusion Studies, The University of Texas at Austin, Austin, TX 78712 (United States); Miloshevich, George, E-mail: gmilosh@physics.utexas.edu [Department of Physics and Institute for Fusion Studies, The University of Texas at Austin, Austin, TX 78712 (United States); Morrison, Philip J., E-mail: morrison@physics.utexas.edu [Department of Physics and Institute for Fusion Studies, The University of Texas at Austin, Austin, TX 78712 (United States)

2016-07-15

Highlights: • Common Hamiltonian structure of the extended MHD models presented. • The generalized helicities of extended MHD shown to be topological invariants analogous to fluid/magnetic helicity. • Generalized helicities can be studied through powerful topological and knot-theoretic methods such as the Jones polynomial. • Each extended MHD model shown to possess two Lie-dragged 2-forms, which are interpreted as the generalized vorticity fluxes. - Abstract: The paper describes the unique geometric properties of ideal magnetohydrodynamics (MHD), and demonstrates how such features are inherited by extended MHD, viz. models that incorporate two-fluid effects (the Hall term and electron inertia). The generalized helicities, and other geometric expressions for these models are presented in a topological context, emphasizing their universal facets. Some of the results presented include: the generalized Kelvin circulation theorems; the existence of two Lie-dragged 2-forms; and two concomitant helicities that can be studied via the Jones polynomial, which is widely utilized in Chern–Simons theory. The ensuing commonality is traced to the existence of an underlying Hamiltonian structure for all the extended MHD models, exemplified by the presence of a unique noncanonical Poisson bracket, and its associated energy.

Compatible topologies and parameters for NMR structure determination of carbohydrates by simulated annealing.

Science.gov (United States)

Feng, Yingang

2017-01-01

The use of NMR methods to determine the three-dimensional structures of carbohydrates and glycoproteins is still challenging, in part because of the lack of standard protocols. In order to increase the convenience of structure determination, the topology and parameter files for carbohydrates in the program Crystallography & NMR System (CNS) were investigated and new files were developed to be compatible with the standard simulated annealing protocols for proteins and nucleic acids. Recalculating the published structures of protein-carbohydrate complexes and glycosylated proteins demonstrates that the results are comparable to the published structures which employed more complex procedures for structure calculation. Integrating the new carbohydrate parameters into the standard structure calculation protocol will facilitate three-dimensional structural study of carbohydrates and glycosylated proteins by NMR spectroscopy.

Control strategy research of two stage topology for pulsed power supply

International Nuclear Information System (INIS)

Shi Chunfeng; Wang Rongkun; Huang Yuzhen; Chen Youxin; Yan Hongbin; Gao Daqing

2013-01-01

A kind of pulsed power supply of HIRFL-CSR was introduced, the ripple and the current error of the topological structure of the power in the operation process were analyzed, and two stage topology of pulsed power supply was given. The control strategy was simulated and the experiment was done in digital power platform. The results show that the main circuit structure and control method are feasible. (authors)

Topology optimization for simplified structural fire safety

DEFF Research Database (Denmark)

Madsen, Søren; Lange, Nis P.; Giuliani, Luisa

2016-01-01

Topology optimization is applied in an idealized structural fire safety model, where the minimum compliance problem is constrained by temperature-controlled structural degradation. The constraint ensures a certain structural stiffness after a prescribed time. As this time period is extended......, resulting optimized topologies tend to become thicker or introduce redundant members that can take over when structural parts near the origin of the fire lose their load carrying capability. Hence, the structural degradation model acts as an erosion operator on the topology and indirectly enforces a minimum...

High-Harmonic Generation in Solids with and without Topological Edge States

Science.gov (United States)

Bauer, Dieter; Hansen, Kenneth K.

2018-04-01

High-harmonic generation in the two topological phases of a finite, one-dimensional, periodic structure is investigated using a self-consistent time-dependent density functional theory approach. For harmonic photon energies smaller than the band gap, the harmonic yield is found to differ by up to 14 orders of magnitude for the two topological phases. This giant topological effect is explained by the degree of destructive interference in the harmonic emission of all valence-band (and edge-state) electrons, which strongly depends on whether or not topological edge states are present. The combination of strong-field laser physics with topological condensed matter opens up new possibilities to electronically control strong-field-based light or particle sources or—conversely—to steer by all optical means topological electronics.

Three dimensional nonlinear magnetic AdS solutions through topological defects

International Nuclear Information System (INIS)

Hendi, S.H.; Panah, B.E.; Momennia, M.; Panahiyan, S.

2015-01-01

Inspired by large applications of topological defects in describing different phenomena in physics, and considering the importance of three dimensional solutions in AdS/CFT correspondence, in this paper we obtain magnetic anti-de Sitter solutions of nonlinear electromagnetic fields. We take into account three classes of nonlinear electrodynamic models; first two classes are the well-known Born-Infeld like models including logarithmic and exponential forms and third class is known as the power Maxwell invariant nonlinear electrodynamics. We investigate the effects of these nonlinear sources on three dimensional magnetic solutions. We show that these asymptotical AdS solutions do not have any curvature singularity and horizon. We also generalize the static metric to the case of rotating solutions and find that the value of the electric charge depends on the rotation parameter. Finally, we consider the quadratic Maxwell invariant as a correction of Maxwell theory and we investigate the effects of nonlinearity as a correction. We study the behavior of the deficit angle in presence of these theories of nonlinearity and compare them with each other. We also show that some cases with negative deficit angle exists which are representing objects with different geometrical structure. We also show that in case of the static only magnetic field exists whereas by boosting the metric to rotating one, electric field appears too. (orig.)

Effect of disorders on topological phases in one-dimensional optical superlattices

International Nuclear Information System (INIS)

Wang Zhizhou; Wu Yidong; Du Huijing; Jing Xili

2016-01-01

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. (paper)

Topological Oxide Insulator in Cubic Perovskite Structure

Science.gov (United States)

Jin, Hosub; Rhim, Sonny H.; Im, Jino; Freeman, Arthur J.

2013-01-01

The emergence of topologically protected conducting states with the chiral spin texture is the most prominent feature at the surface of topological insulators. On the application side, large band gap and high resistivity to distinguish surface from bulk degrees of freedom should be guaranteed for the full usage of the surface states. Here, we suggest that the oxide cubic perovskite YBiO3, more than just an oxide, defines itself as a new three-dimensional topological insulator exhibiting both a large bulk band gap and a high resistivity. Based on first-principles calculations varying the spin-orbit coupling strength, the non-trivial band topology of YBiO3 is investigated, where the spin-orbit coupling of the Bi 6p orbital plays a crucial role. Taking the exquisite synthesis techniques in oxide electronics into account, YBiO3 can also be used to provide various interface configurations hosting exotic topological phenomena combined with other quantum phases. PMID:23575973

A topological analysis of large-scale structure, studied using the CMASS sample of SDSS-III

International Nuclear Information System (INIS)

Parihar, Prachi; Gott, J. Richard III; Vogeley, Michael S.; Choi, Yun-Young; Kim, Juhan; Kim, Sungsoo S.; Speare, Robert; Brownstein, Joel R.; Brinkmann, J.

2014-01-01

We study the three-dimensional genus topology of large-scale structure using the northern region of the CMASS Data Release 10 (DR10) sample of the SDSS-III Baryon Oscillation Spectroscopic Survey. We select galaxies with redshift 0.452 < z < 0.625 and with a stellar mass M stellar > 10 11.56 M ☉ . We study the topology at two smoothing lengths: R G = 21 h –1 Mpc and R G = 34 h –1 Mpc. The genus topology studied at the R G = 21 h –1 Mpc scale results in the highest genus amplitude observed to date. The CMASS sample yields a genus curve that is characteristic of one produced by Gaussian random phase initial conditions. The data thus support the standard model of inflation where random quantum fluctuations in the early universe produced Gaussian random phase initial conditions. Modest deviations in the observed genus from random phase are as expected from shot noise effects and the nonlinear evolution of structure. We suggest the use of a fitting formula motivated by perturbation theory to characterize the shift and asymmetries in the observed genus curve with a single parameter. We construct 54 mock SDSS CMASS surveys along the past light cone from the Horizon Run 3 (HR3) N-body simulations, where gravitationally bound dark matter subhalos are identified as the sites of galaxy formation. We study the genus topology of the HR3 mock surveys with the same geometry and sampling density as the observational sample and find the observed genus topology to be consistent with ΛCDM as simulated by the HR3 mock samples. We conclude that the topology of the large-scale structure in the SDSS CMASS sample is consistent with cosmological models having primordial Gaussian density fluctuations growing in accordance with general relativity to form galaxies in massive dark matter halos.

TopologyNet: Topology based deep convolutional and multi-task neural networks for biomolecular property predictions

Science.gov (United States)

2017-01-01

Although deep learning approaches have had tremendous success in image, video and audio processing, computer vision, and speech recognition, their applications to three-dimensional (3D) biomolecular structural data sets have been hindered by the geometric and biological complexity. To address this problem we introduce the element-specific persistent homology (ESPH) method. ESPH represents 3D complex geometry by one-dimensional (1D) topological invariants and retains important biological information via a multichannel image-like representation. This representation reveals hidden structure-function relationships in biomolecules. We further integrate ESPH and deep convolutional neural networks to construct a multichannel topological neural network (TopologyNet) for the predictions of protein-ligand binding affinities and protein stability changes upon mutation. To overcome the deep learning limitations from small and noisy training sets, we propose a multi-task multichannel topological convolutional neural network (MM-TCNN). We demonstrate that TopologyNet outperforms the latest methods in the prediction of protein-ligand binding affinities, mutation induced globular protein folding free energy changes, and mutation induced membrane protein folding free energy changes. Availability: weilab.math.msu.edu/TDL/ PMID:28749969

Hydrothermal preparation of nickel(II)/uranium(IV) fluorides with one-, two-, and three-dimensional topologies.

Science.gov (United States)

Bean, Amanda C; Sullens, Tyler A; Runde, Wolfgang; Albrecht-Schmitt, Thomas E

2003-04-21

A modified compositional diagram for the reactions of Ni(C(2)H(3)O(2))(2).4H(2)O with UO(2)(C(2)H(3)O(2))(2).2H(2)O and HF in aqueous media under mild hydrothermal conditions (200 degrees C) has been completed to yield three Ni(II)/U(IV) fluorides, Ni(H(2)O)(4)UF(6).1.5H(2)O (1), Ni(2)(H(2)O)(6)U(3)F(16).3H(2)O (2), and Ni(H(2)O)(2)UF(6)(H(2)O) (3). The structure of 1 consists of one-dimensional columns constructed from two parallel chains of edge-sharing dodecahedral [UF(8)] units. The sides of the columns are terminated by octahedral Ni(II) units that occur as cis-[Ni(H(2)O)(4)F(2)] polyhedra. In contrast, the crystal structure of 2 reveals a two-dimensional Ni(II)/U(IV) architecture built from edge-sharing tricapped trigonal prismatic [UF(9)] units. The top and bottom of the sheets are capped by fac-[Ni(H(2)O)(3)F(3)] octahedra. The structure of 3 is formed from [UF(8)(H(2)O)] tricapped trigonal prisms that edge share with one another to form one-dimensional chains. These chains are then joined together into a three-dimensional network by corner sharing with trans-[Ni(H(2)O)(2)F(4)] octahedra. Crystallographic data: 1, orthorhombic, space group Cmcm, a = 14.3383(8) A, b = 15.6867(8) A, c = 8.0282(4) A, Z = 8; 2, hexagonal, space group P6(3)/mmc, a = 7.9863(5) A, c = 16.566(1) A, Z = 2; 3, monoclinic, space group C2/c, a = 12.059(1) A, b = 6.8895(6) A, c = 7.9351(7) A, beta = 92.833(2) degrees, Z = 4.

Non-Abelian string and particle braiding in topological order: Modular SL (3 ,Z ) representation and (3 +1 ) -dimensional twisted gauge theory

Science.gov (United States)

Wang, Juven C.; Wen, Xiao-Gang

2015-01-01

String and particle braiding statistics are examined in a class of topological orders described by discrete gauge theories with a gauge group G and a 4-cocycle twist ω4 of G 's cohomology group H4(G ,R /Z ) in three-dimensional space and one-dimensional time (3 +1 D ) . We establish the topological spin and the spin-statistics relation for the closed strings and their multistring braiding statistics. The 3 +1 D twisted gauge theory can be characterized by a representation of a modular transformation group, SL (3 ,Z ) . We express the SL (3 ,Z ) generators Sx y z and Tx y in terms of the gauge group G and the 4-cocycle ω4. As we compactify one of the spatial directions z into a compact circle with a gauge flux b inserted, we can use the generators Sx y and Tx y of an SL (2 ,Z ) subgroup to study the dimensional reduction of the 3D topological order C3 D to a direct sum of degenerate states of 2D topological orders Cb2 D in different flux b sectors: C3 D=⊕bCb2 D . The 2D topological orders Cb2 D are described by 2D gauge theories of the group G twisted by the 3-cocycle ω3 (b ), dimensionally reduced from the 4-cocycle ω4. We show that the SL (2 ,Z ) generators, Sx y and Tx y, fully encode a particular type of three-string braiding statistics with a pattern that is the connected sum of two Hopf links. With certain 4-cocycle twists, we discover that, by threading a third string through two-string unlink into a three-string Hopf-link configuration, Abelian two-string braiding statistics is promoted to non-Abelian three-string braiding statistics.

Robustness of Topological Superconductivity in Solid State Hybrid Structures

Science.gov (United States)

Sitthison, Piyapong

The non-Abelian statistics of Majorana fermions (MFs) makes them an ideal platform for implementing topological quantum computation. In addition to the fascinating fundamental physics underlying the emergence of MFs, this potential for applications makes the study of these quasiparticles an extremely popular subject in condensed matter physics. The commonly called `Majorana fermions' are zero-energy bound states that emerge near boundaries and defects in topological superconducting phases, which can be engineered, for example, by proximity coupling strong spin-orbit coupling semiconductor nanowires and ordinary s-wave superconductors. The stability of these bound states is determined by the stability of the underlying topological superconducting phase. Hence, understanding their stability (which is critical for quantum computation), involves studying the robustness of the engineered topological superconductors. This work addresses this important problem in the context of two types of hybrid structures that have been proposed for realizing topological superconductivity: topological insulator - superconductor (TI-SC) and semiconductor - superconductor (SM-SC) nanostructures. In both structures, electrostatic effects due to applied external potentials and interface-induced potentials are significant. This work focuses on developing a theoretical framework for understanding these effects, to facilitate the optimization of the nanostructures studied in the laboratory. The approach presented in this thesis is based on describing the low-energy physics of the hybrid structure using effective tight-binding models that explicitly incorporate the proximity effects emerging at interfaces. Generically, as a result of the proximity coupling to the superconductor, an induced gap emerges in the semiconductor (topological insulator) sub-system. The strength of the proximity-induced gap is determined by the transparency of the interface and by the amplitude of the low- energy SM

From Two- to Three-Dimensional Structures of a Supertetrahedral Boran Using Density Functional Calculations.

Science.gov (United States)

Getmanskii, Iliya V; Minyaev, Ruslan M; Steglenko, Dmitrii V; Koval, Vitaliy V; Zaitsev, Stanislav A; Minkin, Vladimir I

2017-08-14

With help of the DFT calculations and imposing of periodic boundary conditions the geometrical and electronic structures were investigated of two- and three-dimensional boron systems designed on the basis of graphane and diamond lattices in which carbons were replaced with boron tetrahedrons. The consequent studies of two- and three-layer systems resulted in the construction of a three-dimensional supertetrahedral borane crystal structure. The two-dimensional supertetrahedral borane structures with less than seven layers are dynamically unstable. At the same time the three-dimensional superborane systems were found to be dynamically stable. Lack of the forbidden electronic zone for the studied boron systems testifies that these structures can behave as good conductors. The low density of the supertetrahedral borane crystal structures (0.9 g cm -3 ) is close to that of water, which offers the perspective for their application as aerospace and cosmic materials. © 2017 The Authors. Published by Wiley-VCH Verlag GmbH & Co. KGaA.

Topological phase transition in the quench dynamics of a one-dimensional Fermi gas

OpenAIRE

Wang, Pei; Yi, Wei; Xianlong, Gao

2014-01-01

We study the quench dynamics of a one-dimensional ultracold Fermi gas in an optical lattice potential with synthetic spin-orbit coupling. At equilibrium, the ground state of the system can undergo a topological phase transition and become a topological superfluid with Majorana edge states. As the interaction is quenched near the topological phase boundary, we identify an interesting dynamical phase transition of the quenched state in the long-time limit, characterized by an abrupt change of t...

Low-dimensional morphospace of topological motifs in human fMRI brain networks

Directory of Open Access Journals (Sweden)

Sarah E. Morgan

2018-06-01

Full Text Available We present a low-dimensional morphospace of fMRI brain networks, where axes are defined in a data-driven manner based on the network motifs. The morphospace allows us to identify the key variations in healthy fMRI networks in terms of their underlying motifs, and we observe that two principal components (PCs can account for 97% of the motif variability. The first PC of the motif distribution is correlated with efficiency and inversely correlated with transitivity. Hence this axis approximately conforms to the well-known economical small-world trade-off between integration and segregation in brain networks. Finally, we show that the economical clustering generative model proposed by Vértes et al. (2012 can approximately reproduce the motif morphospace of the real fMRI brain networks, in contrast to other generative models. Overall, the motif morphospace provides a powerful way to visualize the relationships between network properties and to investigate generative or constraining factors in the formation of complex human brain functional networks. Motifs have been described as the building blocks of complex networks. Meanwhile, a morphospace allows networks to be placed in a common space and can reveal the relationships between different network properties and elucidate the driving forces behind network topology. We combine the concepts of motifs and morphospaces to create the first motif morphospace of fMRI brain networks. Crucially, the morphospace axes are defined by the motifs, in a data-driven manner. We observe strong correlations between the networks’ positions in morphospace and their global topological properties, suggesting that motif morphospaces are a powerful way to capture the topology of networks in a low-dimensional space and to compare generative models of brain networks. Motif morphospaces could also be used to study other complex networks’ topologies.

Topological Magnon Bands in a Kagome Lattice Ferromagnet.

Science.gov (United States)

Chisnell, R; Helton, J S; Freedman, D E; Singh, D K; Bewley, R I; Nocera, D G; Lee, Y S

2015-10-02

There is great interest in finding materials possessing quasiparticles with topological properties. Such materials may have novel excitations that exist on their boundaries which are protected against disorder. We report experimental evidence that magnons in an insulating kagome ferromagnet can have a topological band structure. Our neutron scattering measurements further reveal that one of the bands is flat due to the unique geometry of the kagome lattice. Spin wave calculations show that the measured band structure follows from a simple Heisenberg Hamiltonian with a Dzyaloshinkii-Moriya interaction. This serves as the first realization of an effectively two-dimensional topological magnon insulator--a new class of magnetic material that should display both a magnon Hall effect and protected chiral edge modes.

Optimized set of two-dimensional experiments for fast sequential assignment, secondary structure determination, and backbone fold validation of 13C/15N-labelled proteins

International Nuclear Information System (INIS)

Bersch, Beate; Rossy, Emmanuel; Coves, Jacques; Brutscher, Bernhard

2003-01-01

NMR experiments are presented which allow backbone resonance assignment, secondary structure identification, and in favorable cases also molecular fold topology determination from a series of two-dimensional 1 H- 15 N HSQC-like spectra. The 1 H- 15 N correlation peaks are frequency shifted by an amount ± ω X along the 15 N dimension, where ω X is the C α , C β , or H α frequency of the same or the preceding residue. Because of the low dimensionality (2D) of the experiments, high-resolution spectra are obtained in a short overall experimental time. The whole series of seven experiments can be performed in typically less than one day. This approach significantly reduces experimental time when compared to the standard 3D-based methods. The here presented methodology is thus especially appealing in the context of high-throughput NMR studies of protein structure, dynamics or molecular interfaces

Topological Invariants and Ground-State Wave functions of Topological Insulators on a Torus

Directory of Open Access Journals (Sweden)

Zhong Wang

2014-01-01

Full Text Available We define topological invariants in terms of the ground-state wave functions on a torus. This approach leads to precisely defined formulas for the Hall conductance in four dimensions and the topological magnetoelectric θ term in three dimensions, and their generalizations in higher dimensions. They are valid in the presence of arbitrary many-body interactions and disorder. These topological invariants systematically generalize the two-dimensional Niu-Thouless-Wu formula and will be useful in numerical calculations of disordered topological insulators and strongly correlated topological insulators, especially fractional topological insulators.

Two-Loop Master Integrals for $\\gamma^{*} \\to 3$ Jets the Non-Planar Topologies

CERN Document Server

Gehrmann, T

2001-01-01

The calculation of the two-loop corrections to the three-jet production rate and to event shapes in electron--positron annihilation requires the computation of a number of two-loop four-point master integrals with one off-shell and three on-shell legs. Up to now, only those master integrals corresponding to planar topologies were known. In this paper, we compute the yet outstanding non-planar master integrals by solving differential equations in the external invariants which are fulfilled by these master integrals. We obtain the master integrals as expansions in $\\e=(4-d)/2$, where $d$ is the space-time dimension. The fully analytic results are expressed in terms of the two-dimensional harmonic polylogarithms already introduced in the evaluation of the planar topologies.

Interfacial Dirac cones from alternating topological invariant superlattice structures of Bi2Se3.

Science.gov (United States)

Song, Jung-Hwan; Jin, Hosub; Freeman, Arthur J

2010-08-27

When the three-dimensional topological insulators Bi2Se3 and Bi2Te3 have an interface with vacuum, i.e., a surface, they show remarkable features such as topologically protected and spin-momentum locked surface states. However, for practical applications, one often requires multiple interfaces or channels rather than a single surface. Here, for the first time, we show that an interfacial and ideal Dirac cone is realized by alternating band and topological insulators. The multichannel Dirac fermions from the superlattice structures open a new way for applications such as thermoelectric and spintronics devices. Indeed, utilizing the interfacial Dirac fermions, we also demonstrate the possible power factor improvement for thermoelectric applications.

Photonic topological boundary pumping as a probe of 4D quantum Hall physics.

Science.gov (United States)

Zilberberg, Oded; Huang, Sheng; Guglielmon, Jonathan; Wang, Mohan; Chen, Kevin P; Kraus, Yaacov E; Rechtsman, Mikael C

2018-01-03

When a two-dimensional (2D) electron gas is placed in a perpendicular magnetic field, its in-plane transverse conductance becomes quantized; this is known as the quantum Hall effect. It arises from the non-trivial topology of the electronic band structure of the system, where an integer topological invariant (the first Chern number) leads to quantized Hall conductance. It has been shown theoretically that the quantum Hall effect can be generalized to four spatial dimensions, but so far this has not been realized experimentally because experimental systems are limited to three spatial dimensions. Here we use tunable 2D arrays of photonic waveguides to realize a dynamically generated four-dimensional (4D) quantum Hall system experimentally. The inter-waveguide separation in the array is constructed in such a way that the propagation of light through the device samples over momenta in two additional synthetic dimensions, thus realizing a 2D topological pump. As a result, the band structure has 4D topological invariants (known as second Chern numbers) that support a quantized bulk Hall response with 4D symmetry. In a finite-sized system, the 4D topological bulk response is carried by localized edge modes that cross the sample when the synthetic momenta are modulated. We observe this crossing directly through photon pumping of our system from edge to edge and corner to corner. These crossings are equivalent to charge pumping across a 4D system from one three-dimensional hypersurface to the spatially opposite one and from one 2D hyperedge to another. Our results provide a platform for the study of higher-dimensional topological physics.

Photonic topological boundary pumping as a probe of 4D quantum Hall physics

Science.gov (United States)

Zilberberg, Oded; Huang, Sheng; Guglielmon, Jonathan; Wang, Mohan; Chen, Kevin P.; Kraus, Yaacov E.; Rechtsman, Mikael C.

2018-01-01

When a two-dimensional (2D) electron gas is placed in a perpendicular magnetic field, its in-plane transverse conductance becomes quantized; this is known as the quantum Hall effect. It arises from the non-trivial topology of the electronic band structure of the system, where an integer topological invariant (the first Chern number) leads to quantized Hall conductance. It has been shown theoretically that the quantum Hall effect can be generalized to four spatial dimensions, but so far this has not been realized experimentally because experimental systems are limited to three spatial dimensions. Here we use tunable 2D arrays of photonic waveguides to realize a dynamically generated four-dimensional (4D) quantum Hall system experimentally. The inter-waveguide separation in the array is constructed in such a way that the propagation of light through the device samples over momenta in two additional synthetic dimensions, thus realizing a 2D topological pump. As a result, the band structure has 4D topological invariants (known as second Chern numbers) that support a quantized bulk Hall response with 4D symmetry. In a finite-sized system, the 4D topological bulk response is carried by localized edge modes that cross the sample when the synthetic momenta are modulated. We observe this crossing directly through photon pumping of our system from edge to edge and corner to corner. These crossings are equivalent to charge pumping across a 4D system from one three-dimensional hypersurface to the spatially opposite one and from one 2D hyperedge to another. Our results provide a platform for the study of higher-dimensional topological physics.

Two-dimensional dynamics of a free molecular chain with a secondary structure

DEFF Research Database (Denmark)

Zolotaryuk, Alexander; Christiansen, Peter Leth; Savin, A.V.

1996-01-01

A simple two-dimensional (2D) model of an isolated (free) molecular chain with primary and secondary structures has been suggested and investigated both analytically and numerically. This model can be considered as the simplest generalization of the well-known Fermi-Pasta-Ulam model of an anharmo......A simple two-dimensional (2D) model of an isolated (free) molecular chain with primary and secondary structures has been suggested and investigated both analytically and numerically. This model can be considered as the simplest generalization of the well-known Fermi-Pasta-Ulam model...

Determination of structure of oriented samples using two-dimensional solid state NMR techniques

International Nuclear Information System (INIS)

Jin Hong; Harbison, G.S.

1990-01-01

One dimensional and two-dimensional MAS techniques can give detailed information about the structure and dynamics of oriented systems. We describe the application of such techniques to the liquid-crystalline polymer poly(p-phenyleneterphtalimide) (PPTA), and thence deduce the solid-state structure of the material. (author). 9 refs.; 6 figs

Ranking beta sheet topologies with applications to protein structure prediction

DEFF Research Database (Denmark)

Fonseca, Rasmus; Helles, Glennie; Winter, Pawel

2011-01-01

One reason why ab initio protein structure predictors do not perform very well is their inability to reliably identify long-range interactions between amino acids. To achieve reliable long-range interactions, all potential pairings of ß-strands (ß-topologies) of a given protein are enumerated......, including the native ß-topology. Two very different ß-topology scoring methods from the literature are then used to rank all potential ß-topologies. This has not previously been attempted for any scoring method. The main result of this paper is a justification that one of the scoring methods, in particular......, consistently top-ranks native ß-topologies. Since the number of potential ß-topologies grows exponentially with the number of ß-strands, it is unrealistic to expect that all potential ß-topologies can be enumerated for large proteins. The second result of this paper is an enumeration scheme of a subset of ß-topologies...

Contact and symplectic topology

CERN Document Server

Colin, Vincent; Stipsicz, András

2014-01-01

Symplectic and contact geometry naturally emerged from the mathematical description of classical physics. The discovery of new rigidity phenomena and properties satisfied by these geometric structures launched a new research field worldwide. The intense activity of many European research groups in this field is reflected by the ESF Research Networking Programme "Contact And Symplectic Topology" (CAST). The lectures of the Summer School in Nantes (June 2011) and of the CAST Summer School in Budapest (July 2012) provide a nice panorama of many aspects of the present status of contact and symplectic topology. The notes of the minicourses offer a gentle introduction to topics which have developed in an amazing speed in the recent past. These topics include 3-dimensional and higher dimensional contact topology, Fukaya categories, asymptotically holomorphic methods in contact topology, bordered Floer homology, embedded contact homology, and flexibility results for Stein manifolds.

HgTe based topological insulators

International Nuclear Information System (INIS)

Bruene, Christoph

2014-01-01

This PhD thesis summarizes the discovery of topological insulators and highlights the developments on their experimental observations. The work focuses on HgTe. The thesis is structured as follows: - The first chapter of this thesis will give a brief overview on discoveries in the field of topological insulators. It focuses on works relevant to experimental results presented in the following chapters. This includes a short outline of the early predictions and a summary of important results concerning 2-dimensional topological insulators while the final section discusses observations concerning 3-dimensional topological insulators. - The discovery of the quantum spin Hall effect in HgTe marked the first experimental observation of a topological insulator. Chapter 2 focuses on HgTe quantum wells and the quantum spin Hall effect. The growth of high quality HgTe quantum wells was one of the major goals for this work. In a final set of experiments the spin polarization of the edge channels was investigated. Here, we could make use of the advantage that HgTe quantum well structures exhibit a large Rashba spin orbit splitting. - HgTe as a 3-dimensional topological insulator is presented in chapter 3. - Chapters 4-6 serve as in depth overviews of selected works: Chapter 4 presents a detailed overview on the all electrical detection of the spin Hall effect in HgTe quantum wells. The detection of the spin polarization of the quantum spin Hall effect is shown in chapter 5 and chapter 6 gives a detailed overview on the quantum Hall effect originating from the topological surface state in strained bulk HgTe.

Topological patterns of mesh textures in serpentinites

Science.gov (United States)

Miyazawa, M.; Suzuki, A.; Shimizu, H.; Okamoto, A.; Hiraoka, Y.; Obayashi, I.; Tsuji, T.; Ito, T.

2017-12-01

Serpentinization is a hydration process that forms serpentine minerals and magnetite within the oceanic lithosphere. Microfractures crosscut these minerals during the reactions, and the structures look like mesh textures. It has been known that the patterns of microfractures and the system evolutions are affected by the hydration reaction and fluid transport in fractures and within matrices. This study aims at quantifying the topological patterns of the mesh textures and understanding possible conditions of fluid transport and reaction during serpentinization in the oceanic lithosphere. Two-dimensional simulation by the distinct element method (DEM) generates fracture patterns due to serpentinization. The microfracture patterns are evaluated by persistent homology, which measures features of connected components of a topological space and encodes multi-scale topological features in the persistence diagrams. The persistence diagrams of the different mesh textures are evaluated by principal component analysis to bring out the strong patterns of persistence diagrams. This approach help extract feature values of fracture patterns from high-dimensional and complex datasets.

Topological BF field theory description of topological insulators

International Nuclear Information System (INIS)

Cho, Gil Young; Moore, Joel E.

2011-01-01

Research highlights: → We show that a BF theory is the effective theory of 2D and 3D topological insulators. → The non-gauge-invariance of the bulk theory yields surface terms for a bosonized Dirac fermion. → The 'axion' term in electromagnetism is correctly obtained from gapped surfaces. → Generalizations to possible fractional phases are discussed in closing. - Abstract: Topological phases of matter are described universally by topological field theories in the same way that symmetry-breaking phases of matter are described by Landau-Ginzburg field theories. We propose that topological insulators in two and three dimensions are described by a version of abelian BF theory. For the two-dimensional topological insulator or quantum spin Hall state, this description is essentially equivalent to a pair of Chern-Simons theories, consistent with the realization of this phase as paired integer quantum Hall effect states. The BF description can be motivated from the local excitations produced when a π flux is threaded through this state. For the three-dimensional topological insulator, the BF description is less obvious but quite versatile: it contains a gapless surface Dirac fermion when time-reversal-symmetry is preserved and yields 'axion electrodynamics', i.e., an electromagnetic E . B term, when time-reversal symmetry is broken and the surfaces are gapped. Just as changing the coefficients and charges of 2D Chern-Simons theory allows one to obtain fractional quantum Hall states starting from integer states, BF theory could also describe (at a macroscopic level) fractional 3D topological insulators with fractional statistics of point-like and line-like objects.

Multilocality and fusion rules on the generalized structure functions in two-dimensional and three-dimensional Navier-Stokes turbulence.

Science.gov (United States)

Gkioulekas, Eleftherios

2016-09-01

Using the fusion-rules hypothesis for three-dimensional and two-dimensional Navier-Stokes turbulence, we generalize a previous nonperturbative locality proof to multiple applications of the nonlinear interactions operator on generalized structure functions of velocity differences. We call this generalization of nonperturbative locality to multiple applications of the nonlinear interactions operator "multilocality." The resulting cross terms pose a new challenge requiring a new argument and the introduction of a new fusion rule that takes advantage of rotational symmetry. Our main result is that the fusion-rules hypothesis implies both locality and multilocality in both the IR and UV limits for the downscale energy cascade of three-dimensional Navier-Stokes turbulence and the downscale enstrophy cascade and inverse energy cascade of two-dimensional Navier-Stokes turbulence. We stress that these claims relate to nonperturbative locality of generalized structure functions on all orders and not the term-by-term perturbative locality of diagrammatic theories or closure models that involve only two-point correlation and response functions.

Emergence of geometry: A two-dimensional toy model

International Nuclear Information System (INIS)

Alfaro, Jorge; Espriu, Domene; Puigdomenech, Daniel

2010-01-01

We review the similarities between the effective chiral Lagrangrian, relevant for low-energy strong interactions, and the Einstein-Hilbert action. We use these analogies to suggest a specific mechanism whereby gravitons would emerge as Goldstone bosons of a global SO(D)xGL(D) symmetry broken down to SO(D) by fermion condensation. We propose a two-dimensional toy model where a dynamical zweibein is generated from a topological theory without any preexisting metric structure, the space being endowed only with an affine connection. A metric appears only after the symmetry breaking; thus the notion of distance is an induced effective one. In spite of several nonstandard features this simple toy model appears to be renormalizable and at long distances is described by an effective Lagrangian that corresponds to that of two-dimensional gravity (Liouville theory). The induced cosmological constant is related to the dynamical mass M acquired by the fermion fields in the breaking, which also acts as an infrared regulator. The low-energy expansion is valid for momenta k>M, i.e. for supra-horizon scales. We briefly discuss a possible implementation of a similar mechanism in four dimensions.

Compatible topologies and parameters for NMR structure determination of carbohydrates by simulated annealing

OpenAIRE

Feng, Yingang

2017-01-01

The use of NMR methods to determine the three-dimensional structures of carbohydrates and glycoproteins is still challenging, in part because of the lack of standard protocols. In order to increase the convenience of structure determination, the topology and parameter files for carbohydrates in the program Crystallography & NMR System (CNS) were investigated and new files were developed to be compatible with the standard simulated annealing protocols for proteins and nucleic acids. Recalculat...

Topology optimization of acoustic-structure interaction problems using a mixed finite element formulation

DEFF Research Database (Denmark)

Yoon, Gil Ho; Jensen, Jens Stissing; Sigmund, Ole

2007-01-01

given during the optimization process. In this paper we circumvent the explicit boundary representation by using a mixed finite element formulation with displacements and pressure as primary variables (a u/p-formulation). The Helmholtz equation is obtained as a special case of the mixed formulation...... for the elastic shear modulus equating to zero. Hence, by spatial variation of the mass density, shear and bulk moduli we are able to solve the coupled problem by the mixed formulation. Using this modelling approach, the topology optimization procedure is simply implemented as a standard density approach. Several...... two-dimensional acoustic-structure problems are optimized in order to verify the proposed method....

Topological energy conversion through the bulk or the boundary of driven systems

Science.gov (United States)

Peng, Yang; Refael, Gil

2018-04-01

Combining physical and synthetic dimensions allows a controllable realization and manipulation of high-dimensional topological states. In our work, we introduce two quasiperiodically driven one-dimensional systems which enable tunable topological energy conversion between different driving sources. Using three drives, we realize a four-dimensional quantum Hall state which allows energy conversion between two of the drives within the bulk of the one-dimensional system. With only two drives, we achieve energy conversion between the two at the edge of the chain. Both effects are a manifestation of the effective axion electrodynamics in a three-dimensional time-reversal-invariant topological insulator. Furthermore, we explore the effects of disorder and commensurability of the driving frequencies, and show the phenomena are robust. We propose two experimental platforms, based on semiconductor heterostructures and ultracold atoms in optical lattices, in order to observe the topological energy conversion.

Riemann, topology, and physics

CERN Document Server

Monastyrsky, Michael I

2008-01-01

This significantly expanded second edition of Riemann, Topology, and Physics combines a fascinating account of the life and work of Bernhard Riemann with a lucid discussion of current interaction between topology and physics. The author, a distinguished mathematical physicist, takes into account his own research at the Riemann archives of Göttingen University and developments over the last decade that connect Riemann with numerous significant ideas and methods reflected throughout contemporary mathematics and physics. Special attention is paid in part one to results on the Riemann–Hilbert problem and, in part two, to discoveries in field theory and condensed matter such as the quantum Hall effect, quasicrystals, membranes with nontrivial topology, "fake" differential structures on 4-dimensional Euclidean space, new invariants of knots and more. In his relatively short lifetime, this great mathematician made outstanding contributions to nearly all branches of mathematics; today Riemann’s name appears prom...

Strictly local one-dimensional topological quantum error correction with symmetry-constrained cellular automata

Directory of Open Access Journals (Sweden)

Nicolai Lang, Hans Peter Büchler

2018-01-01

Full Text Available Active quantum error correction on topological codes is one of the most promising routes to long-term qubit storage. In view of future applications, the scalability of the used decoding algorithms in physical implementations is crucial. In this work, we focus on the one-dimensional Majorana chain and construct a strictly local decoder based on a self-dual cellular automaton. We study numerically and analytically its performance and exploit these results to contrive a scalable decoder with exponentially growing decoherence times in the presence of noise. Our results pave the way for scalable and modular designs of actively corrected one-dimensional topological quantum memories.

Numerical studies of unsteady coherent structures and transport in two-dimensional flows

Energy Technology Data Exchange (ETDEWEB)

Hesthaven, J.S.

1995-08-01

The dynamics of unsteady two-dimensional coherent structures in various physical systems is studied through direct numerical solution of the dynamical equations using spectral methods. The relation between the Eulerian and the Lagrangian auto-correlation functions in two-dimensional homogeneous, isotropic turbulence is studied. A simple analytic expression for the Eulerian and Lagrangian auto-correlation function for the fluctuating velocity field is derived solely on the basis of the one-dimensional power spectrum. The long-time evolution of monopolar and dipolar vortices in anisotropic systems relevant for geophysics and plasma physics is studied by direct numerical solution. Transport properties and spatial reorganization of vortical structures are found to depend strongly on the initial conditions. Special attention is given to the dynamics of strong monopoles and the development of unsteady tripolar structures. The development of coherent structures in fluid flows, incompressible as well as compressible, is studied by novel numerical schemes. The emphasis is on the development of spectral methods sufficiently advanced as to allow for detailed and accurate studies of the self-organizing processes. (au) 1 ill., 94 refs.

Topological Optimization of Continuum Structure based on ANSYS

Directory of Open Access Journals (Sweden)

Li Xue-ping

2017-01-01

Full Text Available Topology optimization is at the phase of structural concept design and the result of it is foundation for succeeding design, therefore, structural topology optimization is more important to engineering design. in this thesis, in order to seek the optimal structure shape of the winch’s mounting bracket of ROV simulator, topology optimization design of it by finite element analysis software ANSYS was carried out. the results show that the topology optimization method is an effective optimization method and indicate that the method is correct and effective, it has a certain engineering application prospect.

Phase-Field Simulations of Topological Structures and Topological Phase Transitions in Ferroelectric Oxide Heterostructures

Science.gov (United States)

Zijian Hong

of insulating STO is further revealed, which shows that a rich phase diagram can be formed by simply tuning the thickness of this layer. Wave-like polar spiral phase is simulated by substituting part of the PTO with BiFeO3 (BFO) in the PTO/STO superlattice (i.e., in a (PTO) 4/(BFO)4/(PTO)4/(STO)12 tricolor system) which has demonstrate ordered polar vortex lattice. This spiral phase is made up of semi-vortex cores that are floating up-down in the ferroelectric PTO layers, giving rise to a net in-plane polarization. An increase of Curie temperature and topological to regular domain transition temperature (over 200 K) is observed, due to the higher Curie temperature and larger spontaneous polarization in BFO layers. This unidirectional spiral state can be reversibly switched by experimentally feasible in-plane field, which evolves into a metastable vortex structure in-between two spiral phases with opposite in-plane directions. (Abstract shortened by ProQuest.).

Atomic structure of a metal-supported two-dimensional germania film

Science.gov (United States)

Lewandowski, Adrián Leandro; Schlexer, Philomena; Büchner, Christin; Davis, Earl M.; Burrall, Hannah; Burson, Kristen M.; Schneider, Wolf-Dieter; Heyde, Markus; Pacchioni, Gianfranco; Freund, Hans-Joachim

2018-03-01

The growth and microscopic characterization of two-dimensional germania films is presented. Germanium oxide monolayer films were grown on Ru(0001) by physical vapor deposition and subsequent annealing in oxygen. We obtain a comprehensive image of the germania film structure by combining intensity-voltage low-energy electron diffraction (I/V-LEED) and ab initio density functional theory (DFT) analysis with atomic-resolution scanning tunneling microscopy (STM) imaging. For benchmarking purposes, the bare Ru(0001) substrate and the (2 ×2 )3 O covered Ru(0001) were analyzed with I/V-LEED with respect to previous reports. STM topographic images of the germania film reveal a hexagonal network where the oxygen and germanium atom positions appear in different imaging contrasts. For quantitative LEED, the best agreement has been achieved with DFT structures where the germanium atoms are located preferentially on the top and fcc hollow sites of the Ru(0001) substrate. Moreover, in these atomically flat germania films, local site geometries, i.e., tetrahedral building blocks, ring structures, and domain boundaries, have been identified, indicating possible pathways towards two-dimensional amorphous networks.

Bubble Divergences: Sorting out Topology from Cell Structure

Science.gov (United States)

Bonzom, Valentin; Smerlak, Matteo

2012-02-01

We conclude our analysis of bubble divergences in the flat spinfoam model. In [arXiv:1008.1476] we showed that the divergence degree of an arbitrary two-complex Gamma can be evaluated exactly by means of twisted cohomology. Here, we specialize this result to the case where Gamma is the two-skeleton of the cell decomposition of a pseudomanifold, and sharpen it with a careful analysis of the cellular and topological structures involved. Moreover, we explain in detail how this approach reproduces all the previous powercounting results for the Boulatov-Ooguri (colored) tensor models, and sheds light on algebraic-topological aspects of Gurau's 1/N expansion.

Topological strings from Liouville gravity

International Nuclear Information System (INIS)

Ishibashi, N.; Li, M.

1991-01-01

We study constrained SU(2) WZW models, which realize a class of two-dimensional conformal field theories. We show that they give rise to topological gravity coupled to the topological minimal models when they are coupled to Liouville gravity. (orig.)

Photonic Structure-Integrated Two-Dimensional Material Optoelectronics

Directory of Open Access Journals (Sweden)

Tianjiao Wang

2016-12-01

Full Text Available The rapid development and unique properties of two-dimensional (2D materials, such as graphene, phosphorene and transition metal dichalcogenides enable them to become intriguing candidates for future optoelectronic applications. To maximize the potential of 2D material-based optoelectronics, various photonic structures are integrated to form photonic structure/2D material hybrid systems so that the device performance can be manipulated in controllable ways. Here, we first introduce the photocurrent-generation mechanisms of 2D material-based optoelectronics and their performance. We then offer an overview and evaluation of the state-of-the-art of hybrid systems, where 2D material optoelectronics are integrated with photonic structures, especially plasmonic nanostructures, photonic waveguides and crystals. By combining with those photonic structures, the performance of 2D material optoelectronics can be further enhanced, and on the other side, a high-performance modulator can be achieved by electrostatically tuning 2D materials. Finally, 2D material-based photodetector can also become an efficient probe to learn the light-matter interactions of photonic structures. Those hybrid systems combine the advantages of 2D materials and photonic structures, providing further capacity for high-performance optoelectronics.

Topological superconductor in quasi-one-dimensional Tl2 -xMo6Se6

Science.gov (United States)

Huang, Shin-Ming; Hsu, Chuang-Han; Xu, Su-Yang; Lee, Chi-Cheng; Shiau, Shiue-Yuan; Lin, Hsin; Bansil, Arun

2018-01-01

We propose that the quasi-one-dimensional molybdenum selenide compound Tl2 -xMo6Se6 is a time-reversal-invariant topological superconductor induced by intersublattice pairing, even in the absence of spin-orbit coupling (SOC). No noticeable change in superconductivity is observed in Tl-deficient (0 ≤x ≤0.1 ) compounds. At weak SOC, the superconductor prefers the triplet d vector lying perpendicular to the chain direction and two-dimensional E2 u symmetry, which is driven to a nematic order by spontaneous rotation symmetry breaking. The locking energy of the d vector is estimated to be weak and hence the proof of its direction would rely on tunneling or phase-sensitive measurements.

Uniform topology on EQ-algebras

Directory of Open Access Journals (Sweden)

Yang Jiang

2017-04-01

Full Text Available In this paper, we use filters of an EQ-algebra E to induce a uniform structure (E, , and then the part induce a uniform topology in E. We prove that the pair (E, is a topological EQ-algebra, and some properties of (E, are investigated. In particular, we show that (E, is a first-countable, zero-dimensional, disconnected and completely regular space. Finally, by using convergence of nets, the convergence of topological EQ-algebras is obtained.

New topological structures of Skyrme theory: baryon number and monopole number

Energy Technology Data Exchange (ETDEWEB)

Cho, Y.M. [Chinese Academy of Science, Institute of Modern Physics, Lanzhou (China); Konkuk University, Seoul (Korea, Republic of); Seoul National University, School of Physics and Astronomy, Seoul (Korea, Republic of); Kimm, Kyoungtae [Seoul National University, Faculty of Liberal Education, Seoul (Korea, Republic of); Yoon, J.H. [Konkuk University, Department of Physics, Seoul (Korea, Republic of); Zhang, Pengming [Chinese Academy of Science, Institute of Modern Physics, Lanzhou (China)

2017-02-15

Based on the observation that the skyrmion in Skyrme theory can be viewed as a dressed monopole, we show that the skyrmions have two independent topology, the baryon topology π{sub 3}(S{sup 3}) and the monopole topology π{sub 2}(S{sup 2}). With this we propose to classify the skyrmions by two topological numbers (m, n), the monopole number m and the shell (radial) number n. In this scheme the popular (non spherically symmetric) skyrmions are classified as the (m, 1) skyrmions but the spherically symmetric skyrmions are classified as the (1, n) skyrmions, and the baryon number B is given by B = mn. Moreover, we show that the vacuum of the Skyrme theory has the structure of the vacuum of the Sine-Gordon theory and QCD combined together, which can also be classified by two topological numbers (p, q). This puts the Skyrme theory in a totally new perspective. (orig.)

Visualizing nD Point Clouds as Topological Landscape Profiles to Guide Local Data Analysis

Energy Technology Data Exchange (ETDEWEB)

Oesterling, Patrick [Univ. of Leipzig (Germany). Computer Science Dept.; Heine, Christian [Univ. of Leipzig (Germany). Computer Science Dept.; Federal Inst. of Technology (ETH), Zurich (Switzerland). Dept. of Computer Science; Weber, Gunther H. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division; Scheuermann, Gerik [Univ. of Leipzig (Germany). Computer Science Dept.

2012-05-04

Analyzing high-dimensional point clouds is a classical challenge in visual analytics. Traditional techniques, such as projections or axis-based techniques, suffer from projection artifacts, occlusion, and visual complexity.We propose to split data analysis into two parts to address these shortcomings. First, a structural overview phase abstracts data by its density distribution. This phase performs topological analysis to support accurate and non-overlapping presentation of the high-dimensional cluster structure as a topological landscape profile. Utilizing a landscape metaphor, it presents clusters and their nesting as hills whose height, width, and shape reflect cluster coherence, size, and stability, respectively. A second local analysis phase utilizes this global structural knowledge to select individual clusters or point sets for further, localized data analysis. Focusing on structural entities significantly reduces visual clutter in established geometric visualizations and permits a clearer, more thorough data analysis. In conclusion, this analysis complements the global topological perspective and enables the user to study subspaces or geometric properties, such as shape.

Ordered groups and topology

CERN Document Server

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.

Twistor-theoretic approach to topological field theories

International Nuclear Information System (INIS)

Ito, Kei.

1991-12-01

The two-dimensional topological field theory which describes a four-dimensional self-dual space-time (gravitational instanton) as a target space, which we constructed before, is shown to be deeply connected with Penrose's 'twistor theory'. The relations are presented in detail. Thus our theory offers a 'twistor theoretic' approach to topological field theories. (author)

Protein structure: geometry, topology and classification

Energy Technology Data Exchange (ETDEWEB)

Taylor, William R.; May, Alex C.W.; Brown, Nigel P.; Aszodi, Andras [Division of Mathematical Biology, National Institute for Medical Research, London (United Kingdom)

2001-04-01

The structural principals of proteins are reviewed and analysed from a geometric perspective with a view to revealing the underlying regularities in their construction. Computer methods for the automatic comparison and classification of these structures are then reviewed with an analysis of the statistical significance of comparing different shapes. Following an analysis of the current state of the classification of proteins, more abstract geometric and topological representations are explored, including the occurrence of knotted topologies. The review concludes with a consideration of the origin of higher-level symmetries in protein structure. (author)

Correlation based method for comparing and reconstructing quasi-identical two-dimensional structures

International Nuclear Information System (INIS)

Mejia-Barbosa, Y.

2000-03-01

We show a method for comparing and reconstructing two similar amplitude-only structures, which are composed by the same number of identical apertures. The structures are two-dimensional and differ only in the location of one of the apertures. The method is based on a subtraction algorithm, which involves the auto-correlations and cross-correlation functions of the compared structures. Experimental results illustrate the feasibility of the method. (author)

Photoinduced Topological Phase Transitions in Topological Magnon Insulators.

Science.gov (United States)

Owerre, S A

2018-03-13

Topological magnon insulators are the bosonic analogs of electronic topological insulators. They are manifested in magnetic materials with topologically nontrivial magnon bands as realized experimentally in a quasi-two-dimensional (quasi-2D) kagomé ferromagnet Cu(1-3, bdc), and they also possess protected magnon edge modes. These topological magnetic materials can transport heat as well as spin currents, hence they can be useful for spintronic applications. Moreover, as magnons are charge-neutral spin-1 bosonic quasiparticles with a magnetic dipole moment, topological magnon materials can also interact with electromagnetic fields through the Aharonov-Casher effect. In this report, we study photoinduced topological phase transitions in intrinsic topological magnon insulators in the kagomé ferromagnets. Using magnonic Floquet-Bloch theory, we show that by varying the light intensity, periodically driven intrinsic topological magnetic materials can be manipulated into different topological phases with different sign of the Berry curvatures and the thermal Hall conductivity. We further show that, under certain conditions, periodically driven gapped topological magnon insulators can also be tuned to synthetic gapless topological magnon semimetals with Dirac-Weyl magnon cones. We envision that this work will pave the way for interesting new potential practical applications in topological magnetic materials.

Algebraic topology of spin glasses

International Nuclear Information System (INIS)

Koma, Tohru

2011-01-01

We study the topology of frustration in d-dimensional Ising spin glasses with d ≥ 2 with nearest-neighbor interactions. We prove the following. For any given spin configuration, the domain walls on the unfrustration network are all transverse to a frustrated loop on the unfrustration network, where a domain wall is defined to be a connected element of the collection of all the (d - 1)-cells which are dual to the bonds having an unfavorable energy, and the unfrustration network is the collection of all the unfrustrated plaquettes. These domain walls are topologically nontrivial because they are all related to the global frustration of a loop on the unfrustration network. Taking account of the thermal stability for the domain walls, we can explain the numerical results that three- or higher-dimensional systems exhibit a spin glass phase, whereas two-dimensional ones do not. Namely, in two dimensions, the thermal fluctuations of the topologically nontrivial domain walls destroy the order of the frozen spins on the unfrustration network, whereas they do not in three or higher dimensions. This may be interpreted as a global topological effect of the frustrations.

Homogenization and structural topology optimization theory, practice and software

CERN Document Server

Hassani, Behrooz

1999-01-01

Structural topology optimization is a fast growing field that is finding numerous applications in automotive, aerospace and mechanical design processes. Homogenization is a mathematical theory with applications in several engineering problems that are governed by partial differential equations with rapidly oscillating coefficients Homogenization and Structural Topology Optimization brings the two concepts together and successfully bridges the previously overlooked gap between the mathematical theory and the practical implementation of the homogenization method. The book is presented in a unique self-teaching style that includes numerous illustrative examples, figures and detailed explanations of concepts. The text is divided into three parts which maintains the book's reader-friendly appeal.

Clapeyron equation and phase equilibrium properties in higher dimensional charged topological dilaton AdS black holes with a nonlinear source

Energy Technology Data Exchange (ETDEWEB)

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.)

Synthesis and characterization of two new zinc(II) coordination polymers with bidentate flexible ligands: Formation of a 2D structure with (44.62)-sql topology

Science.gov (United States)

Lalegani, Arash; Khaledi Sardashti, Mohammad; Gajda, Roman; Woźniak, Krzysztof

2017-12-01

Zinc(II) coordination polymers [Zn(bip)2(NCS)2]n (1) and [Zn(μ-bbd)(N3)2]n (2) were synthesized by using the neutral flexible bidentate N-donor ligands 1,4-bis(3,5-dimethylpyrazolyl)butane (bbd) and 1,3-bis(imidazolyl)propane (bip), mono-anionic NCS- or N3-ligand and zinc(II) chloride salts. The results of the X-ray analyses demonstrate that in the structure of 1, the zinc(II) ion is located on an inversion center and exhibits an ZnN6 octahedral arrangement while, in the structure of 2, the zinc(II) ion adopts an ZnN4 tetrahedral geometry. In the polymer 1, the NCS groups are terminally N-bonded to the metal center and the each bip with anti-gauche conformation acts as bridging connecting four zinc(II) ions to form a two-dimensional network with a sql [point symbol (44.62)] topology while, in the polymer 1, the N3 groups are terminally bonded to the metal center and each bbd with anti-anti-anti conformation acts as bridging ligand connecting two zinc(II) ions to form a one-dimensional zig-zag chain. Coordination compounds 1 and 2 have been characterized by infrared spectroscopy, elemental analyses and single-crystal X-ray diffraction. Thermal analyses of polymers were also presented.

A two-dimensional bilayered Cd(II) coordination polymer with a three-dimensional supramolecular architecture incorporating 1,2-bis(pyridin-4-yl)ethene and 2,2'-(diazenediyl)dibenzoic acid.

Science.gov (United States)

Liu, Lei-Lei; Zhou, Yan; Li, Ping; Tian, Jiang-Ya

2014-02-01

In poly[[μ2-1,2-bis(pyridin-4-yl)ethene-κ(2)N:N'][μ2-2,2'-(diazenediyl)dibenzoato-κ(3)O,O':O'']cadmium(II)], [Cd(C14H8N2O4)(C12H10N2)]n, the asymmetric unit contains one Cd(II) cation, one 2,2'-(diazenediyl)dibenzoate anion (denoted L(2-)) and one 1,2-bis(pyridin-4-yl)ethene ligand (denoted bpe). Each Cd(II) centre is six-coordinated by four O atoms of bridging/chelating carboxylate groups from three L(2-) ligands and by two N atoms from two bpe ligands, forming a distorted octahedron. The Cd(II) cations are bridged by L(2-) and bpe ligands to give a two-dimensional (4,4) layer. The layers are interlinked through bridging carboxylate O atoms from L(2-) ligands, generating a two-dimensional bilayered structure with a 3(6)4(13)6(2) topology. The bilayered structures are further extended to form a three-dimensional supramolecular architecture via a combination of hydrogen-bonding and aromatic stacking interactions.

The spectrum of a Dirac-like operator class and the topology in two dimensions

International Nuclear Information System (INIS)

Botelho, Luiz C.L.

1998-05-01

It is shown, in a relatively simple way and based on Seeley pseudo-differential operator theory, that the main result of Atiyah-Singer in which the trace of the evolution operator associated to a Dirac-like operator class defined in two-dimensional manifolds and coming out of Quantum Physics has a deep topological meaning

Topologically-protected one-way leaky waves in nonreciprocal plasmonic structures

Science.gov (United States)

Hassani Gangaraj, S. Ali; Monticone, Francesco

2018-03-01

We investigate topologically-protected unidirectional leaky waves on magnetized plasmonic structures acting as homogeneous photonic topological insulators. Our theoretical analyses and numerical experiments aim at unveiling the general properties of these exotic surface waves, and their nonreciprocal and topological nature. In particular, we study the behavior of topological leaky modes in stratified structures composed of a magnetized plasma at the interface with isotropic conventional media, and we show how to engineer their propagation and radiation properties, leading to topologically-protected backscattering-immune wave propagation, and highly directive and tunable radiation. Taking advantage of the non-trivial topological properties of these leaky modes, we also theoretically demonstrate advanced functionalities, including arbitrary re-routing of leaky waves on the surface of bodies with complex shapes, as well as the realization of topological leaky-wave (nano)antennas with isolated channels of radiation that are completely independent and separately tunable. Our findings help shedding light on the behavior of topologically-protected modes in open wave-guiding structures, and may open intriguing directions for future antenna generations based on topological structures, at microwaves and optical frequencies.

Two- and three-dimensional cadmium-organic frameworks with trimesic acid and 4,4'-trimethylenedipyridine.

Science.gov (United States)

Almeida Paz, Filipe A; Klinowski, Jacek

2004-06-28

Three novel cadmium-organic frameworks built-up from 1,3,5-benzenetricarboxylate anions (HXBTC(x-3)) and 4,4'-trimethylenedipyridine (TMD) have been hydrothermally synthesized, and characterized using single-crystal X-ray diffraction, thermoanalytical measurements, elemental analysis, and IR and Raman spectroscopies: [Cd(HBTC)(TMD)(2)].8.5H(2)O (I), [Cd(HBTC)(TMD)(H(2)O)].4.5H(2)O (II), and [Cd(2)(BTC)(TMD)(2)(NO(3))].3H(2)O (III), with structures I and II being isolated as a mixture of crystals. Structure I contains an undulating infinite two-dimensional [Cd(HBTC)(TMD)(2)] framework, with a (4,4) topology and rectangular pores, ca. 3.4 x 11.0 A in cross-section, distributed in a herringbone manner. The crystal structure of I is obtained by parallel packing of this 2D framework in an [ABAB.] fashion. Compound II has a porous 3D diamondoid framework with channels running in several directions of the unit cell, which allows 2-fold interpenetration to occur. The most prominent channels are distributed in a brick-wall fashion along the c axis and have a cross-section of ca. 3.2 x 13.2 A. Structure III can be seen as the three-dimensional assembly of binuclear secondary building units (SBU), which leads to a compact, neutral, and coordinatively bonded eight-connected framework, [Cd(2)(BTC)(TMD)(2)(NO(3))], exhibiting an unusual 3(6)4(22) topology. The increased flexibility of the TMD ligands (brought about by the three methylene groups between the two 4-pyridyl rings) can lead, for the same reactive system, to a large variety of crystal architectures.

Topological Valley Transport in Two-dimensional Honeycomb Photonic Crystals.

Science.gov (United States)

Yang, Yuting; Jiang, Hua; Hang, Zhi Hong

2018-01-25

Two-dimensional photonic crystals, in analogy to AB/BA stacking bilayer graphene in electronic system, are studied. Inequivalent valleys in the momentum space for photons can be manipulated by simply engineering diameters of cylinders in a honeycomb lattice. The inequivalent valleys in photonic crystal are selectively excited by a designed optical chiral source and bulk valley polarizations are visualized. Unidirectional valley interface states are proved to exist on a domain wall connecting two photonic crystals with different valley Chern numbers. With the similar optical vortex index, interface states can couple with bulk valley polarizations and thus valley filter and valley coupler can be designed. Our simple dielectric PC scheme can help to exploit the valley degree of freedom for future optical devices.

Zak phase and band inversion in dimerized one-dimensional locally resonant metamaterials

Science.gov (United States)

Zhu, Weiwei; Ding, Ya-qiong; Ren, Jie; Sun, Yong; Li, Yunhui; Jiang, Haitao; Chen, Hong

2018-05-01

The Zak phase, which refers to Berry's phase picked up by a particle moving across the Brillouin zone, characterizes the topological properties of Bloch bands in a one-dimensional periodic system. Here the Zak phase in dimerized one-dimensional locally resonant metamaterials is investigated. It is found that there are some singular points in the bulk band across which the Bloch states contribute π to the Zak phase, whereas in the rest of the band the contribution is nearly zero. These singular points associated with zero reflection are caused by two different mechanisms: the dimerization-independent antiresonance of each branch and the dimerization-dependent destructive interference in multiple backscattering. The structure undergoes a topological phase-transition point in the band structure where the band inverts, and the Zak phase, which is determined by the numbers of singular points in the bulk band, changes following a shift in dimerization parameter. Finally, the interface state between two dimerized metamaterial structures with different topological properties in the first band gap is demonstrated experimentally. The quasi-one-dimensional configuration of the system allows one to explore topology-inspired new methods and applications on the subwavelength scale.

Topological insulators Dirac equation in condensed matter

CERN Document Server

Shen, Shun-Qing

2017-01-01

This new edition presents a unified description of these insulators from one to three dimensions based on the modified Dirac equation. It derives a series of solutions of the bound states near the boundary, and describes the current status of these solutions. Readers are introduced to topological invariants and their applications to a variety of systems from one-dimensional polyacetylene, to two-dimensional quantum spin Hall effect and p-wave superconductors, three-dimensional topological insulators and superconductors or superfluids, and topological Weyl semimetals, helping them to better understand this fascinating field. To reflect research advances in topological insulators, several parts of the book have been updated for the second edition, including: Spin-Triplet Superconductors, Superconductivity in Doped Topological Insulators, Detection of Majorana Fermions and so on. In particular, the book features a new chapter on Weyl semimetals, a topic that has attracted considerable attention and has already b...

Topological insulators and superconductors from string theory

International Nuclear Information System (INIS)

Ryu, Shinsei; Takayanagi, Tadashi

2010-01-01

Topological insulators and superconductors in different spatial dimensions and with different discrete symmetries have been fully classified recently, revealing a periodic structure for the pattern of possible types of topological insulators and superconductors, both in terms of spatial dimensions and in terms of symmetry classes. It was proposed that K theory is behind the periodicity. On the other hand, D-branes, a solitonic object in string theory, are also known to be classified by K theory. In this paper, by inspecting low-energy effective field theories realized by two parallel D-branes, we establish a one-to-one correspondence between the K-theory classification of topological insulators/superconductors and D-brane charges. In addition, the string theory realization of topological insulators and superconductors comes naturally with gauge interactions, and the Wess-Zumino term of the D-branes gives rise to a gauge field theory of topological nature, such as ones with the Chern-Simons term or the θ term in various dimensions. This sheds light on topological insulators and superconductors beyond noninteracting systems, and the underlying topological field theory description thereof. In particular, our string theory realization includes the honeycomb lattice Kitaev model in two spatial dimensions, and its higher-dimensional extensions. Increasing the number of D-branes naturally leads to a realization of topological insulators and superconductors in terms of holography (AdS/CFT).

Lectures on 2d gauge theories. Topological aspects and path integral techniques

International Nuclear Information System (INIS)

Blau, M.; Thompson, G.

1993-10-01

In these lectures are discussed two classes of two-dimensional field theories which are not obviously topological, but which nevertheless exhibit an intriguing equivalence with certain topological theories. These classes are two-dimensional Yang-Mills theory and the so-called G/G gauged Wess-Zumino-Witten model. The aim is to exhibit and extract the topological information contained in these theories and to present a technique which allows to calculate directly their partition functions and topological correlation functions on arbitrary closed surfaces. 34 refs

Generalized zeta function representation of groups and 2-dimensional topological Yang-Mills theory: The example of GL(2, _q) and PGL(2, _q)

International Nuclear Information System (INIS)

Roche, Ph.

2016-01-01

We recall the relation between zeta function representation of groups and two-dimensional topological Yang-Mills theory through Mednikh formula. We prove various generalisations of Mednikh formulas and define generalization of zeta function representations of groups. We compute some of these functions in the case of the finite group GL(2, _q) and PGL(2, _q). We recall the table characters of these groups for any q, compute the Frobenius-Schur indicator of their irreducible representations, and give the explicit structure of their fusion rings.

Experimental investigation of two-dimensional critical surface structure, stimulated Raman scattering, and two-plasmon decay instability. Annual report, January 1, 1981-April 30, 1982

International Nuclear Information System (INIS)

Wong, A.Y.; Eggleston, D.L.; Tanikawa, T.; Qian, S.J.

1982-11-01

Experimental observations of the space and time evolution of resonantly enhanced electrostatic electric fields and plasma density in cylindrical geometry demonstrate the development of two-dimensional caviton structure when an initial density perturbation is imposed on the plasma in the direction perpendicular to the driver field. This two-dimensional structure is observed after the development of profile modification and grows on the ion time scale. The existence of a large azimuthal electric field component is an observational signature of two-dimensional structure. Enhanced electric field maxima are found to be azimuthally correlated with the density minima. Both the density cavities and electric field peaks exhibit increased azimuthal location with the growth of two-dimensional structure. The two-dimensional development exhibits a strong dependence on both perturbation wavenumber and driver power. The related theoretical literature is reviewed and numerical, analytical, and qualitative hybrid models for a driven, two-dimensional, inhomogeneous plasma are presented. Preliminary work is presented in the following additional areas: weak magnetic field effects on critical surface physics, optical measurements of fast electron production, two-dimensional effects in microwave-plasma interactions, Langmuir wave trapping, stimulated Raman scattering and two-plasmon decay instability

Dynamical topological invariant after a quantum quench

Science.gov (United States)

Yang, Chao; Li, Linhu; Chen, Shu

2018-02-01

We show how to define a dynamical topological invariant for one-dimensional two-band topological systems after a quantum quench. By analyzing general two-band models of topological insulators, we demonstrate that the reduced momentum-time manifold can be viewed as a series of submanifolds S2, and thus we are able to define a dynamical topological invariant on each of the spheres. We also unveil the intrinsic relation between the dynamical topological invariant and the difference in the topological invariant of the initial and final static Hamiltonian. By considering some concrete examples, we illustrate the calculation of the dynamical topological invariant and its geometrical meaning explicitly.

Topological map of the Hofstadter butterfly: Fine structure of Chern numbers and Van Hove singularities

International Nuclear Information System (INIS)

Naumis, Gerardo G.

2016-01-01

The Hofstadter butterfly is a quantum fractal with a highly complex nested set of gaps, where each gap represents a quantum Hall state whose quantized conductivity is characterized by topological invariants known as the Chern numbers. Here we obtain simple rules to determine the Chern numbers at all scales in the butterfly fractal and lay out a very detailed topological map of the butterfly by using a method used to describe quasicrystals: the cut and projection method. Our study reveals the existence of a set of critical points that separates orderly patterns of both positive and negative Cherns that appear as a fine structure in the butterfly. This fine structure can be understood as a small tilting of the projection subspace in the cut and projection method and by using a Chern meeting formula. Finally, we prove that the critical points are identified with the Van Hove singularities that exist at every band center in the butterfly landscape. - Highlights: • Use a higher dimensional approach to build a topological map of the Hofstadter butterfly. • There is a fine structure of Chern numbers around each rational flux. • Van Hove singularities are limiting points for topological sequences of the fine flux.

Topological map of the Hofstadter butterfly: Fine structure of Chern numbers and Van Hove singularities

Energy Technology Data Exchange (ETDEWEB)

Naumis, Gerardo G., E-mail: naumis@fisica.unam.mx [Departamento de Física–Química, Instituto de Física, Universidad Nacional Autónoma de México (UNAM), Apartado Postal 20-364, 01000 México, Distrito Federal (Mexico); Department of Physics and Astronomy, George Mason University, Fairfax, VA 22030 (United States); Escuela Superior de Física y Matemáticas, ESIA-Zacatenco, Instituto Politécnico Nacional, México D.F. (Mexico)

2016-04-29

The Hofstadter butterfly is a quantum fractal with a highly complex nested set of gaps, where each gap represents a quantum Hall state whose quantized conductivity is characterized by topological invariants known as the Chern numbers. Here we obtain simple rules to determine the Chern numbers at all scales in the butterfly fractal and lay out a very detailed topological map of the butterfly by using a method used to describe quasicrystals: the cut and projection method. Our study reveals the existence of a set of critical points that separates orderly patterns of both positive and negative Cherns that appear as a fine structure in the butterfly. This fine structure can be understood as a small tilting of the projection subspace in the cut and projection method and by using a Chern meeting formula. Finally, we prove that the critical points are identified with the Van Hove singularities that exist at every band center in the butterfly landscape. - Highlights: • Use a higher dimensional approach to build a topological map of the Hofstadter butterfly. • There is a fine structure of Chern numbers around each rational flux. • Van Hove singularities are limiting points for topological sequences of the fine flux.

Strongly anisotropic spin-orbit splitting in a two-dimensional electron gas

DEFF Research Database (Denmark)

Michiardi, Matteo; Bianchi, Marco; Dendzik, Maciej

2015-01-01

Near-surface two-dimensional electron gases on the topological insulator Bi$_2$Te$_2$Se are induced by electron doping and studied by angle-resolved photoemission spectroscopy. A pronounced spin-orbit splitting is observed for these states. The $k$-dependent splitting is strongly anisotropic to a...

Edge states of a three-dimensional topological insulator

International Nuclear Information System (INIS)

Deb, Oindrila; Sen, Diptiman; Soori, Abhiram

2014-01-01

We use the bulk Hamiltonian for a three-dimensional topological insulator such as Bi 2 Se 3 to study the states which appear on its various surfaces and along the edge between two surfaces. We use both analytical methods based on the surface Hamiltonians (which are derived from the bulk Hamiltonian) and numerical methods based on a lattice discretization of the bulk Hamiltonian. We find that the application of a potential barrier along an edge can give rise to states localized at that edge. These states have an unusual energy-momentum dispersion which can be controlled by applying a potential along the edge; in particular, the velocity of these states can be tuned to zero. The scattering and conductance across the edge is studied as a function of the edge potential. We show that a magnetic field in a particular direction can also give rise to zero energy states on certain edges. We point out possible experimental ways of looking for the various edge states. (paper)

Aharonov–Bohm interference in topological insulator nanoribbons

KAUST Repository

Peng, Hailin

2009-12-13

Topological insulators represent unusual phases of quantum matter with an insulating bulk gap and gapless edges or surface states. The two-dimensional topological insulator phase was predicted in HgTe quantum wells and confirmed by transport measurements. Recently, Bi2 Se3 and related materials have been proposed as three-dimensional topological insulators with a single Dirac cone on the surface, protected by time-reversal symmetry. The topological surface states have been observed by angle-resolved photoemission spectroscopy experiments. However, few transport measurements in this context have been reported, presumably owing to the predominance of bulk carriers from crystal defects or thermal excitations. Here we show unambiguous transport evidence of topological surface states through periodic quantum interference effects in layered single-crystalline Bi2 Se3 nanoribbons, which have larger surface-to-volume ratios than bulk materials and can therefore manifest surface effects. Pronounced Aharonov-Bohm oscillations in the magnetoresistance clearly demonstrate the coherent propagation of two-dimensional electrons around the perimeter of the nanoribbon surface, as expected from the topological nature of the surface states. The dominance of the primary h/e oscillation, where h is Plancks constant and e is the electron charge, and its temperature dependence demonstrate the robustness of these states. Our results suggest that topological insulator nanoribbons afford promising materials for future spintronic devices at room temperature.

Topological Field Theory of Time-Reversal Invariant Insulators

Energy Technology Data Exchange (ETDEWEB)

Qi, Xiao-Liang; Hughes, Taylor; Zhang, Shou-Cheng; /Stanford U., Phys. Dept.

2010-03-19

We show that the fundamental time reversal invariant (TRI) insulator exists in 4 + 1 dimensions, where the effective field theory is described by the 4 + 1 dimensional Chern-Simons theory and the topological properties of the electronic structure is classified by the second Chern number. These topological properties are the natural generalizations of the time reversal breaking (TRB) quantum Hall insulator in 2 + 1 dimensions. The TRI quantum spin Hall insulator in 2 + 1 dimensions and the topological insulator in 3 + 1 dimension can be obtained as descendants from the fundamental TRI insulator in 4 + 1 dimensions through a dimensional reduction procedure. The effective topological field theory, and the Z{sub 2} topological classification for the TRI insulators in 2+1 and 3+1 dimensions are naturally obtained from this procedure. All physically measurable topological response functions of the TRI insulators are completely described by the effective topological field theory. Our effective topological field theory predicts a number of novel and measurable phenomena, the most striking of which is the topological magneto-electric effect, where an electric field generates a magnetic field in the same direction, with an universal constant of proportionality quantized in odd multiples of the fine structure constant {alpha} = e{sup 2}/hc. Finally, we present a general classification of all topological insulators in various dimensions, and describe them in terms of a unified topological Chern-Simons field theory in phase space.

ALGEBRAIC TOPOLOGY

Indian Academy of Sciences (India)

tion - 6. How Architectural Features Affect. Building During Earthquakes? C VRMurty. 48 Turbulence and Dispersion. K 5 Gandhi. BOOK REVIEWS. 86 Algebraic Topology. Siddhartha Gadgil. Front Cover. - .. ..-.......... -. Back Cover. Two-dimensional vertical section through a turbulent plume. (Courtesy: G S Shat, CAOS, IISc.).

Two-dimensional silicon and carbon monochalcogenides with the structure of phosphorene.

Science.gov (United States)

Rocca, Dario; Abboud, Ali; Vaitheeswaran, Ganapathy; Lebègue, Sébastien

2017-01-01

Phosphorene has recently attracted significant interest for applications in electronics and optoelectronics. Inspired by this material an ab initio study was carried out on new two-dimensional binary materials with a structure analogous to phosphorene. Specifically, carbon and silicon monochalcogenides have been considered. After structural optimization, a series of binary compounds were found to be dynamically stable in a phosphorene-like geometry: CS, CSe, CTe, SiO, SiS, SiSe, and SiTe. The electronic properties of these monolayers were determined using density functional theory. By using accurate hybrid functionals it was found that these materials are semiconductors and span a broad range of bandgap values and types. Similarly to phosphorene, the computed effective masses point to a strong in-plane anisotropy of carrier mobilities. The variety of electronic properties carried by these compounds have the potential to broaden the technological applicability of two-dimensional materials.

Two-dimensional silicon and carbon monochalcogenides with the structure of phosphorene

Directory of Open Access Journals (Sweden)

Dario Rocca

2017-06-01

Full Text Available Phosphorene has recently attracted significant interest for applications in electronics and optoelectronics. Inspired by this material an ab initio study was carried out on new two-dimensional binary materials with a structure analogous to phosphorene. Specifically, carbon and silicon monochalcogenides have been considered. After structural optimization, a series of binary compounds were found to be dynamically stable in a phosphorene-like geometry: CS, CSe, CTe, SiO, SiS, SiSe, and SiTe. The electronic properties of these monolayers were determined using density functional theory. By using accurate hybrid functionals it was found that these materials are semiconductors and span a broad range of bandgap values and types. Similarly to phosphorene, the computed effective masses point to a strong in-plane anisotropy of carrier mobilities. The variety of electronic properties carried by these compounds have the potential to broaden the technological applicability of two-dimensional materials.

The topology of large-scale structure. VI - Slices of the universe

Science.gov (United States)

Park, Changbom; Gott, J. R., III; Melott, Adrian L.; Karachentsev, I. D.

1992-03-01

Results of an investigation of the topology of large-scale structure in two observed slices of the universe are presented. Both slices pass through the Coma cluster and their depths are 100 and 230/h Mpc. The present topology study shows that the largest void in the CfA slice is divided into two smaller voids by a statistically significant line of galaxies. The topology of toy models like the white noise and bubble models is shown to be inconsistent with that of the observed slices. A large N-body simulation was made of the biased cloud dark matter model and the slices are simulated by matching them in selection functions and boundary conditions. The genus curves for these simulated slices are spongelike and have a small shift in the direction of a meatball topology like those of observed slices.

The topology of large-scale structure. VI - Slices of the universe

Science.gov (United States)

Park, Changbom; Gott, J. R., III; Melott, Adrian L.; Karachentsev, I. D.

1992-01-01

Results of an investigation of the topology of large-scale structure in two observed slices of the universe are presented. Both slices pass through the Coma cluster and their depths are 100 and 230/h Mpc. The present topology study shows that the largest void in the CfA slice is divided into two smaller voids by a statistically significant line of galaxies. The topology of toy models like the white noise and bubble models is shown to be inconsistent with that of the observed slices. A large N-body simulation was made of the biased cloud dark matter model and the slices are simulated by matching them in selection functions and boundary conditions. The genus curves for these simulated slices are spongelike and have a small shift in the direction of a meatball topology like those of observed slices.

Functionalization of group-14 two-dimensional materials

Science.gov (United States)

Krawiec, Mariusz

2018-06-01

The great success of graphene has boosted intensive search for other single-layer thick materials, mainly composed of group-14 atoms arranged in a honeycomb lattice. This new class of two-dimensional (2D) crystals, known as 2D-Xenes, has become an emerging field of intensive research due to their remarkable electronic properties and the promise for a future generation of nanoelectronics. In contrast to graphene, Xenes are not completely planar, and feature a low buckled geometry with two sublattices displaced vertically as a result of the interplay between sp2 and sp3 orbital hybridization. In spite of the buckling, the outstanding electronic properties of graphene governed by Dirac physics are preserved in Xenes too. The buckled structure also has several advantages over graphene. Together with the spin–orbit (SO) interaction it may lead to the emergence of various experimentally accessible topological phases, like the quantum spin Hall effect. This in turn would lead to designing and building new electronic and spintronic devices, like topological field effect transistors. In this regard an important issue concerns the electron energy gap, which for Xenes naturally exists owing to the buckling and SO interaction. The electronic properties, including the magnitude of the energy gap, can further be tuned and controlled by external means. Xenes can easily be functionalized by substrate, chemical adsorption, defects, charge doping, external electric field, periodic potential, in-plane uniaxial and biaxial stress, and out-of-plane long-range structural deformation, to name a few. This topical review explores structural, electronic and magnetic properties of Xenes and addresses the question of their functionalization in various ways, including external factors acting simultaneously. It also points to future directions to be explored in functionalization of Xenes. The results of experimental and theoretical studies obtained so far have many promising features making

One-and two-dimensional topological charge distributions in stochastic optical fields

CSIR Research Space (South Africa)

Roux, FS

2011-06-01

Full Text Available The presentation on topological charge distributions in stochastic optical fields concludes that by using a combination of speckle fields one can produce inhomogeneous vortex distributions that allow both analytical calculations and numerical...

Aharonov–Bohm interference in topological insulator nanoribbons

KAUST Repository

Peng, Hailin; Lai, Keji; Kong, Desheng; Meister, Stefan; Chen, Yulin; Qi, Xiao-Liang; Zhang, Shou-Cheng; Shen, Zhi-Xun; Cui, Yi

2009-01-01

Topological insulators represent unusual phases of quantum matter with an insulating bulk gap and gapless edges or surface states. The two-dimensional topological insulator phase was predicted in HgTe quantum wells and confirmed by transport

Search for Majorana fermions in topological superconductors.

Energy Technology Data Exchange (ETDEWEB)

Pan, Wei [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Shi, Xiaoyan [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Hawkins, Samuel D. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Klem, John Frederick [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2014-10-01

The goal of this project is to search for Majorana fermions (a new quantum particle) in a topological superconductor (a new quantum matter achieved in a topological insulator proximitized by an s-wave superconductor). Majorana fermions (MFs) are electron-like particles that are their own anti-particles. MFs are shown to obey non-Abelian statistics and, thus, can be harnessed to make a fault-resistant topological quantum computer. With the arrival of topological insulators, novel schemes to create MFs have been proposed in hybrid systems by combining a topological insulator with a conventional superconductor. In this LDRD project, we will follow the theoretical proposals to search for MFs in one-dimensional (1D) topological superconductors. 1D topological superconductor will be created inside of a quantum point contact (with the metal pinch-off gates made of conventional s-wave superconductors such as niobium) in a two-dimensional topological insulator (such as inverted type-II InAs/GaSb heterostructure).

Topological Structures on DMC Spaces †

Directory of Open Access Journals (Sweden)

Rajai Nasser

2018-05-01

Full Text Available Two channels are said to be equivalent if they are degraded from each other. The space of equivalent channels with input alphabet X and output alphabet Y can be naturally endowed with the quotient of the Euclidean topology by the equivalence relation. A topology on the space of equivalent channels with fixed input alphabet X and arbitrary but finite output alphabet is said to be natural if and only if it induces the quotient topology on the subspaces of equivalent channels sharing the same output alphabet. We show that every natural topology is σ -compact, separable and path-connected. The finest natural topology, which we call the strong topology, is shown to be compactly generated, sequential and T 4 . On the other hand, the strong topology is not first-countable anywhere, hence it is not metrizable. We introduce a metric distance on the space of equivalent channels which compares the noise levels between channels. The induced metric topology, which we call the noisiness topology, is shown to be natural. We also study topologies that are inherited from the space of meta-probability measures by identifying channels with their Blackwell measures.

Charges and Electromagnetic Radiation as Topological Excitations

Directory of Open Access Journals (Sweden)

Manfried Faber

2017-01-01

Full Text Available We discuss a model with stable topological solitons in Minkowski space with only three degrees of freedom, the rotational angles of a spatial Dreibein. This model has four types of solitons differing in two topological quantum numbers which we identify with electric charge and spin. The vacuum has a two-dimensional degeneracy leading to two types of massless excitations, characterised by a topological quantum number which could have a physical equivalent in the photon number.

Rendering the Topological Spines

Energy Technology Data Exchange (ETDEWEB)

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.

Wigner functions from the two-dimensional wavelet group.

Science.gov (United States)

Ali, S T; Krasowska, A E; Murenzi, R

2000-12-01

Following a general procedure developed previously [Ann. Henri Poincaré 1, 685 (2000)], here we construct Wigner functions on a phase space related to the similitude group in two dimensions. Since the group space in this case is topologically homeomorphic to the phase space in question, the Wigner functions so constructed may also be considered as being functions on the group space itself. Previously the similitude group was used to construct wavelets for two-dimensional image analysis; we discuss here the connection between the wavelet transform and the Wigner function.

(3+1)-dimensional topological phases and self-dual quantum geometries encoded on Heegaard surfaces

Energy Technology Data Exchange (ETDEWEB)

Dittrich, Bianca [Perimeter Institute for Theoretical Physics,31 Caroline Street North, Waterloo, Ontario N2L 2Y5 (Canada)

2017-05-22

We apply the recently suggested strategy to lift state spaces and operators for (2+1)-dimensional topological quantum field theories to state spaces and operators for a (3+1)-dimensional TQFT with defects. We start from the (2+1)-dimensional Turaev-Viro theory and obtain a state space, consistent with the state space expected from the Crane-Yetter model with line defects. This work has important applications for quantum gravity as well as the theory of topological phases in (3+1) dimensions. It provides a self-dual quantum geometry realization based on a vacuum state peaked on a homogeneously curved geometry. The state spaces and operators we construct here provide also an improved version of the Walker-Wang model, and simplify its analysis considerably. We in particular show that the fusion bases of the (2+1)-dimensional theory lead to a rich set of bases for the (3+1)-dimensional theory. This includes a quantum deformed spin network basis, which in a loop quantum gravity context diagonalizes spatial geometry operators. We also obtain a dual curvature basis, that diagonalizes the Walker-Wang Hamiltonian. Furthermore, the construction presented here can be generalized to provide state spaces for the recently introduced dichromatic four-dimensional manifold invariants.

Design and fabrication of topologically optimized structures;

DEFF Research Database (Denmark)

Feringa, Jelle; Søndergaard, Asbjørn

2012-01-01

Integral structural optimization and fabrication seeks the synthesis of two original approaches; that of topological optimization (TO) and robotic hotwire cutting (HWC) (Mcgee 2011). TO allows for the reduction of up to 70% of the volume of concrete to support a given structure (Sondergaard...... & Dombernowsky 2011). A strength of the method is that it allows to come up with structural designs that lie beyond the grasp of traditional means of design. A design space is a discretized volume, delimiting where the optimization will take place. The number of cells used to discretize the design space thus...

Topological excitations in semiconductor heterostructures

International Nuclear Information System (INIS)

Koushik, R.; Mukerjee, Subroto; Ghosh, Arindam; Baenninger, Matthias; Narayan, Vijay; Pepper, Michael; Farrer, Ian; Ritchie, David A.

2013-01-01

Topological defects play an important role in the melting phenomena in two-dimensions. In this work, we report experimental observation of topological defect induced melting in two-dimensional electron systems (2DES) in the presence of strong Coulomb interaction and disorder. The phenomenon is characterised by measurement of conductivity which goes to zero in a Berezinskii-Kosterlitz-Thouless like transition. Further evidence is provided via low-frequency conductivity noise measurements

Grassmannian topological Kazama-Suzuki models and cohomology

International Nuclear Information System (INIS)

Blau, M.; Hussain, F.; Thompson, G.

1995-10-01

We investigate in detail the topological gauged Wess-Zumino-Witten models describing topological Kazama-Suzuki models based on complex Grassmannians. We show that there is a topological sector in which the ring of observables (constructed from the Grassmann odd scalars of the theory) coincides with the classical cohomology ring of the Grassmanian for all values of the level k. We also analyze the general ring structure of bosonic correlation functions, uncovering a whole hierarchy of level-rank relations (including the standard level-rank duality) among models based on different Grassmannians. Using the previously established localization of the topological Kazama-Suzuki model to an Abelian topological field theory, we reduce the correlators to finite-dimensional purely algebraic expressions. As an application, these are evaluated explicitly for the CP(2) model at level k and shown for all k to coincide with the cohomological intersection numbers of the two-plane Grassmannian G(2,K + 2), thus realizing the level-rank duality between this model and the G(2, k + 2) model at level one. (author). 28 refs

Superfluid transition of homogeneous and trapped two-dimensional Bose gases.

Science.gov (United States)

Holzmann, Markus; Baym, Gordon; Blaizot, Jean-Paul; Laloë, Franck

2007-01-30

Current experiments on atomic gases in highly anisotropic traps present the opportunity to study in detail the low temperature phases of two-dimensional inhomogeneous systems. Although, in an ideal gas, the trapping potential favors Bose-Einstein condensation at finite temperature, interactions tend to destabilize the condensate, leading to a superfluid Kosterlitz-Thouless-Berezinskii phase with a finite superfluid mass density but no long-range order, as in homogeneous fluids. The transition in homogeneous systems is conveniently described in terms of dissociation of topological defects (vortex-antivortex pairs). However, trapped two-dimensional gases are more directly approached by generalizing the microscopic theory of the homogeneous gas. In this paper, we first derive, via a diagrammatic expansion, the scaling structure near the phase transition in a homogeneous system, and then study the effects of a trapping potential in the local density approximation. We find that a weakly interacting trapped gas undergoes a Kosterlitz-Thouless-Berezinskii transition from the normal state at a temperature slightly below the Bose-Einstein transition temperature of the ideal gas. The characteristic finite superfluid mass density of a homogeneous system just below the transition becomes strongly suppressed in a trapped gas.

Topology Optimization of Thermal Heat Sinks

DEFF Research Database (Denmark)

Klaas Haertel, Jan Hendrik; Engelbrecht, Kurt; Lazarov, Boyan Stefanov

2015-01-01

In this paper, topology optimization is applied to optimize the cooling performance of thermal heat sinks. The coupled two-dimensional thermofluid model of a heat sink cooled with forced convection and a density-based topology optimization including density filtering and projection are implemented...... in COMSOL Multiphysics. The optimization objective is to minimize the heat sink’s temperature for a prescribed pressure drop and fixed heat generation. To conduct the optimization, COMSOL’s Optimization Module with GCMMA as the optimization method is used. The implementation of this topology optimization...... approach in COMSOL Multiphysics is described in this paper and results for optimized two-dimensional heat sinks are presented. Furthermore, parameter studies regarding the effect of the prescribed pressure drop of the system on Reynolds number and realized heat sink temperature are presented and discussed....

Topological higher gauge theory: From BF to BFCG theory

International Nuclear Information System (INIS)

Girelli, F.; Pfeiffer, H.; Popescu, E. M.

2008-01-01

We study generalizations of three- and four-dimensional BF theories in the context of higher gauge theory. First, we construct topological higher gauge theories as discrete state sum models and explain how they are related to the state sums of Yetter, Mackaay, and Porter. Under certain conditions, we can present their corresponding continuum counterparts in terms of classical Lagrangians. We then explain that two of these models are already familiar from the literature: the ΣΦEA model of three-dimensional gravity coupled to topological matter and also a four-dimensional model of BF theory coupled to topological matter

Crystal structure of a mixed-ligand terbium(III coordination polymer containing oxalate and formate ligands, having a three-dimensional fcu topology

Directory of Open Access Journals (Sweden)

Chainok Kittipong

2016-01-01

Full Text Available The title compound, poly[(μ3-formato(μ4-oxalatoterbium(III], [Tb(CHO2(C2O4]n, is a three-dimensional coordination polymer, and is isotypic with the LaIII, CeIII and SmIII analogues. The asymmetric unit contains one TbIII ion, one formate anion (CHO2− and half of an oxalate anion (C2O42−, the latter being completed by application of inversion symmetry. The TbIII ion is nine-coordinated in a distorted tricapped trigonal–prismatic manner by two chelating carboxylate groups from two C2O42− ligands, two carboxylate oxygen atoms from another two C2O42− ligands and three oxygen atoms from three CHO2− ligands, with the Tb—O bond lengths and the O—Tb—O bond angles ranging from 2.4165 (19 to 2.478 (3 Å and 64.53 (6 to 144.49 (4°, respectively. The CHO2− and C2O42− anions adopt μ3-bridging and μ4-chelating-bridging coordination modes, respectively, linking adjacent TbIII ions into a three-dimensional 12-connected fcu topology with point symbol (324.436.56. The title compound exhibits thermal stability up to 623 K, and also displays strong green photoluminescence in the solid state at room temperature.

Investigating the topological structure of quenched lattice QCD with overlap fermions using a multi-probing approximation

Science.gov (United States)

Zou, You-Hao; Zhang, Jian-Bo; Xiong, Guang-Yi; Chen, Ying; Liu, Chuan; Liu, Yu-Bin; Ma, Jian-Ping

2017-10-01

The topological charge density and topological susceptibility are determined by a multi-probing approximation using overlap fermions in quenched SU(3) gauge theory. Then we investigate the topological structure of the quenched QCD vacuum, and compare it with results from the all-scale topological density. The results are consistent. Random permuted topological charge density is used to check whether these structures represent underlying ordered properties. The pseudoscalar glueball mass is extracted from the two-point correlation function of the topological charge density. We study 3 ensembles of different lattice spacing a with the same lattice volume 163×32. The results are compatible with the results of all-scale topological charge density, and the topological structures revealed by multi-probing are much closer to all-scale topological charge density than those from eigenmode expansion. Supported by National Natural Science Foundation of China (NSFC) (11335001, 11275169, 11075167), It is also supported in part by the DFG and the NSFC (11261130311) through funds provided to the Sino-German CRC 110 "Symmetries and the Emergence of Structure in QCD". This work was also funded in part by National Basic Research Program of China (973 Program) (2015CB856700)

Topological acoustic polaritons: robust sound manipulation at the subwavelength scale

International Nuclear Information System (INIS)

Yves, Simon; Fleury, Romain; Lemoult, Fabrice; Fink, Mathias; Lerosey, Geoffroy

2017-01-01

Topological insulators, a hallmark of condensed matter physics, have recently reached the classical realm of acoustic waves. A remarkable property of time-reversal invariant topological insulators is the presence of unidirectional spin-polarized propagation along their edges, a property that could lead to a wealth of new opportunities in the ability to guide and manipulate sound. Here, we demonstrate and study the possibility to induce topologically non-trivial acoustic states at the deep subwavelength scale, in a structured two-dimensional metamaterial composed of Helmholtz resonators. Radically different from previous designs based on non-resonant sonic crystals, our proposal enables robust sound manipulation on a surface along predefined, subwavelength pathways of arbitrary shapes. (paper)

Topological acoustic polaritons: robust sound manipulation at the subwavelength scale

Science.gov (United States)

Yves, Simon; Fleury, Romain; Lemoult, Fabrice; Fink, Mathias; Lerosey, Geoffroy

2017-07-01

Topological insulators, a hallmark of condensed matter physics, have recently reached the classical realm of acoustic waves. A remarkable property of time-reversal invariant topological insulators is the presence of unidirectional spin-polarized propagation along their edges, a property that could lead to a wealth of new opportunities in the ability to guide and manipulate sound. Here, we demonstrate and study the possibility to induce topologically non-trivial acoustic states at the deep subwavelength scale, in a structured two-dimensional metamaterial composed of Helmholtz resonators. Radically different from previous designs based on non-resonant sonic crystals, our proposal enables robust sound manipulation on a surface along predefined, subwavelength pathways of arbitrary shapes.

Topological anisotropy of stone-wales waves in graphenic fragments.

Science.gov (United States)

Ori, Ottorino; Cataldo, Franco; Putz, Mihai V

2011-01-01

Stone-Wales operators interchange four adjacent hexagons with two pentagon-heptagon 5|7 pairs that, graphically, may be iteratively propagated in the graphene layer, originating a new interesting structural defect called here Stone-Wales wave. By minimization, the Wiener index topological invariant evidences a marked anisotropy of the Stone-Wales defects that, topologically, are in fact preferably generated and propagated along the diagonal of the graphenic fragments, including carbon nanotubes and graphene nanoribbons. This peculiar edge-effect is shown in this paper having a predominant topological origin, leaving to future experimental investigations the task of verifying the occurrence in nature of wave-like defects similar to the ones proposed here. Graph-theoretical tools used in this paper for the generation and the propagation of the Stone-Wales defects waves are applicable to investigate isomeric modifications of chemical structures with various dimensionality like fullerenes, nanotubes, graphenic layers, schwarzites, zeolites.

Majorana fermion exchange in strictly one dimensional structures

OpenAIRE

Chiu, Ching-Kai; Vazifeh, M. M.; Franz, M.

2014-01-01

It is generally thought that adiabatic exchange of two identical particles is impossible in one spatial dimension. Here we describe a simple protocol that permits adiabatic exchange of two Majorana fermions in a one-dimensional topological superconductor wire. The exchange relies on the concept of "Majorana shuttle" whereby a $\\pi$ domain wall in the superconducting order parameter which hosts a pair of ancillary Majoranas delivers one zero mode across the wire while the other one tunnels in ...

Effects of behavioral patterns and network topology structures on Parrondo’s paradox

Science.gov (United States)

Ye, Ye; Cheong, Kang Hao; Cen, Yu-Wan; Xie, Neng-Gang

2016-11-01

A multi-agent Parrondo’s model based on complex networks is used in the current study. For Parrondo’s game A, the individual interaction can be categorized into five types of behavioral patterns: the Matthew effect, harmony, cooperation, poor-competition-rich-cooperation and a random mode. The parameter space of Parrondo’s paradox pertaining to each behavioral pattern, and the gradual change of the parameter space from a two-dimensional lattice to a random network and from a random network to a scale-free network was analyzed. The simulation results suggest that the size of the region of the parameter space that elicits Parrondo’s paradox is positively correlated with the heterogeneity of the degree distribution of the network. For two distinct sets of probability parameters, the microcosmic reasons underlying the occurrence of the paradox under the scale-free network are elaborated. Common interaction mechanisms of the asymmetric structure of game B, behavioral patterns and network topology are also revealed.

Liquid structure and freezing of the two-dimensional classical electron fluid

International Nuclear Information System (INIS)

Ballone, P.; Pastore, G.; Rovere, M.; Tosi, M.P.

1984-11-01

Accurate theoretical results are reported for the pair correlation function of the classical two-dimensional electron liquid with r -1 interactions at strong coupling. The approach involves an evaluation of the bridge diagram corrections to the hypernetted-chain approximation, the role of low dimensionality being evident, relative to the case of the three-dimensional classical plasma, in an enhanced sensitivity to long range correlations. The liquid structure results are utilized in a density-wave theory of first-order freezing into the triangular lattice, the calculated coupling strength at freezing being in reasonable agreement with computer simulation results and with data on electron films on a liquid-He surface. The stability of the triangular electron lattice against deformation into a body-centered rectangular lattice is also discussed. (author)

Models and Methods for Structural Topology Optimization with Discrete Design Variables

DEFF Research Database (Denmark)

Stolpe, Mathias

in the conceptual design phase to find innovative designs. The strength of topology optimization is the capability of determining both the optimal shape and the topology of the structure. In some cases also the optimal material properties can be determined. Optimal structural design problems are modeled...... such as bridges, airplanes, wind turbines, cars, etc. Topology optimization is a collection of theory, mathematical models, and numerical methods and is often used in the conceptual design phase to find innovative designs. The strength of topology optimization is the capability of determining both the optimal......Structural topology optimization is a multi-disciplinary research field covering optimal design of load carrying mechanical structures such as bridges, airplanes, wind turbines, cars, etc. Topology optimization is a collection of theory, mathematical models, and numerical methods and is often used...

Topological orders in rigid states

International Nuclear Information System (INIS)

Wen, X.G.

1990-01-01

The authors study a new kind of ordering topological order in rigid states (the states with no local gapless excitations). This paper concentrates on characterization of the different topological orders. As an example the authors discuss in detail chiral spin states of 2+1 dimensional spin systems. Chiral spin states are described by the topological Chern-Simons theories in the continuum limit. The authors show that the topological orders can be characterized by a non-Abelian gauge structure over the moduli space which parametrizes a family of the model Hamiltonians supporting topologically ordered ground states. In 2 + 1 dimensions, the non-Abelian gauge structure determines possible fractional statistics of the quasi-particle excitations over the topologically ordered ground states. The dynamics of the low lying global excitations is shown to be independent of random spatial dependent perturbations. The ground state degeneracy and the non-Abelian gauge structures discussed in this paper are very robust, even against those perturbations that break translation symmetry. The authors also discuss the symmetry properties of the degenerate ground states of chiral spin states. The authors find that some degenerate ground states of chiral spin states on torus carry non-trivial quantum numbers of the 90 degrees rotation

Interpenetrated Uranyl-Organic Frameworks with bor and pts Topology: Structure, Spectroscopy, and Computation.

Science.gov (United States)

Liu, Chao; Chen, Fang-Yuan; Tian, Hong-Rui; Ai, Jing; Yang, Weiting; Pan, Qing-Jiang; Sun, Zhong-Ming

2017-11-20

Two novel three-dimensional interpenetrated uranyl-organic frameworks, (NH 4 ) 4 [(UO 2 ) 4 (L 1 ) 3 ]·6H 2 O (1) and [(UO 2 ) 2 (H 2 O) 2 L 2 ]·2H 2 O (2), where L 1 = tetrakis(3-carboxyphenyl)silicon and L 2 = tetrakis(4-carboxyphenyl)silicon, were synthesized by a combination of two isomeric tetrahedral silicon-centered ligands with 3-connected triangular [(UO 2 )(COO) 3 ] - and 4-connected dinuclear [(UO 2 ) 2 (COO) 4 ] units, respectively. Structural analyses indicate that 1 possesses a 2-fold interpenetrating anion bor network, while 2 exhibits a 3-fold interpenetrated 4,4-connected neutral network with pts topology. Both compounds were characterized by thermogravimetric analysis and IR, UV-vis, and photoluminescence spectroscopy. A relativistic density functional theory (DFT) investigation on 10 model compounds of 1 and 2 shows good agreement of the structural parameters, stretching vibrational frequencies, and absorption with experimental results; the time-dependent DFT calculations unravel that low-energy absorption bands originate from ligand-to-uranium charge transfer.

Structure-topology-property correlations of sodium phosphosilicate glasses.

Science.gov (United States)

Hermansen, Christian; Guo, Xiaoju; Youngman, Randall E; Mauro, John C; Smedskjaer, Morten M; Yue, Yuanzheng

2015-08-14

In this work, we investigate the correlations among structure, topology, and properties in a series of sodium phosphosilicate glasses with [SiO2]/[SiO2 + P2O5] ranging from 0 to 1. The network structure is characterized by (29)Si and (31)P magic-angle spinning nuclear magnetic resonance and Raman spectroscopy. The results show the formation of six-fold coordinated silicon species in phosphorous-rich glasses. Based on the structural data, we propose a formation mechanism of the six-fold coordinated silicon, which is used to develop a quantitative structural model for predicting the speciation of the network forming units as a function of chemical composition. The structural model is then used to establish a temperature-dependent constraint description of phosphosilicate glass topology that enables prediction of glass transition temperature, liquid fragility, and indentation hardness. The topological constraint model provides insight into structural origin of the mixed network former effect in phosphosilicate glasses.

Topology determines force distributions in one-dimensional random spring networks

Science.gov (United States)

Heidemann, Knut M.; Sageman-Furnas, Andrew O.; Sharma, Abhinav; Rehfeldt, Florian; Schmidt, Christoph F.; Wardetzky, Max

2018-02-01

Networks of elastic fibers are ubiquitous in biological systems and often provide mechanical stability to cells and tissues. Fiber-reinforced materials are also common in technology. An important characteristic of such materials is their resistance to failure under load. Rupture occurs when fibers break under excessive force and when that failure propagates. Therefore, it is crucial to understand force distributions. Force distributions within such networks are typically highly inhomogeneous and are not well understood. Here we construct a simple one-dimensional model system with periodic boundary conditions by randomly placing linear springs on a circle. We consider ensembles of such networks that consist of N nodes and have an average degree of connectivity z but vary in topology. Using a graph-theoretical approach that accounts for the full topology of each network in the ensemble, we show that, surprisingly, the force distributions can be fully characterized in terms of the parameters (N ,z ) . Despite the universal properties of such (N ,z ) ensembles, our analysis further reveals that a classical mean-field approach fails to capture force distributions correctly. We demonstrate that network topology is a crucial determinant of force distributions in elastic spring networks.

Topological Classification of Crystalline Insulators through Band Structure Combinatorics

Science.gov (United States)

Kruthoff, Jorrit; de Boer, Jan; van Wezel, Jasper; Kane, Charles L.; Slager, Robert-Jan

2017-10-01

We present a method for efficiently enumerating all allowed, topologically distinct, electronic band structures within a given crystal structure in all physically relevant dimensions. The algorithm applies to crystals without time-reversal, particle-hole, chiral, or any other anticommuting or anti-unitary symmetries. The results presented match the mathematical structure underlying the topological classification of these crystals in terms of K -theory and therefore elucidate this abstract mathematical framework from a simple combinatorial perspective. Using a straightforward counting procedure, we classify all allowed topological phases of spinless particles in crystals in class A . Employing this classification, we study transitions between topological phases within class A that are driven by band inversions at high-symmetry points in the first Brillouin zone. This enables us to list all possible types of phase transitions within a given crystal structure and to identify whether or not they give rise to intermediate Weyl semimetallic phases.

Topological and sizing optimization of reinforced ribs for a machining centre

Science.gov (United States)

Chen, T. Y.; Wang, C. B.

2008-01-01

The topology optimization technique is applied to improve rib designs of a machining centre. The ribs of the original design are eliminated and new ribs are generated by topology optimization in the same 3D design space containing the original ribs. Two-dimensional plate elements are used to replace the optimum rib topologies formed by 3D rectangular elements. After topology optimization, sizing optimization is used to determine the optimum thicknesses of the ribs. When forming the optimum design problem, multiple configurations of the structure are considered simultaneously. The objective is to minimize rib weight. Static constraints confine displacements of the cutting tool and the workpiece due to cutting forces and the heat generated by spindle bearings. The dynamic constraint requires the fundamental natural frequency of the structure to be greater than a given value in order to reduce dynamic deflection. Compared with the original design, the improvement resulting from this approach is significant.

Converting topological insulators into topological metals within the tetradymite family

Science.gov (United States)

Chen, K.-W.; Aryal, N.; Dai, J.; Graf, D.; Zhang, S.; Das, S.; Le Fèvre, P.; Bertran, F.; Yukawa, R.; Horiba, K.; Kumigashira, H.; Frantzeskakis, E.; Fortuna, F.; Balicas, L.; Santander-Syro, A. F.; Manousakis, E.; Baumbach, R. E.

2018-04-01

We report the electronic band structures and concomitant Fermi surfaces for a family of exfoliable tetradymite compounds with the formula T2C h2P n , obtained as a modification to the well-known topological insulator binaries Bi2(Se,Te ) 3 by replacing one chalcogen (C h ) with a pnictogen (P n ) and Bi with the tetravalent transition metals T = Ti, Zr, or Hf. This imbalances the electron count and results in layered metals characterized by relatively high carrier mobilities and bulk two-dimensional Fermi surfaces whose topography is well-described by first-principles calculations. Intriguingly, slab electronic structure calculations predict Dirac-like surface states. In contrast to Bi2Se3 , where the surface Dirac bands are at the Γ point, for (Zr,Hf ) 2Te2 (P,As) there are Dirac cones of strong topological character around both the Γ ¯ and M ¯ points, which are above and below the Fermi energy, respectively. For Ti2Te2P , the surface state is predicted to exist only around the M ¯ point. In agreement with these predictions, the surface states that are located below the Fermi energy are observed by angle-resolved photoemission spectroscopy measurements, revealing that they coexist with the bulk metallic state. Thus this family of materials provides a foundation upon which to develop novel phenomena that exploit both the bulk and surface states (e.g., topological superconductivity).

Terahertz imaging of Landau levels in HgTe-based topological insulators

Energy Technology Data Exchange (ETDEWEB)

Kadykov, Aleksandr M.; Krishtopenko, Sergey S. [Laboratoire Charles Coulomb (L2C), UMR 5221 CNRS–Université de Montpellier, Montpellier (France); Institute for Physics of Microstructures, Russian Academy of Sciences, GSP-105, 603950 Nizhny Novgorod (Russian Federation); Torres, Jeremie [Institut d' Electronique et des Systèmes (IES), UMR 5214 CNRS–Université de Montpellier, Montpellier (France); Consejo, Christophe; Ruffenach, Sandra; Marcinkiewicz, Michal; But, Dmytro; Teppe, Frederic, E-mail: frederic.teppe@umontpellier.fr [Laboratoire Charles Coulomb (L2C), UMR 5221 CNRS–Université de Montpellier, Montpellier (France); Knap, Wojciech [Laboratoire Charles Coulomb (L2C), UMR 5221 CNRS–Université de Montpellier, Montpellier (France); Institute of High Pressure Institute Physics, Polish Academy of Sciences, 01-447 Warsaw (Poland); Morozov, Sergey V.; Gavrilenko, Vladimir I. [Institute for Physics of Microstructures, Russian Academy of Sciences, GSP-105, 603950 Nizhny Novgorod (Russian Federation); Lobachevsky State University of Nizhny Novgorod, 603950 Nizhny Novgorod (Russian Federation); Mikhailov, Nikolai N. [Institute of Semiconductor Physics, Siberian Branch, Russian Academy of Sciences, pr. Akademika Lavrent' eva 13, 630090 Novosibirsk (Russian Federation); Novosibirsk State University, 630090 Novosibirsk (Russian Federation); Dvoretsky, Sergey A. [Institute of Semiconductor Physics, Siberian Branch, Russian Academy of Sciences, pr. Akademika Lavrent' eva 13, 630090 Novosibirsk (Russian Federation)

2016-06-27

We report on sub-terahertz photoconductivity under the magnetic field of a two dimensional topological insulator based on HgTe quantum wells. We perform a detailed visualization of Landau levels by means of photoconductivity measured at different gate voltages. This technique allows one to determine a critical magnetic field, corresponding to topological phase transition from inverted to normal band structure, even in almost gapless samples. The comparison with realistic calculations of Landau levels reveals a smaller role of bulk inversion asymmetry in HgTe quantum wells than it was assumed previously.

Manipulating topological-insulator properties using quantum confinement

International Nuclear Information System (INIS)

Kotulla, M; Zülicke, U

2017-01-01

Recent discoveries have spurred the theoretical prediction and experimental realization of novel materials that have topological properties arising from band inversion. Such topological insulators are insulating in the bulk but have conductive surface or edge states. Topological materials show various unusual physical properties and are surmised to enable the creation of exotic Majorana-fermion quasiparticles. How the signatures of topological behavior evolve when the system size is reduced is interesting from both a fundamental and an application-oriented point of view, as such understanding may form the basis for tailoring systems to be in specific topological phases. This work considers the specific case of quantum-well confinement defining two-dimensional layers. Based on the effective-Hamiltonian description of bulk topological insulators, and using a harmonic-oscillator potential as an example for a softer-than-hard-wall confinement, we have studied the interplay of band inversion and size quantization. Our model system provides a useful platform for systematic study of the transition between the normal and topological phases, including the development of band inversion and the formation of massless-Dirac-fermion surface states. The effects of bare size quantization, two-dimensional-subband mixing, and electron–hole asymmetry are disentangled and their respective physical consequences elucidated. (paper)

Mathematical modeling of human glioma growth based on brain topological structures: study of two clinical cases.

Directory of Open Access Journals (Sweden)

Cecilia Suarez

Full Text Available Gliomas are the most common primary brain tumors and yet almost incurable due mainly to their great invasion capability. This represents a challenge to present clinical oncology. Here, we introduce a mathematical model aiming to improve tumor spreading capability definition. The model consists in a time dependent reaction-diffusion equation in a three-dimensional spatial domain that distinguishes between different brain topological structures. The model uses a series of digitized images from brain slices covering the whole human brain. The Talairach atlas included in the model describes brain structures at different levels. Also, the inclusion of the Brodmann areas allows prediction of the brain functions affected during tumor evolution and the estimation of correlated symptoms. The model is solved numerically using patient-specific parametrization and finite differences. Simulations consider an initial state with cellular proliferation alone (benign tumor, and an advanced state when infiltration starts (malign tumor. Survival time is estimated on the basis of tumor size and location. The model is used to predict tumor evolution in two clinical cases. In the first case, predictions show that real infiltrative areas are underestimated by current diagnostic imaging. In the second case, tumor spreading predictions were shown to be more accurate than those derived from previous models in the literature. Our results suggest that the inclusion of differential migration in glioma growth models constitutes another step towards a better prediction of tumor infiltration at the moment of surgical or radiosurgical target definition. Also, the addition of physiological/psychological considerations to classical anatomical models will provide a better and integral understanding of the patient disease at the moment of deciding therapeutic options, taking into account not only survival but also life quality.

Use of dimensionality reduction for structural mapping of hip joint osteoarthritis data

International Nuclear Information System (INIS)

Theoharatos, C; Fotopoulos, S; Boniatis, I; Panayiotakis, G; Panagiotopoulos, E

2009-01-01

A visualization-based, computer-oriented, classification scheme is proposed for assessing the severity of hip osteoarthritis (OA) using dimensionality reduction techniques. The introduced methodology tries to cope with the confined ability of physicians to structurally organize the entire available set of medical data into semantically similar categories and provide the capability to make visual observations among the ensemble of data using low-dimensional biplots. In this work, 18 pelvic radiographs of patients with verified unilateral hip OA are evaluated by experienced physicians and assessed into Normal, Mild and Severe following the Kellgren and Lawrence scale. Two regions of interest corresponding to radiographic hip joint spaces are determined and representative features are extracted using a typical texture analysis technique. The structural organization of all hip OA data is accomplished using distance and topology preservation-based dimensionality reduction techniques. The resulting map is a low-dimensional biplot that reflects the intrinsic organization of the ensemble of available data and which can be directly accessed by the physician. The conceivable visualization scheme can potentially reveal critical data similarities and help the operator to visually estimate their initial diagnosis. In addition, it can be used to detect putative clustering tendencies, examine the presence of data similarities and indicate the existence of possible false alarms in the initial perceptual evaluation

Universal Distribution of Centers and Saddles in Two-Dimensional Turbulence

International Nuclear Information System (INIS)

Rivera, Michael; Wu, Xiao-Lun; Yeung, Chuck

2001-01-01

The statistical properties of the local topology of two-dimensional turbulence are investigated using an electromagnetically forced soap film. The local topology of the incompressible 2D flow is characterized by the Jacobian determinant Λ(x,y)=1/4 (ω 2 -σ 2 ) , where ω(x,y) is the local vorticity and σ(x,y) is the local strain rate. For turbulent flows driven by different external force configurations, P(Λ) is found to be a universal function when rescaled using the turbulent intensity. A simple model that agrees with the measured functional form of P(Λ) is constructed using the assumption that the stream function, ψ(x,y) , is a Gaussian random field

On some fundamental properties of structural topology optimization problems

DEFF Research Database (Denmark)

Stolpe, Mathias

2010-01-01

We study some fundamental mathematical properties of discretized structural topology optimization problems. Either compliance is minimized with an upper bound on the volume of the structure, or volume is minimized with an upper bound on the compliance. The design variables are either continuous o....... The presented examples can be used as teaching material in graduate and undergraduate courses on structural topology optimization....

Effects of nuclear spins on the transport properties of the edge of two-dimensional topological insulators

Science.gov (United States)

Hsu, Chen-Hsuan; Stano, Peter; Klinovaja, Jelena; Loss, Daniel

2018-03-01

The electrons in the edge channels of two-dimensional topological insulators can be described as a helical Tomonaga-Luttinger liquid. They couple to nuclear spins embedded in the host materials through the hyperfine interaction, and are therefore subject to elastic spin-flip backscattering on the nuclear spins. We investigate the nuclear-spin-induced edge resistance due to such backscattering by performing a renormalization-group analysis. Remarkably, the effect of this backscattering mechanism is stronger in a helical edge than in nonhelical channels, which are believed to be present in the trivial regime of InAs/GaSb quantum wells. In a system with sufficiently long edges, the disordered nuclear spins lead to an edge resistance which grows exponentially upon lowering the temperature. On the other hand, electrons from the edge states mediate an anisotropic Ruderman-Kittel-Kasuya-Yosida nuclear spin-spin interaction, which induces a spiral nuclear spin order below the transition temperature. We discuss the features of the spiral order, as well as its experimental signatures. In the ordered phase, we identify two backscattering mechanisms, due to charge impurities and magnons. The backscattering on charge impurities is allowed by the internally generated magnetic field, and leads to an Anderson-type localization of the edge states. The magnon-mediated backscattering results in a power-law resistance, which is suppressed at zero temperature. Overall, we find that in a sufficiently long edge the nuclear spins, whether ordered or not, suppress the edge conductance to zero as the temperature approaches zero.

Topology optimization for submerged buoyant structures

NARCIS (Netherlands)

Picelli, R.; van Dijk, R.; Vicente, W.M.; Pavanello, R.; Langelaar, M.; van Keulen, A.

2017-01-01

This paper presents an evolutionary structural topology optimization method for the design of completely submerged buoyant modules with design-dependent fluid pressure loading. This type of structure is used to support offshore rig installation and pipeline transportation at all water depths. The

Influence of topology in a quantum ring

International Nuclear Information System (INIS)

Netto, A.L. Silva; Chesman, C.; Furtado, C.

2008-01-01

In this Letter we study the quantum rings in the presence of a topological defect. We use geometric theory of defects to describe one and two-dimensional quantum rings in the presence of a single screw dislocation. In addition we consider some potential in a two dimensional ring and calculate their energy spectrum. It is shown that the energy spectrum depend on the parabolic way on the burgers vectors of the screw dislocation. We also show that the presence of a topological defect introduces a new contribution for the Aharonov-Bohm effect in the quantum ring

Finite-size scaling of clique percolation on two-dimensional Moore lattices

Science.gov (United States)

Dong, Jia-Qi; Shen, Zhou; Zhang, Yongwen; Huang, Zi-Gang; Huang, Liang; Chen, Xiaosong

2018-05-01

Clique percolation has attracted much attention due to its significance in understanding topological overlap among communities and dynamical instability of structured systems. Rich critical behavior has been observed in clique percolation on Erdős-Rényi (ER) random graphs, but few works have discussed clique percolation on finite dimensional systems. In this paper, we have defined a series of characteristic events, i.e., the historically largest size jumps of the clusters, in the percolating process of adding bonds and developed a new finite-size scaling scheme based on the interval of the characteristic events. Through the finite-size scaling analysis, we have found, interestingly, that, in contrast to the clique percolation on an ER graph where the critical exponents are parameter dependent, the two-dimensional (2D) clique percolation simply shares the same critical exponents with traditional site or bond percolation, independent of the clique percolation parameters. This has been corroborated by bridging two special types of clique percolation to site percolation on 2D lattices. Mechanisms for the difference of the critical behaviors between clique percolation on ER graphs and on 2D lattices are also discussed.

Terahertz spectroscopy of two-dimensional subwavelength plasmonic structures

Energy Technology Data Exchange (ETDEWEB)

Azad, Abul K [Los Alamos National Laboratory; Chen, Houtong [Los Alamos National Laboratory; Taylor, Antoinette [Los Alamos National Laboratory; O' Hara, John F [Los Alamos National Laboratory; Han, Jiaguang [OSU; Lu, Xinchao [OSU; Zhang, Weili [OSU

2009-01-01

The fascinating properties of plasmonic structures have had significant impact on the development of next generation ultracompact photonic and optoelectronic components. We study two-dimensional plasmonic structures functioning at terahertz frequencies. Resonant terahertz response due to surface plasmons and dipole localized surface plasmons were investigated by the state-of-the-art terahertz time domain spectroscopy (THz-TDS) using both transmission and reflection configurations. Extraordinary terahertz transmission was demonstrated through the subwavelength metallic hole arrays made from good conducting metals as well as poor metals. Metallic arrays m!lde from Pb, generally a poor metal, and having optically thin thicknesses less than one-third of a skin depth also contributed in enhanced THz transmission. A direct transition of a surface plasmon resonance from a photonic crystal minimum was observed in a photo-doped semiconductor array. Electrical controls of the surface plasmon resonances by hybridization of the Schottkey diode between the metallic grating and the semiconductor substrate are investigated as a function of the applied reverse bias. In addition, we have demonstrated photo-induced creation and annihilation of surface plasmons with appropriate semiconductors at room temperature. According to the Fano model, the transmission properties are characterized by two essential contributions: resonant excitation of surface plasmons and nonresonant direct transmission. Such plasmonic structures may find fascinating applications in terahertz imaging, biomedical sensing, subwavelength terahertz spectroscopy, tunable filters, and integrated terahertz devices.

Edge states and integer quantum Hall effect in topological insulator thin films.

Science.gov (United States)

Zhang, Song-Bo; Lu, Hai-Zhou; Shen, Shun-Qing

2015-08-25

The integer quantum Hall effect is a topological state of quantum matter in two dimensions, and has recently been observed in three-dimensional topological insulator thin films. Here we study the Landau levels and edge states of surface Dirac fermions in topological insulators under strong magnetic field. We examine the formation of the quantum plateaux of the Hall conductance and find two different patterns, in one pattern the filling number covers all integers while only odd integers in the other. We focus on the quantum plateau closest to zero energy and demonstrate the breakdown of the quantum spin Hall effect resulting from structure inversion asymmetry. The phase diagrams of the quantum Hall states are presented as functions of magnetic field, gate voltage and chemical potential. This work establishes an intuitive picture of the edge states to understand the integer quantum Hall effect for Dirac electrons in topological insulator thin films.

Direct experimental visualization of the global Hamiltonian progression of two-dimensional Lagrangian flow topologies from integrable to chaotic state

Energy Technology Data Exchange (ETDEWEB)

Baskan, O.; Clercx, H. J. H [Fluid Dynamics Laboratory, Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven (Netherlands); Speetjens, M. F. M. [Energy Technology Laboratory, Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven (Netherlands); Metcalfe, G. [Commonwealth Scientific and Industrial Research Organisation, Melbourne, Victoria 3190 (Australia); Swinburne University of Technology, Department of Mechanical Engineering, Hawthorn VIC 3122 (Australia)

2015-10-15

Countless theoretical/numerical studies on transport and mixing in two-dimensional (2D) unsteady flows lean on the assumption that Hamiltonian mechanisms govern the Lagrangian dynamics of passive tracers. However, experimental studies specifically investigating said mechanisms are rare. Moreover, they typically concern local behavior in specific states (usually far away from the integrable state) and generally expose this indirectly by dye visualization. Laboratory experiments explicitly addressing the global Hamiltonian progression of the Lagrangian flow topology entirely from integrable to chaotic state, i.e., the fundamental route to efficient transport by chaotic advection, appear non-existent. This motivates our study on experimental visualization of this progression by direct measurement of Poincaré sections of passive tracer particles in a representative 2D time-periodic flow. This admits (i) accurate replication of the experimental initial conditions, facilitating true one-to-one comparison of simulated and measured behavior, and (ii) direct experimental investigation of the ensuing Lagrangian dynamics. The analysis reveals a close agreement between computations and observations and thus experimentally validates the full global Hamiltonian progression at a great level of detail.

Direct experimental visualization of the global Hamiltonian progression of two-dimensional Lagrangian flow topologies from integrable to chaotic state.

Science.gov (United States)

Baskan, O; Speetjens, M F M; Metcalfe, G; Clercx, H J H

2015-10-01

Countless theoretical/numerical studies on transport and mixing in two-dimensional (2D) unsteady flows lean on the assumption that Hamiltonian mechanisms govern the Lagrangian dynamics of passive tracers. However, experimental studies specifically investigating said mechanisms are rare. Moreover, they typically concern local behavior in specific states (usually far away from the integrable state) and generally expose this indirectly by dye visualization. Laboratory experiments explicitly addressing the global Hamiltonian progression of the Lagrangian flow topology entirely from integrable to chaotic state, i.e., the fundamental route to efficient transport by chaotic advection, appear non-existent. This motivates our study on experimental visualization of this progression by direct measurement of Poincaré sections of passive tracer particles in a representative 2D time-periodic flow. This admits (i) accurate replication of the experimental initial conditions, facilitating true one-to-one comparison of simulated and measured behavior, and (ii) direct experimental investigation of the ensuing Lagrangian dynamics. The analysis reveals a close agreement between computations and observations and thus experimentally validates the full global Hamiltonian progression at a great level of detail.

On two examples in linear topological spaces

International Nuclear Information System (INIS)

Iyahen, S.O.

1985-11-01

This note first gives examples of B-complete linear topological spaces, and shows that neither the closed graph theorem nor the open mapping theorem holds for linear mappings from such a space to itself. It then looks at Hausdorff linear topological spaces for which coarser Hausdorff linear topologies can be extended from hyperplanes. For B-complete spaces, those which are barrelled necessarily have countable dimension, and conversely. The paper had been motivated by two questions arising in earlier studies related to the closed graph and open mapping theorems; answers to these questions are contained therein. (author)

Topological color codes and two-body quantum lattice Hamiltonians

Science.gov (United States)

Kargarian, M.; Bombin, H.; Martin-Delgado, M. A.

2010-02-01

Topological color codes are among the stabilizer codes with remarkable properties from the quantum information perspective. In this paper, we construct a lattice, the so-called ruby lattice, with coordination number 4 governed by a two-body Hamiltonian. In a particular regime of coupling constants, in a strong coupling limit, degenerate perturbation theory implies that the low-energy spectrum of the model can be described by a many-body effective Hamiltonian, which encodes the color code as its ground state subspace. Ground state subspace corresponds to a vortex-free sector. The gauge symmetry Z2×Z2 of the color code could already be realized by identifying three distinct plaquette operators on the ruby lattice. All plaquette operators commute with each other and with the Hamiltonian being integrals of motion. Plaquettes are extended to closed strings or string-net structures. Non-contractible closed strings winding the space commute with Hamiltonian but not always with each other. This gives rise to exact topological degeneracy of the model. A connection to 2-colexes can be established via the coloring of the strings. We discuss it at the non-perturbative level. The particular structure of the two-body Hamiltonian provides a fruitful interpretation in terms of mapping onto bosons coupled to effective spins. We show that high-energy excitations of the model have fermionic statistics. They form three families of high-energy excitations each of one color. Furthermore, we show that they belong to a particular family of topological charges. The emergence of invisible charges is related to the string-net structure of the model. The emerging fermions are coupled to nontrivial gauge fields. We show that for particular 2-colexes, the fermions can see the background fluxes in the ground state. Also, we use the Jordan-Wigner transformation in order to test the integrability of the model via introducing Majorana fermions. The four-valent structure of the lattice prevents the

On RNA-RNA interaction structures of fixed topological genus.

Science.gov (United States)

Fu, Benjamin M M; Han, Hillary S W; Reidys, Christian M

2015-04-01

Interacting RNA complexes are studied via bicellular maps using a filtration via their topological genus. Our main result is a new bijection for RNA-RNA interaction structures and a linear time uniform sampling algorithm for RNA complexes of fixed topological genus. The bijection allows to either reduce the topological genus of a bicellular map directly, or to lose connectivity by decomposing the complex into a pair of single stranded RNA structures. Our main result is proved bijectively. It provides an explicit algorithm of how to rewire the corresponding complexes and an unambiguous decomposition grammar. Using the concept of genus induction, we construct bicellular maps of fixed topological genus g uniformly in linear time. We present various statistics on these topological RNA complexes and compare our findings with biological complexes. Furthermore we show how to construct loop-energy based complexes using our decomposition grammar. Copyright © 2015 Elsevier Inc. All rights reserved.

On the topology of flux transfer events

Science.gov (United States)

Hesse, Michael; Birn, Joachim; Schindler, Karl

1990-01-01

A topological analysis is made of a simple model magnetic field of a perturbation at the magnetopause that shares magnetic properties with flux transfer events. The aim is to clarify a number of topological aspects that arise in the case of fully three-dimensional magnetic fields. It is shown that a localized perturbation at the magnetopause can in principle open a closed magnetosphere by establishing magnetic connections across the magnetopause by the formation of a ropelike magnetic field structure. For this purpose a global topological model of a closed magnetosphere is considered as the unperturbed state. The topological substructure of the model flux rope is discussed in detail.

A heuristic approach to optimization of structural topology including self-weight

Science.gov (United States)

Tajs-Zielińska, Katarzyna; Bochenek, Bogdan

2018-01-01

Topology optimization of structures under a design-dependent self-weight load is investigated in this paper. The problem deserves attention because of its significant importance in the engineering practice, especially nowadays as topology optimization is more often applied when designing large engineering structures, for example, bridges or carrying systems of tall buildings. It is worth noting that well-known approaches of topology optimization which have been successfully applied to structures under fixed loads cannot be directly adapted to the case of design-dependent loads, so that topology generation can be a challenge also for numerical algorithms. The paper presents the application of a simple but efficient non-gradient method to topology optimization of elastic structures under self-weight loading. The algorithm is based on the Cellular Automata concept, the application of which can produce effective solutions with low computational cost.

Time-Space Topology Optimization

DEFF Research Database (Denmark)

Jensen, Jakob Søndergaard

2008-01-01

A method for space-time topology optimization is outlined. The space-time optimization strategy produces structures with optimized material distributions that vary in space and in time. The method is demonstrated for one-dimensional wave propagation in an elastic bar that has a time-dependent Young......’s modulus and is subjected to a transient load. In the example an optimized dynamic structure is demonstrated that compresses a propagating Gauss pulse....

Exploring photonic topological insulator states in a circuit-QED lattice

Science.gov (United States)

Li, Jing-Ling; Shan, Chuan-Jia; Zhao, Feng

2018-04-01

We propose a simple protocol to explore the topological properties of photonic integer quantum Hall states in a one-dimensional circiut-QED lattice. By periodically modulating the on-site photonic energies in such a lattice, we demonstrate that this one-dimensional lattice model can be mapped into a two-dimensional integer quantum Hall insulator model. Based on the lattice-based cavity input-output theory, we show that both the photonic topological protected edge states and topological invariants can be clearly measured from the final steady state of the resonator lattice after taking into account cavity dissipation. Interestingly, we also find that the measurement signals associated with the above topological features are quite unambitious even in five coupled dissipative resonators. Our work opens up a new prospect of exploring topological states with a small-size dissipative quantum artificial lattice, which is quite attractive to the current quantum optics community.

Interaction Deep Excavation Adjacent Structure Numerical Two and Three Dimensional Modeling

International Nuclear Information System (INIS)

Abdallah, M.; Chehade, F. H.; Chehade, W.; Fawaz, A.

2011-01-01

Urban development often requires the construction of deep excavations near to buildings or other structures. We have to study complex material structure interactions where we should take into consideration several particularities. In this paper, we perform a numerical modeling with the finite element method, using PLAXIS software, of the interaction deep excavation-diaphragm wall-soil-structure in the case of non linear soil behavior. We focus our study on a comparison of the results given respectively by two and three dimensional modelings. This allows us to give some recommendations concerning the validity of twodimensional study. We perform a parametric study according to the initial loading on the structure and the struts number. (author)

Signature of Topological Phases in Zitterbewegung

KAUST Repository

Ghosh, Sumit

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.

Signature of Topological Phases in Zitterbewegung

KAUST Repository

Ghosh, Sumit; Manchon, Aurelien

2016-01-01

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.

Equilibrium states and ground state of two-dimensional fluid foams

International Nuclear Information System (INIS)

Graner, F.; Jiang, Y.; Janiaud, E.; Flament, C.

2001-01-01

We study the equilibrium energies of two-dimensional (2D) noncoarsening fluid foams, which consist of bubbles with fixed areas. The equilibrium states correspond to local minima of the total perimeter. We present a theoretical derivation of energy minima; experiments with ferrofluid foams, which can be either highly distorted, locally relaxed, or globally annealed; and Monte Carlo simulations using the extended large-Q Potts model. For a dry foam with small size variance we develop physical insight and an electrostatic analogy, which enables us to (i) find an approximate value of the global minimum perimeter, accounting for (small) area disorder, the topological distribution, and physical boundary conditions; (ii) conjecture the corresponding pattern and topology: small bubbles sort inward and large bubbles sort outward, topological charges of the same signs ''repel'' while charges of the opposite signs ''attract;'' (iii) define local and global markers to determine directly from an image how far a foam is from its ground state; (iv) conjecture that, in a local perimeter minimum at prescribed topology, the pressure distribution and thus the edge curvature are unique. Some results also apply to 3D foams

On some classes of two-dimensional local models in discrete two-dimensional monatomic FPU lattice with cubic and quartic potential

International Nuclear Information System (INIS)

Quan, Xu; Qiang, Tian

2009-01-01

This paper discusses the two-dimensional discrete monatomic Fermi–Pasta–Ulam lattice, by using the method of multiple-scale and the quasi-discreteness approach. By taking into account the interaction between the atoms in the lattice and their nearest neighbours, it obtains some classes of two-dimensional local models as follows: two-dimensional bright and dark discrete soliton trains, two-dimensional bright and dark line discrete breathers, and two-dimensional bright and dark discrete breather. (condensed matter: structure, thermal and mechanical properties)

Scalar-tensor approach to the construction of theory of topological transformations

International Nuclear Information System (INIS)

Konstantinov, M.Yu.

1985-01-01

Problem of construction of the classical gravitational theory, which solutions in the explicit form contain description of topological transformations, is under study. With this object in view, the scalar-tensor formalism is considered based on a representation of some subclass of space-like hypersurfaces as surfaces of a smooth function level in four-dimensional manifolds. Solutions of the theory along with the Lorentz space-time structure and space-like surface topology define some reference system, but the type of topological transformations is not dependent on the reference system option. All these facts prove the above approach correctness. Two variants of the scalar-tensor theory of topological transformations are considered as an example; one of them is reduced to the Einstein gravitational theory in the regular space region and another represents a nontrivial modification of the Brans-Dikker theory

Two-dimensional spatial structure of the dissipative trapped-electron mode

International Nuclear Information System (INIS)

Rewoldt, G.; Tang, W.M.; Frieman, E.A.

1976-09-01

This paper deals with the complete two-dimensional structure of the dissipative trapped-electron mode over its full width, which may extend over several mode-rational surfaces. The complete integro-differential equation is studied in the limit k/sub r/rho/sub i/ less than 1, where rho/sub i/ is the ion gyroradius, and k/sub r/, the radial wavenumber, is regarded as a differential operator. This is converted into a matrix equation which is then solved by standard numerical methods

Derivation of the Time-Reversal Anomaly for (2 +1 )-Dimensional Topological Phases

Science.gov (United States)

Tachikawa, Yuji; Yonekura, Kazuya

2017-09-01

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 cross-cap state in terms of the modular S matrix and T2 eigenvalues, generalizing the recent analysis by Barkeshli et al. in the bosonic case.

Vortex line topology during vortex tube reconnection

Science.gov (United States)

McGavin, P.; Pontin, D. I.

2018-05-01

This paper addresses reconnection of vortex tubes, with particular focus on the topology of the vortex lines (field lines of the vorticity). This analysis of vortex line topology reveals key features of the reconnection process, such as the generation of many small flux rings, formed when reconnection occurs in multiple locations in the vortex sheet between the tubes. Consideration of three-dimensional reconnection principles leads to a robust measurement of the reconnection rate, even once instabilities break the symmetry. It also allows us to identify internal reconnection of vortex lines within the individual vortex tubes. Finally, the introduction of a third vortex tube is shown to render the vortex reconnection process fully three-dimensional, leading to a fundamental change in the topological structure of the process. An additional interesting feature is the generation of vorticity null points.

Lateral topological crystalline insulator heterostructure

Science.gov (United States)

Sun, Qilong; Dai, Ying; Niu, Chengwang; Ma, Yandong; Wei, Wei; Yu, Lin; Huang, Baibiao

2017-06-01

The emergence of lateral heterostructures fabricated by two-dimensional building blocks brings many exciting realms in material science and device physics. Enriching available nanomaterials for creating such heterostructures and enabling the underlying new physics is highly coveted for the integration of next-generation devices. Here, we report a breakthrough in lateral heterostructure based on the monolayer square transition-metal dichalcogenides MX2 (M  =  W, X  =  S/Se) modules. Our results reveal that the MX2 lateral heterostructure (1S-MX2 LHS) can possess excellent thermal and dynamical stability. Remarkably, the highly desired two-dimensional topological crystalline insulator phase is confirmed by the calculated mirror Chern number {{n}\\text{M}}=-1 . A nontrivial band gap of 65 meV is obtained with SOC, indicating the potential for room-temperature observation and applications. The topologically protected edge states emerge at the edges of two different nanoribbons between the bulk band gap, which is consistent with the mirror Chern number. In addition, a strain-induced topological phase transition in 1S-MX2 LHS is also revealed, endowing the potential utilities in electronics and spintronics. Our predictions not only introduce new member and vitality into the studies of lateral heterostructures, but also highlight the promise of lateral heterostructure as appealing topological crystalline insulator platforms with excellent stability for future devices.

Lattice topological field theory on nonorientable surfaces

International Nuclear Information System (INIS)

Karimipour, V.; Mostafazadeh, A.

1997-01-01

The lattice definition of the two-dimensional topological quantum field theory [Fukuma et al., Commun. Math. Phys. 161, 157 (1994)] is generalized to arbitrary (not necessarily orientable) compact surfaces. It is shown that there is a one-to-one correspondence between real associative *-algebras and the topological state sum invariants defined on such surfaces. The partition and n-point functions on all two-dimensional surfaces (connected sums of the Klein bottle or projective plane and g-tori) are defined and computed for arbitrary *-algebras in general, and for the group ring A=R[G] of discrete groups G, in particular. copyright 1997 American Institute of Physics

Bi-directional evolutionary structural optimization for strut-and-tie modelling of three-dimensional structural concrete

Science.gov (United States)

Shobeiri, Vahid; Ahmadi-Nedushan, Behrouz

2017-12-01

This article presents a method for the automatic generation of optimal strut-and-tie models in reinforced concrete structures using a bi-directional evolutionary structural optimization method. The methodology presented is developed for compliance minimization relying on the Abaqus finite element software package. The proposed approach deals with the generation of truss-like designs in a three-dimensional environment, addressing the design of corbels and joints as well as bridge piers and pile caps. Several three-dimensional examples are provided to show the capabilities of the proposed framework in finding optimal strut-and-tie models in reinforced concrete structures and verifying its efficiency to cope with torsional actions. Several issues relating to the use of the topology optimization for strut-and-tie modelling of structural concrete, such as chequerboard patterns, mesh-dependency and multiple load cases, are studied. In the last example, a design procedure for detailing and dimensioning of the strut-and-tie models is given according to the American Concrete Institute (ACI) 318-08 provisions.

Topological phase transition in the two-dimensional anisotropic Heisenberg model: A study using the Replica Exchange Wang-Landau sampling

Science.gov (United States)

Figueiredo, T. P.; Rocha, J. C. S.; Costa, B. V.

2017-12-01

Although the topological Berezinskii-Kosterlitz-Thouless transition was for the first time described by 40 years ago, it is still a matter of discussion. It has been used to explain several experiments in the most diverse physical systems. In contrast with the ordinary continuous phase transitions the BKT-transition does not break any symmetry. However, in some contexts it can easily be confused with other continuous transitions, in general due to an insufficient data analysis. The two-dimensional XY (or sometimes called planar rotator) spin model is the fruit fly model describing the BKT transition. As demonstrated by Bramwell and Holdsworth (1993) the finite-size effects are more important in two-dimensions than in others due to the logarithmic system size dependence of the properties of the system. Closely related is the anisotropic two dimensional Heisenberg model (AH). Although they have the same Hamiltonian the spin variable in the former has only two degrees of freedom while the AH has three. Many works treat the AH model as undergoing a transition in the same universality class as the XY model. However, its characterization as being in the BKT class of universality deserve some investigation. This paper has two goals. First, we describe an analytical evidence showing that the AH model is in the BKT class of universality. Second, we make an extensive simulation, using the numerical Replica Exchange Wang-Landau method that corroborate our analytical calculations. From our simulation we obtain the BKT transition temperature as TBKT = 0 . 6980(10) by monitoring the susceptibility, the two point correlation function and the helicity modulus. We discuss the misuse of the fourth order Binder's cumulant to locate the transition temperature. The specific heat is shown to have a non-critical behavior as expected in the BKT transition. An analysis of the two point correlation function at low temperature, C(r) ∝r - η(T), shows that the exponent, η, is consistent

Entropic Barriers for Two-Dimensional Quantum Memories

Science.gov (United States)

Brown, Benjamin J.; Al-Shimary, Abbas; Pachos, Jiannis K.

2014-03-01

Comprehensive no-go theorems show that information encoded over local two-dimensional topologically ordered systems cannot support macroscopic energy barriers, and hence will not maintain stable quantum information at finite temperatures for macroscopic time scales. However, it is still well motivated to study low-dimensional quantum memories due to their experimental amenability. Here we introduce a grid of defect lines to Kitaev's quantum double model where different anyonic excitations carry different masses. This setting produces a complex energy landscape which entropically suppresses the diffusion of excitations that cause logical errors. We show numerically that entropically suppressed errors give rise to superexponential inverse temperature scaling and polynomial system size scaling for small system sizes over a low-temperature regime. Curiously, these entropic effects are not present below a certain low temperature. We show that we can vary the system to modify this bound and potentially extend the described effects to zero temperature.

Radiation-Induced Topological Disorder in Irradiated Network Structures

International Nuclear Information System (INIS)

Hobbs, Linn W.

2002-12-01

This report summarizes results of a research program investigating the fundamental principles underlying the phenomenon of topological disordering in a radiation environment. This phenomenon is known popularly as amorphization, but is more formally described as a process of radiation-induced structural arrangement that leads in crystals to loss of long-range translational and orientational correlations and in glasses to analogous alteration of connectivity topologies. The program focus has been on a set compound ceramic solids with directed bonding exhibiting structures that can be described as networks. Such solids include SiO2, Si3N4, SiC, which are of interest to applications in fusion energy production, nuclear waste storage, and device manufacture involving ion implantation or use in radiation fields. The principal investigative tools comprise a combination of experimental diffraction-based techniques, topological modeling, and molecular-dynamics simulations that have proven a rich source of information in the preceding support period. The results from the present support period fall into three task areas. The first comprises enumeration of the rigidity constraints applying to (1) more complex ceramic structures (such as rutile, corundum, spinel and olivine structures) that exhibit multiply polytopic coordination units or multiple modes of connecting such units, (2) elemental solids (such as graphite, silicon and diamond) for which a correct choice of polytope is necessary to achieve correct representation of the constraints, and (3) compounds (such as spinel and silicon carbide) that exhibit chemical disorder on one or several sublattices. With correct identification of the topological constraints, a unique correlation is shown to exist between constraint and amorphizability which demonstrates that amorphization occurs at a critical constraint loss. The second task involves the application of molecular dynamics (MD) methods to topologically-generated models

Topology Optimization of Sub-Wavelength Antennas

DEFF Research Database (Denmark)

Erentok, Aycan; Sigmund, Ole

2011-01-01

We propose a topology optimization strategy for the systematic design of a three-dimensional (3D), conductor-based sub-wavelength antenna. The post-processed finite-element (FE) models of the optimized structure are shown to be self-resonant, efficient and exhibit distorted omnidirectional...

Selective buckling via states of self-stress in topological metamaterials.

Science.gov (United States)

Paulose, Jayson; Meeussen, Anne S; Vitelli, Vincenzo

2015-06-23

States of self-stress--tensions and compressions of structural elements that result in zero net forces--play an important role in determining the load-bearing ability of structures ranging from bridges to metamaterials with tunable mechanical properties. We exploit a class of recently introduced states of self-stress analogous to topological quantum states to sculpt localized buckling regions in the interior of periodic cellular metamaterials. Although the topological states of self-stress arise in the linear response of an idealized mechanical frame of harmonic springs connected by freely hinged joints, they leave a distinct signature in the nonlinear buckling behavior of a cellular material built out of elastic beams with rigid joints. The salient feature of these localized buckling regions is that they are indistinguishable from their surroundings as far as material parameters or connectivity of their constituent elements are concerned. Furthermore, they are robust against a wide range of structural perturbations. We demonstrate the effectiveness of this topological design through analytical and numerical calculations as well as buckling experiments performed on two- and three-dimensional metamaterials built out of stacked kagome lattices.

Topological dynamics of vortex-line networks in hexagonal manganites

Science.gov (United States)

Xue, Fei; Wang, Nan; Wang, Xueyun; Ji, Yanzhou; Cheong, Sang-Wook; Chen, Long-Qing

2018-01-01

The two-dimensional X Y model is the first well-studied system with topological point defects. On the other hand, although topological line defects are common in three-dimensional systems, the evolution mechanism of line defects is not fully understood. The six domains in hexagonal manganites converge to vortex lines in three dimensions. Using phase-field simulations, we predicted that during the domain coarsening process, the vortex-line network undergoes three types of basic topological changes, i.e., vortex-line loop shrinking, coalescence, and splitting. It is shown that the vortex-antivortex annihilation controls the scaling dynamics.

Topological phase transition in the quench dynamics of a one-dimensional Fermi gas with spin–orbit coupling

International Nuclear Information System (INIS)

Wang, Pei; Yi, Wei; Xianlong, Gao

2015-01-01

We study the quench dynamics of a one-dimensional ultracold Fermi gas with synthetic spin-orbit coupling. At equilibrium, the ground state of the system can undergo a topological phase transition and become a topological superfluid with Majorana edge states. As the interaction is quenched near the topological phase boundary, we identify an interesting dynamical phase transition of the quenched state in the long-time limit, characterized by an abrupt change of the pairing gap at a critical quenched interaction strength. We further demonstrate the topological nature of this dynamical phase transition from edge-state analysis of the quenched states. Our findings provide interesting clues for the understanding of topological phase transitions in dynamical processes, and can be useful for the dynamical detection of Majorana edge states in corresponding systems. (paper)

Topological phase transition in the quench dynamics of a one-dimensional Fermi gas with spin-orbit coupling

Science.gov (United States)

Wang, Pei; Yi, Wei; Xianlong, Gao

2015-01-01

We study the quench dynamics of a one-dimensional ultracold Fermi gas with synthetic spin-orbit coupling. At equilibrium, the ground state of the system can undergo a topological phase transition and become a topological superfluid with Majorana edge states. As the interaction is quenched near the topological phase boundary, we identify an interesting dynamical phase transition of the quenched state in the long-time limit, characterized by an abrupt change of the pairing gap at a critical quenched interaction strength. We further demonstrate the topological nature of this dynamical phase transition from edge-state analysis of the quenched states. Our findings provide interesting clues for the understanding of topological phase transitions in dynamical processes, and can be useful for the dynamical detection of Majorana edge states in corresponding systems.

Three-dimensional imaging of vortex structure in a ferroelectric nanoparticle driven by an electric field.

Science.gov (United States)

Karpov, D; Liu, Z; Rolo, T Dos Santos; Harder, R; Balachandran, P V; Xue, D; Lookman, T; Fohtung, E

2017-08-17

Topological defects of spontaneous polarization are extensively studied as templates for unique physical phenomena and in the design of reconfigurable electronic devices. Experimental investigations of the complex topologies of polarization have been limited to surface phenomena, which has restricted the probing of the dynamic volumetric domain morphology in operando. Here, we utilize Bragg coherent diffractive imaging of a single BaTiO 3 nanoparticle in a composite polymer/ferroelectric capacitor to study the behavior of a three-dimensional vortex formed due to competing interactions involving ferroelectric domains. Our investigation of the structural phase transitions under the influence of an external electric field shows a mobile vortex core exhibiting a reversible hysteretic transformation path. We also study the toroidal moment of the vortex under the action of the field. Our results open avenues for the study of the structure and evolution of polar vortices and other topological structures in operando in functional materials under cross field configurations.Imaging of topological states of matter such as vortex configurations has generally been limited to 2D surface effects. Here Karpov et al. study the volumetric structure and dynamics of a vortex core mediated by electric-field induced structural phase transition in a ferroelectric BaTiO 3 nanoparticle.

Renormalization of topological field theory

International Nuclear Information System (INIS)

Birmingham, D.; Rakowski, M.; Thompson, G.

1988-11-01

One loop corrections to topological field theory in three and four dimensions are presented. By regularizing determinants, we compute the effective action and β-function in four dimensional topological Yang-Mills theory and find that the BRST symmetry is preserved. Moreover, the minima of the effective action still correspond to instanton configurations. In three dimensions, an analysis of the Chern-Simons theory shows that the topological nature of the theory is also preserved to this order. In addition, we find that this theory possesses an extra supersymmetry when quantized in the Landau gauge. Using dimensional regularization, we then study the Ward identities of the extended BRST symmetry in the three dimensional topological Yang-Mills-Higgs model. (author). 22 refs

Quantum oscillation evidence for a topological semimetal phase in ZrSnTe

Science.gov (United States)

Hu, Jin; Zhu, Yanglin; Gui, Xin; Graf, David; Tang, Zhijie; Xie, Weiwei; Mao, Zhiqiang

2018-04-01

The layered WHM-type (W =Zr /Hf /La , H =Si /Ge /Sn /Sb , M =S /Se /Te ) materials represent a large family of topological semimetals, which provides an excellent platform to study the evolution of topological semimetal state with the fine tuning of spin-orbit coupling and structural dimensionality for various combinations of W , H , and M elements. In this work, through high field de Haas-van Alphen (dHvA) quantum oscillation studies, we have found evidence for the predicted topological nontrivial bands in ZrSnTe. Furthermore, from the angular dependence of quantum oscillation frequency, we have revealed the three-dimensional Fermi surface topologies of this layered material owing to strong interlayer coupling.

Periodic trajectories for two-dimensional nonintegrable Hamiltonians

International Nuclear Information System (INIS)

Davies, K.T.R.

1990-02-01

I want to report on some calculations of classical periodic trajectories in a two-dimensional nonintegrable potential. After a brief introduction, I will present some details of the theory. The main part of this report will be devoted to showing pictures of the various families of trajectories and to discussing the topology (in E-τ space) and branching behavior of these families. Then I will demonstrate the connection between periodic trajectories and ''nearby'' nonperiodic trajectories, which nicely illustrates the relationship of this work to chaos. Finally, I will discuss very briefly how periodic trajectories can be used to calculate tori. 12 refs., 40 figs

Nonlinear excitations in two-dimensional molecular structures with impurities

DEFF Research Database (Denmark)

Gaididei, Yuri Borisovich; Rasmussen, Kim; Christiansen, Peter Leth

1995-01-01

We study the nonlinear dynamics of electronic excitations interacting with acoustic phonons in two-dimensional molecular structures with impurities. We show that the problem is reduced to the nonlinear Schrodinger equation with a varying coefficient. The latter represents the influence...... of the impurity. Transforming the equation to the noninertial frame of reference coupled with the center of mass we investigate the soliton behavior in the close vicinity of the impurity. With the help of the lens transformation we show that the soliton width is governed by an Ermakov-Pinney equation. We also...... excitations. Analytical results are in good agreement with numerical simulations of the nonlinear Schrodinger equation....

Two- and three-dimensional lanthanide-organic frameworks constructed using 1-hydro-6-oxopyridine-3-carboxylate and oxalate ligands.

Science.gov (United States)

Liu, Cai-Ming; Xiong, Ming; Zhang, De-Qing; Du, Miao; Zhu, Dao-Ben

2009-08-07

6-Hydroxypyridine-3-carboxylic acid (6-HOPy-3-CO(2)H) reacts with Ln(2)O(3) (Ln = Nd, Sm, Eu, Gd) and oxalic acid (H(2)OX) under hydrothermal conditions to generate four novel lanthanide-organic coordination polymeric networks [Ln(2)(1H-6-Opy-3-CO(2))(2)(OX)(2)(H(2)O)(3)] x 2.5 H(2)O (Ln = Nd, 1; Sm, 2; 1H-6-Opy-3-CO(2)(-) = 1-hydro-6-oxopyridine-3-carboxylate) and [Ln(1H-6-Opy-3-CO(2))(OX)(H(2)O)(2)] x H(2)O (Ln = Eu, 3; Gd, 4). The new co-ligand 1H-6-Opy-3-CO(2)(-) anion was generated by the autoisomerization of the single deprotonated 6-HOPy-3-CO(2)(-) anion (from the enol form into the ketone one). 1 and 2 are isomorphous, they possess a three-dimensional architecture constructed from Ln(3+) ions bridged by oxalate anions and two types of 1H-6-Opy-3-CO(2)(-) bridges, showing a three-nodal (4,5)-connected topology (3.4(2).5(2).6(3).7.8)(2)(3.5(3).6(2))(2)(3(2).6.7(2).8) or a simplified uninodal 6-connected topology (3(3).4(6).5(5).6), both topologies are completely new; while only one type of 1H-6-Opy-3-CO(2)(-) bridge is used to construct the two-dimensional layer networks of 3 and 4 besides oxalate bridges, both complexes 3 and 4 are isostructural, exhibiting the honeycomb topology 6(3). The lanthanide contraction effect is believed to play a key role in directing the formation of a particular structure. A magnetic study of 1-3 indicated that the coupling interaction between Ln(3+) ions is weak.

Topology vs. Anderson localization: non-perturbative solutions in one dimension

OpenAIRE

Altland, Alexander; Bagrets, Dmitry; Kamenev, Alex

2014-01-01

We present an analytic theory of quantum criticality in quasi one-dimensional topological Anderson insulators. We describe these systems in terms of two parameters $(g,\\chi)$ representing localization and topological properties, respectively. Certain critical values of $\\chi$ (half-integer for $\\Bbb{Z}$ classes, or zero for $\\Bbb{Z}_2$ classes) define phase boundaries between distinct topological sectors. Upon increasing system size, the two parameters exhibit flow similar to the celebrated t...

Topological phase in two flavor neutrino oscillations

International Nuclear Information System (INIS)

Mehta, Poonam

2009-01-01

We show that the phase appearing in neutrino flavor oscillation formulae has a geometric and topological contribution. We identify a topological phase appearing in the two flavor neutrino oscillation formula using Pancharatnam's prescription of quantum collapses between nonorthogonal states. Such quantum collapses appear naturally in the expression for appearance and survival probabilities of neutrinos. Our analysis applies to neutrinos propagating in vacuum or through matter. For the minimal case of two flavors with CP conservation, our study shows for the first time that there is a geometric interpretation of the neutrino oscillation formulae for the detection probability of neutrino species.

Topology control

NARCIS (Netherlands)

Buchin, K.; Buchin, M.; Wagner, D.; Wattenhofer, R.

2007-01-01

Information between two nodes in a network is sent based on the network topology, the structure of links connecting pairs of nodes of a network. The task of topology control is to choose a connecting subset from all possible links such that the overall network performance is good. For instance, a

Stress-based topology optimization of concrete structures with prestressing reinforcements

Science.gov (United States)

Luo, Yangjun; Wang, Michael Yu; Deng, Zichen

2013-11-01

Following the extended two-material density penalization scheme, a stress-based topology optimization method for the layout design of prestressed concrete structures is proposed. The Drucker-Prager yield criterion is used to predict the asymmetrical strength failure of concrete. The prestress is considered by making a reasonable assumption on the prestressing orientation in each element and adding an additional load vector to the structural equilibrium function. The proposed optimization model is thus formulated as to minimize the reinforcement material volume under Drucker-Prager yield constraints on elemental concrete local stresses. In order to give a reasonable definition of concrete local stress and prevent the stress singularity phenomenon, the local stress interpolation function and the ɛ -relaxation technique are adopted. The topology optimization problem is solved using the method of moving asymptotes combined with an active set strategy. Numerical examples are given to show the efficiency of the proposed optimization method in the layout design of prestressed concrete structures.

Correspondence between the contracted BTZ solution of cosmological topological massive gravity and two-dimensional Galilean conformal algebra

International Nuclear Information System (INIS)

Setare, M R; Kamali, V

2011-01-01

We show that a BTZ black hole solution of cosmological topological massive gravity has a hidden conformal symmetry. In this regard, we consider the wave equation of a massless scalar field propagating in BTZ spacetime and find that the wave equation could be written in terms of the SL(2, R) quadratic Casimir. From the conformal coordinates, the temperatures of the dual conformal field theories (CFTs) could be read directly. Moreover, we compute the microscopic entropy of the dual CFT by the Cardy formula and find a perfect match to the Bekenstein-Hawking entropy of a BTZ black hole. Then, we consider Galilean conformal algebras (GCA), which arises as a contraction of relativistic conformal algebras (x → εx, t → t, ε → 0). We show that there is a correspondence between GCA 2 on the boundary and contracted BTZ in the bulk. For this purpose we obtain the central charges and temperatures of GCA 2 . Then, we compute the microscopic entropy of the GCA 2 by the Cardy formula and find a perfect match to the Bekenstein-Hawking entropy of a BTZ black hole in a non-relativistic limit. The absorption cross section of a near-region scalar field also matches the microscopic absorption cross section of the dual GCA 2 . So we find further evidence that shows correspondence between a contracted BTZ black hole and two-dimensional GCA.

Stiffness design of geometrically nonlinear structures using topology optimization

DEFF Research Database (Denmark)

Buhl, Thomas; Pedersen, Claus B. Wittendorf; Sigmund, Ole

2000-01-01

of the objective functions are found with the adjoint method and the optimization problem is solved using the Method of Moving Asymptotes. A filtering scheme is used to obtain checkerboard-free and mesh-independent designs and a continuation approach improves convergence to efficient designs. Different objective......The paper deals with topology optimization of structures undergoing large deformations. The geometrically nonlinear behaviour of the structures are modelled using a total Lagrangian finite element formulation and the equilibrium is found using a Newton-Raphson iterative scheme. The sensitivities...... functions are tested. Minimizing compliance for a fixed load results in degenerated topologies which are very inefficient for smaller or larger loads. The problem of obtaining degenerated "optimal" topologies which only can support the design load is even more pronounced than for structures with linear...

Simultaneous topology optimization of structures and supports

DEFF Research Database (Denmark)

Buhl, Thomas

2002-01-01

supported areas. The method is applied to compliance minimization and mechanism design. In the case of mechanism design, the large displacements of the mechanism are modelled using geometrically nonlinear FE-analysis. Examples with minimization of the compliance demonstrate the effects of using variable......The purpose of this paper is to demonstrate a method for and the benefits of simultaneously designing structure and support distribution using topology optimization. The support conditions are included in the topology optimization by introducing, a new set of design variables that represents...... cost of supports in a design domain. Other examples show that more efficient mechanisms are obtained by introducing the support conditions in the topology optimization problem....

Three-dimensional investigation of the two-phase flow structure in a bubbly pipe flow

International Nuclear Information System (INIS)

Schmidl, W.; Hassan, Y.A.; Ortiz-Villafuerte, J.

1996-01-01

Particle image velocimetry (PIV) is a nonintrusive measurement technique that can be used to study the structure of various fluid flows. PIV is used to measure the time-varying, full-field velocity data of a particle-seeded flow field within either a two-dimensional plane or three-dimensional volume. PIV is a very efficient measurement technique since it can obtain both qualitative and quantitative spatial information about the flow field being studied. The quantitative spatial velocity information can be further processed into information of flow parameters such as vorticity and turbulence over extended areas. The objective of this study was to apply recent advances and improvements in the PIV flow measurement technique to the full-field, nonintrusive analysis of a three-dimensional, two-phase fluid flow system in such a manner that both components of the two-phase system could be experimentally quantified

Parafermionic wires at the interface of chiral topological states

Science.gov (United States)

Santos, Luiz; Hughes, Taylor

We discuss a scenario where local interactions form one-dimensional gapped interfaces between a pair of distinct chiral two-dimensional topological states such that each gapped region terminates at a domain wall separating the chiral gapless edge states of these phases. We show that this type of T-junction supports point-like fractionalized excitations obeying parafermion statistics, thus implying that the one-dimensional gapped interface forms an effective topological parafermionic wire possessing a non-trivial ground state degeneracy. The physical properties of the anyon condensate that gives rise to the gapped interface are investigated. Remarkably, this condensate causes the gapped interface to behave as a type of anyon ``Andreev reflector'' in the bulk, whereby anyons from one phase, upon hitting the interface, can be transformed into a combination of reflected anyons and outgoing anyons from the other phase. Thus, we conclude that while different topological orders can be connected via gapped interfaces, the interfaces are themselves topological.

Topological nanophononic states by band inversion

Science.gov (United States)

Esmann, Martin; Lamberti, Fabrice Roland; Senellart, Pascale; Favero, Ivan; Krebs, Olivier; Lanco, Loïc; Gomez Carbonell, Carmen; Lemaître, Aristide; Lanzillotti-Kimura, Norberto Daniel

2018-04-01

Nanophononics is essential for the engineering of thermal transport in nanostructured electronic devices, it greatly facilitates the manipulation of mechanical resonators in the quantum regime, and it could unveil a new route in quantum communications using phonons as carriers of information. Acoustic phonons also constitute a versatile platform for the study of fundamental wave dynamics, including Bloch oscillations, Wannier-Stark ladders, and other localization phenomena. Many of the phenomena studied in nanophononics were inspired by their counterparts in optics and electronics. In these fields, the consideration of topological invariants to control wave dynamics has already had a great impact for the generation of robust confined states. Interestingly, the use of topological phases to engineer nanophononic devices remains an unexplored and promising field. Conversely, the use of acoustic phonons could constitute a rich platform to study topological states. Here, we introduce the concept of topological invariants to nanophononics and experimentally implement a nanophononic system supporting a robust topological interface state at 350 GHz. The state is constructed through band inversion, i.e., by concatenating two semiconductor superlattices with inverted spatial mode symmetries. The existence of this state is purely determined by the Zak phases of the constituent superlattices, i.e., the one-dimensional Berry phase. We experimentally evidenced the mode through Raman spectroscopy. The reported robust topological interface states could become part of nanophononic devices requiring resonant structures such as sensors or phonon lasers.

Four Mixed-Ligand Zn(II Three-Dimensional Metal-Organic Frameworks: Synthesis, Structural Diversity, and Photoluminescent Property

Directory of Open Access Journals (Sweden)

Chih-Chieh Wang

2017-11-01

Full Text Available Assemblies of four three-dimensional (3D mixed-ligand coordination polymers (CPs having formulas, {[Zn2(bdc2(4-bpdh]·C2H5OH·2H2O}n (1, [Zn(bdc(4-bpdh]n (2, {[Zn2(bdc2(4-bpdh2]·(4-bpdh}n (3, and {[Zn(bdc(4-bpdh]·C2H5OH}n (4 (bdc2− = dianion of 1,4-benzenedicarboxylic acid, 4-bpdh = 2,5-bis(4-pyridyl-3,4-diaza-2,4-hexadiene have been synthesized and structurally characterized by single-crystal X-ray diffraction method. Structural determination reveals that the coordination numbers (geometry of Zn(II ions in 1, 2, 3, and 4 are five (distorted square-pyramidal (SP, six (distorted octahedral (Oh, five (trigonal-bipyramidal (TBP, and four (tetrahedral (Td, respectively, and are bridged by 4-bpdh with bis-monodentate coordination mode and bdc2− ligands with bis-bidentate in 1, chelating/bidentate in 2, bis-monodentate and bis-bidentate in 3, and bis-monodentate in 4, to generate two-fold interpenetrating 3D cube-like metal-organic framework (MOF with pcu topology, non-interpenetrating 3D MOF, two-fold interpenetrating 3D rectangular-box-like MOF with pcu topology and five-fold interpenetrating diamondoid-like MOF with dia topology, respectively. These different intriguing architectures indicate that the coordination numbers and geometries of Zn(II ions, coordination modes of bdc2− ligand, and guest molecules play important roles in the construction of MOFs and the formation of the structural topologies and interpenetrations. Thermal stabilities, and photoluminescence study of 1–4 were also studied in detail. The complexes exhibit ligands based photoluminescence properties at room temperature.

Band structures of two dimensional solid/air hierarchical phononic crystals

International Nuclear Information System (INIS)

Xu, Y.L.; Tian, X.G.; Chen, C.Q.

2012-01-01

The hierarchical phononic crystals to be considered show a two-order “hierarchical” feature, which consists of square array arranged macroscopic periodic unit cells with each unit cell itself including four sub-units. Propagation of acoustic wave in such two dimensional solid/air phononic crystals is investigated by the finite element method (FEM) with the Bloch theory. Their band structure, wave filtering property, and the physical mechanism responsible for the broadened band gap are explored. The corresponding ordinary phononic crystal without hierarchical feature is used for comparison. Obtained results show that the solid/air hierarchical phononic crystals possess tunable outstanding band gap features, which are favorable for applications such as sound insulation and vibration attenuation.

Band structures of two dimensional solid/air hierarchical phononic crystals

Energy Technology Data Exchange (ETDEWEB)

Xu, Y.L.; Tian, X.G. [State Key Laboratory for Mechanical Structure Strength and Vibration, Xi' an Jiaotong University, Xi' an 710049 (China); Chen, C.Q., E-mail: chencq@tsinghua.edu.cn [Department of Engineering Mechanics, AML and CNMM, Tsinghua University, Beijing 100084 (China)

2012-06-15

The hierarchical phononic crystals to be considered show a two-order 'hierarchical' feature, which consists of square array arranged macroscopic periodic unit cells with each unit cell itself including four sub-units. Propagation of acoustic wave in such two dimensional solid/air phononic crystals is investigated by the finite element method (FEM) with the Bloch theory. Their band structure, wave filtering property, and the physical mechanism responsible for the broadened band gap are explored. The corresponding ordinary phononic crystal without hierarchical feature is used for comparison. Obtained results show that the solid/air hierarchical phononic crystals possess tunable outstanding band gap features, which are favorable for applications such as sound insulation and vibration attenuation.

Real-space mapping of topological invariants using artificial neural networks

Science.gov (United States)

Carvalho, D.; García-Martínez, N. A.; Lado, J. L.; Fernández-Rossier, J.

2018-03-01

Topological invariants allow one to characterize Hamiltonians, predicting the existence of topologically protected in-gap modes. Those invariants can be computed by tracing the evolution of the occupied wave functions under twisted boundary conditions. However, those procedures do not allow one to calculate a topological invariant by evaluating the system locally, and thus require information about the wave functions in the whole system. Here we show that artificial neural networks can be trained to identify the topological order by evaluating a local projection of the density matrix. We demonstrate this for two different models, a one-dimensional topological superconductor and a two-dimensional quantum anomalous Hall state, both with spatially modulated parameters. Our neural network correctly identifies the different topological domains in real space, predicting the location of in-gap states. By combining a neural network with a calculation of the electronic states that uses the kernel polynomial method, we show that the local evaluation of the invariant can be carried out by evaluating a local quantity, in particular for systems without translational symmetry consisting of tens of thousands of atoms. Our results show that supervised learning is an efficient methodology to characterize the local topology of a system.

Exotic Lifshitz transitions in topological materials

Science.gov (United States)

Volovik, G. E.

2018-01-01

Topological Lifshitz transitions involve many types of topological structures in momentum and frequency-momentum spaces, such as Fermi surfaces, Dirac lines, Dirac and Weyl points, etc., each of which has its own stability-supporting topological invariant ( N_1, N_2, N_3, {\\tilde N}_3, etc.). The topology of the shape of Fermi surfaces and Dirac lines and the interconnection of objects of different dimensionalities produce a variety of Lifshitz transition classes. Lifshitz transitions have important implications for many areas of physics. To give examples, transition-related singularities can increase the superconducting transition temperature; Lifshitz transitions are the possible origin of the small masses of elementary particles in our Universe, and a black hole horizon serves as the surface of the Lifshitz transition between vacua with type-I and type-II Weyl points.

An Invitation to the Mathematics of Topological Quantum Computation

International Nuclear Information System (INIS)

Rowell, E C

2016-01-01

Two-dimensional topological states of matter offer a route to quantum computation that would be topologically protected against the nemesis of the quantum circuit model: decoherence. Research groups in industry, government and academic institutions are pursuing this approach. We give a mathematician's perspective on some of the advantages and challenges of this model, highlighting some recent advances. We then give a short description of how we might extend the theory to three-dimensional materials. (paper)

Exploratory Topology Modelling of Form-Active Hybrid Structures

DEFF Research Database (Denmark)

Holden Deleuran, Anders; Pauly, Mark; Tamke, Martin

2016-01-01

The development of novel form-active hybrid structures (FAHS) is impeded by a lack of modelling tools that allow for exploratory topology modelling of shaped assemblies. We present a flexible and real-time computational design modelling pipeline developed for the exploratory modelling of FAHS...... that enables designers and engineers to iteratively construct and manipulate form-active hybrid assembly topology on the fly. The pipeline implements Kangaroo2's projection-based methods for modelling hybrid structures consisting of slender beams and cable networks. A selection of design modelling sketches...

Non-Euclidean geometry and curvature two-dimensional spaces, volume 3

CERN Document Server

Cannon, James W

2017-01-01

This is the final volume of a three volume collection devoted to the geometry, topology, and curvature of 2-dimensional spaces. The collection provides a guided tour through a wide range of topics by one of the twentieth century's masters of geometric topology. The books are accessible to college and graduate students and provide perspective and insight to mathematicians at all levels who are interested in geometry and topology. Einstein showed how to interpret gravity as the dynamic response to the curvature of space-time. Bill Thurston showed us that non-Euclidean geometries and curvature are essential to the understanding of low-dimensional spaces. This third and final volume aims to give the reader a firm intuitive understanding of these concepts in dimension 2. The volume first demonstrates a number of the most important properties of non-Euclidean geometry by means of simple infinite graphs that approximate that geometry. This is followed by a long chapter taken from lectures the author gave at MSRI, wh...

Unique encoding for streamline topologies of incompressible and inviscid flows in multiply connected domains

Energy Technology Data Exchange (ETDEWEB)

Sakajo, T [Department of Mathematics, Kyoto University, Kitashirakawa Oiwake-cho, Sakyo-ku, Kyoto 606-8502 (Japan); Sawamura, Y; Yokoyama, T, E-mail: sakajo@math.kyoto-u.ac.jp [JST CREST, Kawaguchi, Saitama 332-0012 (Japan)

2014-06-01

This study considers the flow of incompressible and inviscid fluid in two-dimensional multiply connected domains. For such flows, encoding algorithms to assign a unique sequence of words to any structurally stable streamline topology based on the theory presented by Yokoyama and Sakajo (2013 Proc. R. Soc. A 469 20120558) are proposed. As an application, we utilize the algorithms to characterize the evolution of an incompressible and viscid flow around a flat plate inclined to the uniform flow in terms of the change of the word representations for their instantaneous streamline topologies. (papers)

Actively Controlling the Topological Transition of Dispersion Based on Electrically Controllable Metamaterials

Directory of Open Access Journals (Sweden)

Zhiwei Guo

2018-04-01

Full Text Available Topological transition of the iso-frequency contour (IFC from a closed ellipsoid to an open hyperboloid provides unique capabilities for controlling the propagation of light. However, the ability to actively tune these effects remains elusive, and the related experimental observations are highly desirable. Here, a tunable electric IFC in a periodic structure composed of graphene/dielectric multilayers is investigated by tuning the chemical potential of the graphene layer. Specially, we present the actively controlled transportation in two kinds of anisotropic zero-index media containing perfect electric conductor/perfect magnetic conductor impurities. Finally, by adding variable capacitance diodes into a two-dimensional transmission-line system, we present an experimental demonstration of the actively controlled magnetic topological transition of dispersion based on electrically controllable metamaterials. With the increase in voltage, we measure the different emission patterns from a point source inside the structure and observe the phase-transition process of IFCs. The realization of an actively tuned topological transition will open up a new avenue in the dynamical control of metamaterials.

On Topological Indices of Certain Dendrimer Structures

Science.gov (United States)

Aslam, Adnan; Bashir, Yasir; Ahmad, Safyan; Gao, Wei

2017-05-01

A topological index can be considered as transformation of chemical structure in to real number. In QSAR/QSPR study, physicochemical properties and topological indices such as Randić, Zagreb, atom-bond connectivity ABC, and geometric-arithmetic GA index are used to predict the bioactivity of chemical compounds. Dendrimers are highly branched, star-shaped macromolecules with nanometer-scale dimensions. Dendrimers are defined by three components: a central core, an interior dendritic structure (the branches), and an exterior surface with functional surface groups. In this paper we determine generalised Randić, general Zagreb, general sum-connectivity indices of poly(propyl) ether imine, porphyrin, and zinc-Porphyrin dendrimers. We also compute ABC and GA indices of these families of dendrimers.

Combined shape and topology optimization of 3D structures

DEFF Research Database (Denmark)

Christiansen, Asger Nyman; Bærentzen, Jakob Andreas; Nobel-Jørgensen, Morten

2015-01-01

We present a method for automatic generation of 3D models based on shape and topology optimization. The optimization procedure, or model generation process, is initialized by a set of boundary conditions, an objective function, constraints and an initial structure. Using this input, the method...... will automatically deform and change the topology of the initial structure such that the objective function is optimized subject to the specified constraints and boundary conditions. For example, this tool can be used to improve the stiffness of a structure before printing, reduce the amount of material needed...

Coupling between Fano and Bragg bands in the photonic band structure of two- dimensional metallic photonic structures

Czech Academy of Sciences Publication Activity Database

Markoš, P.; Kuzmiak, Vladimír

2016-01-01

Roč. 94, č. 3 (2016), č. článku 033845. ISSN 2469-9926 R&D Projects: GA MŠk(CZ) LD14028 Institutional support: RVO:67985882 Keywords : Crystal structure * Photonic crystals * Two-dimensional arrays Subject RIV: BH - Optics, Masers, Lasers Impact factor: 2.925, year: 2016

Evaluating two-dimensional skeletal structure parameters using radiological bone morphometric analysis

International Nuclear Information System (INIS)

Asa, Kensuke; Sakurai, Takashi; Kashima, Isamu; Kumasaka, Satsuki

2005-01-01

The objectives of this study was to investigate the reliability of two-dimensional (2D) skeletal structure parameters obtained using radiological bone morphometric analysis. The 2D skeletal parameters in the regions of interest (ROIs) were measured on computed radiography (CR) images of first phalanges from racehorses, using radiological bone morphometric analysis. Cancellous bone blocks were made from the phalanges in the same position as the ROI determined on CR images. Three-dimensional (3D) trabecular parameters were measured using micro-computed tomography (μCT). The correlations between the 2D skeletal parameters and 3D trabecular parameters were evaluated in relation to the measured bone strength. The following 2D skeletal structure parameters were correlated with bone strength (r=0.61-0.69): skeletal perimeter (Sk.Pm), skeletal number (Sk.N), skeletal separation (Sk.Sp), skeletal spacing (Sk.Spac), fractal dimension (FD), and skeletal pattern factor (SkPf). The 3D trabecular structure parameters were closely correlated with bone strength (r=0.74-0.86). The 2D skeletal parameters Sk.N, Sk.Pm, FD, SkPf, and Sk.Spac were correlated with the 3D trabecular parameters (r=0.61-0.70). The 2D skeletal parameters obtained using radiological bone morphometric analysis may be useful indicators of trabecular strength. (author)

Band structure and unconventional electronic topology of CoSi

Science.gov (United States)

Pshenay-Severin, D. A.; Ivanov, Y. V.; Burkov, A. A.; Burkov, A. T.

2018-04-01

Semimetals with certain crystal symmetries may possess unusual electronic structure topology, distinct from that of the conventional Weyl and Dirac semimetals. Characteristic property of these materials is the existence of band-touching points with multiple (higher than two-fold) degeneracy and nonzero Chern number. CoSi is a representative of this group of materials exhibiting the so-called ‘new fermions’. We report on an ab initio calculation of the electronic structure of CoSi using density functional methods, taking into account the spin-orbit interactions. The linearized \

Two-dimensional layer architecture assembled by Keggin polyoxotungstate, Cu(II)-EDTA complex and sodium linker: Synthesis, crystal structures, and magnetic properties

International Nuclear Information System (INIS)

Liu Hong; Xu Lin; Gao Guanggang; Li Fengyan; Yang Yanyan; Li Zhikui; Sun Yu

2007-01-01

Reaction of Keggin polyoxotungstate with copper(II)-EDTA (EDTA=ethylenediamine tetraacetate) complex under mild conditions led to the formation of hybrid inorganic-organic compounds Na 4 (OH)[(Cu 2 EDTA)PW 12 O 40 ].17H 2 O (1) and Na 4 [(Cu 2 EDTA)SiW 12 O 40 ].19H 2 O (2). The single-crystal X-ray diffraction analyses reveal their two structural features: (1) one-dimensional chain structure consisting of Keggin polyoxotungstate and copper(II)-EDTA complex; (2) Two-dimensional layer architecture assembled by the one-dimensional chain structure and sodium linker. The results of magnetic measurements in the temperature range 300-2 K indicated the existence of ferromagnetic exchange interactions between the Cu II ions for both compounds. In addition, TGA analysis, IR spectra, and electrochemical properties were also investigated to well characterize these two compounds. - Graphical abstract: Two new polyoxometalate-based hybrids, Na 4 (OH)[Cu 2 (EDTA)PW 12 O 40 ].17H 2 O (1) and Na 4 [Cu 2 (EDTA)SiW 12 O 40 ].19H 2 O (2), have been synthesized and structurally characterized, which consist of one-dimensional chain structure assembled by Keggin polyoxotungstate and copper(II)-EDTA complex. The chains are further connected to form two-dimensional layer architecture assembled by the one-dimensional chain structure and sodium linker

Genus Topology of Structure in the Sloan Digital Sky Survey: Model Testing

Science.gov (United States)

Gott, J. Richard, III; Hambrick, D. Clay; Vogeley, Michael S.; Kim, Juhan; Park, Changbom; Choi, Yun-Young; Cen, Renyue; Ostriker, Jeremiah P.; Nagamine, Kentaro

2008-03-01

We measure the three-dimensional topology of large-scale structure in the Sloan Digital Sky Survey (SDSS). This allows the genus statistic to be measured with unprecedented statistical accuracy. The sample size is now sufficiently large to allow the topology to be an important tool for testing galaxy formation models. For comparison, we make mock SDSS samples using several state-of-the-art N-body simulations: the Millennium run of Springel et al. (10 billion particles), the Kim & Park CDM models (1.1 billion particles), and the Cen & Ostriker hydrodynamic code models (8.6 billion cell hydro mesh). Each of these simulations uses a different method for modeling galaxy formation. The SDSS data show a genus curve that is broadly characteristic of that produced by Gaussian random-phase initial conditions. Thus, the data strongly support the standard model of inflation where Gaussian random-phase initial conditions are produced by random quantum fluctuations in the early universe. But on top of this general shape there are measurable differences produced by nonlinear gravitational effects and biasing connected with galaxy formation. The N-body simulations have been tuned to reproduce the power spectrum and multiplicity function but not topology, so topology is an acid test for these models. The data show a "meatball" shift (only partly due to the Sloan Great Wall of galaxies) that differs at the 2.5 σ level from the results of the Millenium run and the Kim & Park dark halo models, even including the effects of cosmic variance.

Direct Measurement of the Band Structure of a Buried Two-Dimensional Electron Gas

DEFF Research Database (Denmark)

Miwa, Jill; Hofmann, Philip; Simmons, Michelle Y.

2013-01-01

We directly measure the band structure of a buried two dimensional electron gas (2DEG) using angle resolved photoemission spectroscopy. The buried 2DEG forms 2 nm beneath the surface of p-type silicon, because of a dense delta-type layer of phosphorus n-type dopants which have been placed there...

Effect of Topology Structures on Synchronization Transition in Coupled Neuron Cells System

International Nuclear Information System (INIS)

Liang Li-Si; Zhang Ji-Qian; Xu Gui-Xia; Liu Le-Zhu; Huang Shou-Fang

2013-01-01

In this paper, by the help of evolutionary algorithm and using Hindmarsh—Rose (HR) neuron model, we investigate the effect of topology structures on synchronization transition between different states in coupled neuron cells system. First, we build different coupling structure with N cells, and found the effect of synchronized transition contact not only closely with the topology of the system, but also with whether there exist the ring structures in the system. In particular, both the size and the number of rings have greater effects on such transition behavior. Secondly, we introduce synchronization error to qualitative analyze the effect of the topology structure. Furthermore, by fitting the simulation results, we find that with the increment of the neurons number, there always exist the optimization structures which have the minimum number of connecting edges in the coupling systems. Above results show that the topology structures have a very crucial role on synchronization transition in coupled neuron system. Biological system may gradually acquire such efficient topology structures through the long-term evolution, thus the systems' information process may be optimized by this scheme. (interdisciplinary physics and related areas of science and technology)

Systematic design of photonic crystal structures using topology optimization: Low-loss waveguide bends

DEFF Research Database (Denmark)

Jensen, Jakob Søndergaard; Sigmund, Ole

2004-01-01

Topology optimization is a promising method for systematic design of optical devices. As an example, we demonstrate how the method can be used to design a 90degrees bend in a two-dimensional photonic crystal waveguide with a transmission loss of less than 0.3% in almost the entire frequency range...... of the guided mode. The method can directly be applied to the design of other optical devices, e.g., multiplexers and wave splitters, with optimized performance. (C) 2004 American Institute of Physics....

Probing the topological structure of the QCD vacuum with overlap fermions

International Nuclear Information System (INIS)

Ilgenfritz, E.M.; Schierholz, G.; Deutsches Elektronen-Synchrotron; Streuer, T.; Weinberg, V.; Freie Univ. Berlin

2005-12-01

Overlap fermions implement exact chiral symmetry on the lattice and are thus an appropriate tool for investigating the chiral and topological structure of the QCD vacuum. We study various chiral and topological aspects on Luescher-Weisz-type quenched gauge field configurations using overlap fermions as a probe. Particular emphasis is placed upon the analysis of the spectral density and the localisation properties of the eigenmodes as well as on the local structure of topological charge fluctuations. (orig.)

STRUCTURE LINE DETECTION FROM LIDAR POINT CLOUDS USING TOPOLOGICAL ELEVATION ANALYSIS

Directory of Open Access Journals (Sweden)

C. Y. Lo

2012-07-01

Full Text Available Airborne LIDAR point clouds, which have considerable points on object surfaces, are essential to building modeling. In the last two decades, studies have developed different approaches to identify structure lines using two main approaches, data-driven and modeldriven. These studies have shown that automatic modeling processes depend on certain considerations, such as used thresholds, initial value, designed formulas, and predefined cues. Following the development of laser scanning systems, scanning rates have increased and can provide point clouds with higher point density. Therefore, this study proposes using topological elevation analysis (TEA to detect structure lines instead of threshold-dependent concepts and predefined constraints. This analysis contains two parts: data pre-processing and structure line detection. To preserve the original elevation information, a pseudo-grid for generating digital surface models is produced during the first part. The highest point in each grid is set as the elevation value, and its original threedimensional position is preserved. In the second part, using TEA, the structure lines are identified based on the topology of local elevation changes in two directions. Because structure lines can contain certain geometric properties, their locations have small relieves in the radial direction and steep elevation changes in the circular direction. Following the proposed approach, TEA can be used to determine 3D line information without selecting thresholds. For validation, the TEA results are compared with those of the region growing approach. The results indicate that the proposed method can produce structure lines using dense point clouds.

A three-dimensional topology optimization model for tooth-root morphology.

Science.gov (United States)

Seitz, K-F; Grabe, J; Köhne, T

2018-02-01

To obtain the root of a lower incisor through structural optimization, we used two methods: optimization with Solid Isotropic Material with Penalization (SIMP) and Soft-Kill Option (SKO). The optimization was carried out in combination with a finite element analysis in Abaqus/Standard. The model geometry was based on cone-beam tomography scans of 10 adult males with healthy bone-tooth interface. Our results demonstrate that the optimization method using SIMP for minimum compliance could not adequately predict the actual root shape. The SKO method, however, provided optimization results that were comparable to the natural root form and is therefore suitable to set up the basic topology of a dental root.

Topology optimization of fluid-structure-interaction problems in poroelasticity

DEFF Research Database (Denmark)

Andreasen, Casper Schousboe; Sigmund, Ole

2013-01-01

This paper presents a method for applying topology optimization to fluid-structure interaction problems in saturated poroelastic media. The method relies on a multiple-scale method applied to periodic media. The resulting model couples the Stokes flow in the pores of the structure with the deform...... by topology optimization in order to optimize the performance of a shock absorber and test the pressure loading capabilities and optimization of an internally pressurized lid. © 2013 Published by Elsevier B.V....

Macroscopic Floquet topological crystalline steel and superconductor pump

Science.gov (United States)

Rossi, Anna M. E. B.; Bugase, Jonas; Fischer, Thomas M.

2017-08-01

The transport of a macroscopic steel sphere and a superconducting sphere on top of two-dimensional periodic magnetic patterns is studied experimentally and compared with the theory and with experiments on topological transport of magnetic colloids. Transport of the steel and superconducting sphere is achieved by moving an external permanent magnet on a closed loop around the two-dimensional crystal. The transport is topological, i.e., the spheres are transported by a primitive unit vector of the lattice when the external magnet loop winds around specific directions. We experimentally determine the set of directions the loops must enclose for nontrivial transport of the spheres into various directions. We show that the loops can be used to sort steel and superconducting spheres. We show that the topological transport is robust with respect to the scale of the system and therefore speculate on its down scalability to the molecular scale.

Single atom anisotropic magnetoresistance on a topological insulator surface

KAUST Repository

Narayan, Awadhesh

2015-03-12

© 2015 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. We demonstrate single atom anisotropic magnetoresistance on the surface of a topological insulator, arising from the interplay between the helical spin-momentum-locked surface electronic structure and the hybridization of the magnetic adatom states. Our first-principles quantum transport calculations based on density functional theory for Mn on Bi2Se3 elucidate the underlying mechanism. We complement our findings with a two dimensional model valid for both single adatoms and magnetic clusters, which leads to a proposed device setup for experimental realization. Our results provide an explanation for the conflicting scattering experiments on magnetic adatoms on topological insulator surfaces, and reveal the real space spin texture around the magnetic impurity.

Higher-order topological insulators and superconductors protected by inversion symmetry

Science.gov (United States)

Khalaf, Eslam

2018-05-01

We study surface states of topological crystalline insulators and superconductors protected by inversion symmetry. These fall into the category of "higher-order" topological insulators and superconductors which possess surface states that propagate along one-dimensional curves (hinges) or are localized at some points (corners) on the surface. We provide a complete classification of inversion-protected higher-order topological insulators and superconductors in any spatial dimension for the 10 symmetry classes by means of a layer construction. We discuss possible physical realizations of such states starting with a time-reversal-invariant topological insulator (class AII) in three dimensions or a time-reversal-invariant topological superconductor (class DIII) in two or three dimensions. The former exhibits one-dimensional chiral or helical modes propagating along opposite edges, whereas the latter hosts Majorana zero modes localized to two opposite corners. Being protected by inversion, such states are not pinned to a specific pair of edges or corners, thus offering the possibility of controlling their location by applying inversion-symmetric perturbations such as magnetic field.

Electronic structure engineering in silicene via atom substitution and a new two-dimensional Dirac structure Si3C

Science.gov (United States)

Yin, Na; Dai, Ying; Wei, Wei; Huang, Baibiao

2018-04-01

A lot of efforts have been made towards the band gap opening in two-dimensional silicene, the silicon version of graphene. In the present work, the electronic structures of single atom doped (B, N, Al and P) and codoped (B/N and Al/P) silicene monolayers are systematically examined on the base of density functional electronic calculations. Our results demonstrate that single atom doping can realize electron or hole doping in the silicene; while codoping, due to the syergistic effects, results in finite band gap in silicene at the Dirac point without significantly degrading the electronic properties. In addition, the characteristic of band gap shows dependence on the doping concentration. Importantly, we predict a new two-dimensional Dirac structure, the graphene-like Si3C, which also shows linear band dispersion relation around the Fermi level. Our results demonstrates an important perspective to engineer the electronic and optical properties of silicene.

A geometrical approach to two-dimensional Conformal Field Theory

Science.gov (United States)

Dijkgraaf, Robertus Henricus

1989-09-01

manifold obtained as the quotient of a smooth manifold by a discrete group. In Chapter 6 our considerations will be of a somewhat complementary nature. We will investigate models with central charge c = 1 by deformation techniques. The central charge is a fundamental parameter in any conformal invariant model, and the value c = 1 is of considerable interest, since it forms in many ways a threshold value. For c 1 is still very much terra incognita. Our results give a partial classification for the intermediate case of c = 1 models. The formulation of these c = 1 CFT's on surfaces of arbitrary topology is central in Chapter 7. Here we will provide many explicit results that provide illustrations for our more abstract discussions of higher genus quantities in Chapters 3 and 1. Unfortunately, our calculations will become at this point rather technical, since we have to make extensive use of the mathematics of Riemann surfaces and their coverings. Finally, in Chapter 8 we leave the two-dimensional point of view that we have been so loyal to up to then , and ascend to threedimensions where we meet topological gauge theories. These so-called Chern-Simons theories encode in a very economic way much of the structure of two-dimensional (rational) conformal field theories, and this direction is generally seen to be very promising. We will show in particular how many of our results of Chapter 5 have a natural interpretation in three dimensions.

Photonic density of states of two-dimensional quasicrystalline photonic structures

International Nuclear Information System (INIS)

Jia Lin; Bita, Ion; Thomas, Edwin L.

2011-01-01

A large photonic band gap (PBG) is highly favorable for photonic crystal devices. One of the most important goals of PBG materials research is identifying structural design strategies for maximizing the gap size. We provide a comprehensive analysis of the PBG properties of two-dimensional (2D) quasicrystals (QCs), where rotational symmetry, dielectric fill factor, and structural morphology were varied systematically in order to identify correlations between structure and PBG width at a given dielectric contrast (13:1, Si:air). The transverse electric (TE) and transverse magnetic (TM) PBGs of 12 types of QCs are investigated (588 structures). We discovered a 12mm QC with a 56.5% TE PBG, the largest reported TE PBG for an aperiodic crystal to date. We also report here a QC morphology comprising ''throwing star''-like dielectric domains, with near-circular air cores and interconnecting veins emanating radially around the core. This interesting morphology leads to a complete PBG of ∼20% , which is the largest reported complete PBG for aperiodic crystals.

The universe as a topological defect in a higher-dimensional Einstein-Yang-Mills theory

International Nuclear Information System (INIS)

Nakamura, A.; Shiraishi, K.

1989-04-01

An interpretation is suggested that a spontaneous compactification of space-time can be regarded as a topological defect in a higher-dimensional Einstein-Yang-Mills (EYM) theory. We start with D-dimensional EYM theory in our present analysis. A compactification leads to a D-2 dimensional effective action of Abelian gauge-Higgs theory. We find a 'vortex' solution in the effective theory. Our universe appears to be confined in a center of a 'vortex', which has D-4 large dimensions. In this paper we show an example with SU (2) symmetry in the original EYM theory, and the resulting solution is found to be equivalent to the 'instanton-induced compactification'. The cosmological implication is also mentioned. (author)

Lateral phase drift of the topological charge density in stochastic optical fields

CSIR Research Space (South Africa)

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...

The direct field boundary impedance of two-dimensional periodic structures with application to high frequency vibration prediction.

Science.gov (United States)

Langley, Robin S; Cotoni, Vincent

2010-04-01

Large sections of many types of engineering construction can be considered to constitute a two-dimensional periodic structure, with examples ranging from an orthogonally stiffened shell to a honeycomb sandwich panel. In this paper, a method is presented for computing the boundary (or edge) impedance of a semi-infinite two-dimensional periodic structure, a quantity which is referred to as the direct field boundary impedance matrix. This terminology arises from the fact that none of the waves generated at the boundary (the direct field) are reflected back to the boundary in a semi-infinite system. The direct field impedance matrix can be used to calculate elastic wave transmission coefficients, and also to calculate the coupling loss factors (CLFs), which are required by the statistical energy analysis (SEA) approach to predicting high frequency vibration levels in built-up systems. The calculation of the relevant CLFs enables a two-dimensional periodic region of a structure to be modeled very efficiently as a single subsystem within SEA, and also within related methods, such as a recently developed hybrid approach, which couples the finite element method with SEA. The analysis is illustrated by various numerical examples involving stiffened plate structures.

Topological Vortex and Knotted Dissipative Optical 3D Solitons Generated by 2D Vortex Solitons.

Science.gov (United States)

Veretenov, N A; Fedorov, S V; Rosanov, N N

2017-12-29

We predict a new class of three-dimensional (3D) topological dissipative optical one-component solitons in homogeneous laser media with fast saturable absorption. Their skeletons formed by vortex lines where the field vanishes are tangles, i.e., N_{c} knotted or unknotted, linked or unlinked closed lines and M unclosed lines that thread all the closed lines and end at the infinitely far soliton periphery. They are generated by embedding two-dimensional laser solitons or their complexes in 3D space after their rotation around an unclosed, infinite vortex line with topological charge M_{0} (N_{c}, M, and M_{0} are integers). With such structure propagation, the "hula-hoop" solitons form; their stability is confirmed numerically. For the solitons found, all vortex lines have unit topological charge: the number of closed lines N_{c}=1 and 2 (unknots, trefoils, and Solomon knots links); unclosed vortex lines are unknotted and unlinked, their number M=1, 2, and 3.

Electronic structure and transport on the surface of topological insulator attached to an electromagnetic superlattice

International Nuclear Information System (INIS)

Wang Haiyan; Chen Xiongwen; Zhou Xiaoying; Zhang Lebo; Zhou Guanghui

2012-01-01

We study the electronic structure and transport for Dirac electron on the surface of a three-dimensional (3D) topological insulator attached to an electromagnetic superlattice. It is found that, by means of the transfer-matrix method, the number of electronic tunneling channels for magnetic barriers in antiparallel alignment is larger than that in parallel alignment, which stems to the energy band structures. Interestingly, a remarkable semiconducting transport behavior appears in this system with a strong magnetic barrier due to low energy band nearly paralleling to the Fermi level. Consequently, there is only small incident angle transport in the higher energy region when the system is modulated mainly by the higher electric barriers. We further find that the spatial distribution of the spin polarization oscillates periodically in the incoming region, but it is almost in-plane with a fixed direction in the transmitting region. The results may provide a further understanding of the nature of 3D TI surface states, and may be useful in the design of topological insulator-based electronic devices such as collimating electron beam.

Emergent Topological Phenomena in Thin Films of Pyrochlore Iridates

Science.gov (United States)

Yang, Bohm-Jung; Nagaosa, Naoto

2014-06-01

Because of the recent development of thin film and artificial superstructure growth techniques, it is possible to control the dimensionality of the system, smoothly between two and three dimensions. In this Letter we unveil the dimensional crossover of emergent topological phenomena in correlated topological materials. In particular, by focusing on the thin film of pyrochlore iridate antiferromagnets grown along the [111] direction, we demonstrate that the thin film can have a giant anomalous Hall conductance, proportional to the thickness of the film, even though there is no Hall effect in 3D bulk material. Moreover, in the case of ultrathin films, a quantized anomalous Hall conductance can be observed, despite the fact that the system is an antiferromagnet. In addition, we uncover the emergence of a new topological phase, the nontrivial topological properties of which are hidden in the bulk insulator and manifest only in thin films. This shows that the thin film of correlated topological materials is a new platform to search for unexplored novel topological phenomena.

Topology optimization of 3D shell structures with porous infill

DEFF Research Database (Denmark)

Clausen, Anders; Andreassen, Erik; Sigmund, Ole

2017-01-01

This paper presents a 3D topology optimization approach for designing shell structures with a porous or void interior. It is shown that the resulting structures are significantly more robust towards load perturbations than completely solid structures optimized under the same conditions. The study...... indicates that the potential benefit of using porous structures is higher for lower total volume fractions. Compared to earlier work dealing with 2D topology optimization, we found several new effects in 3D problems. Most notably, the opportunity for designing closed shells significantly improves...

Design of complex bone internal structure using topology optimization with perimeter control.

Science.gov (United States)

Park, Jaejong; Sutradhar, Alok; Shah, Jami J; Paulino, Glaucio H

2018-03-01

Large facial bone loss usually requires patient-specific bone implants to restore the structural integrity and functionality that also affects the appearance of each patient. Titanium alloys (e.g., Ti-6Al-4V) are typically used in the interfacial porous coatings between the implant and the surrounding bone to promote stability. There exists a property mismatch between the two that in general leads to complications such as stress-shielding. This biomechanical discrepancy is a hurdle in the design of bone replacements. To alleviate the mismatch, the internal structure of the bone replacements should match that of the bone. Topology optimization has proven to be a good technique for designing bone replacements. However, the complex internal structure of the bone is difficult to mimic using conventional topology optimization methods without additional restrictions. In this work, the complex bone internal structure is recovered using a perimeter control based topology optimization approach. By restricting the solution space by means of the perimeter, the intricate design complexity of bones can be achieved. Three different bone regions with well-known physiological loadings are selected to illustrate the method. Additionally, we found that the target perimeter value and the pattern of the initial distribution play a vital role in obtaining the natural curvatures in the bone internal structures as well as avoiding excessive island patterns. Copyright © 2018 Elsevier Ltd. All rights reserved.

A new topology for curved space--time which incorporates the causal, differential, and conformal structures

International Nuclear Information System (INIS)

Hawking, S.W.; King, A.R.; McCarthy, P.J.

1976-01-01

A new topology is proposed for strongly causal space--times. Unlike the standard manifold topology (which merely characterizes continuity properties), the new topology determines the causal, differential, and conformal structures of space--time. The topology is more appealing, physical, and manageable than the topology previously proposed by Zeeman for Minkowski space. It thus seems that many calculations involving the above structures may be made purely topological

Definition of the topological structure of the automatic control system of spacecrafts

International Nuclear Information System (INIS)

KrasnoyarskiyRabochiy prospect, Krasnoyarsk, 660014 (Russian Federation))" data-affiliation=" (Siberian State Aerospace University named after Academician M.F.Reshetnev 31 KrasnoyarskiyRabochiy prospect, Krasnoyarsk, 660014 (Russian Federation))" >Zelenkov, P V; KrasnoyarskiyRabochiy prospect, Krasnoyarsk, 660014 (Russian Federation))" data-affiliation=" (Siberian State Aerospace University named after Academician M.F.Reshetnev 31 KrasnoyarskiyRabochiy prospect, Krasnoyarsk, 660014 (Russian Federation))" >Karaseva, M V; KrasnoyarskiyRabochiy prospect, Krasnoyarsk, 660014 (Russian Federation))" data-affiliation=" (Siberian State Aerospace University named after Academician M.F.Reshetnev 31 KrasnoyarskiyRabochiy prospect, Krasnoyarsk, 660014 (Russian Federation))" >Tsareva, E A; Tsarev, R Y

2015-01-01

The paper considers the problem of selection the topological structure of the automated control system of spacecrafts. The integer linear model of mathematical programming designed to define the optimal topological structure for spacecraft control is proposed. To solve the determination problem of topological structure of the control system of spacecrafts developed the procedure of the directed search of some structure variants according to the scheme 'Branch and bound'. The example of the automated control system of spacecraft development included the combination of ground control stations, managing the spacecraft of three classes with a geosynchronous orbit with constant orbital periods is presented

The topology of large-scale structure. III. Analysis of observations

International Nuclear Information System (INIS)

Gott, J.R. III; Weinberg, D.H.; Miller, J.; Thuan, T.X.; Schneider, S.E.

1989-01-01

A recently developed algorithm for quantitatively measuring the topology of large-scale structures in the universe was applied to a number of important observational data sets. The data sets included an Abell (1958) cluster sample out to Vmax = 22,600 km/sec, the Giovanelli and Haynes (1985) sample out to Vmax = 11,800 km/sec, the CfA sample out to Vmax = 5000 km/sec, the Thuan and Schneider (1988) dwarf sample out to Vmax = 3000 km/sec, and the Tully (1987) sample out to Vmax = 3000 km/sec. It was found that, when the topology is studied on smoothing scales significantly larger than the correlation length (i.e., smoothing length, lambda, not below 1200 km/sec), the topology is spongelike and is consistent with the standard model in which the structure seen today has grown from small fluctuations caused by random noise in the early universe. When the topology is studied on the scale of lambda of about 600 km/sec, a small shift is observed in the genus curve in the direction of a meatball topology. 66 refs

The topology of large-scale structure. III - Analysis of observations

Science.gov (United States)

Gott, J. Richard, III; Miller, John; Thuan, Trinh X.; Schneider, Stephen E.; Weinberg, David H.; Gammie, Charles; Polk, Kevin; Vogeley, Michael; Jeffrey, Scott; Bhavsar, Suketu P.; Melott, Adrian L.; Giovanelli, Riccardo; Hayes, Martha P.; Tully, R. Brent; Hamilton, Andrew J. S.

1989-05-01

A recently developed algorithm for quantitatively measuring the topology of large-scale structures in the universe was applied to a number of important observational data sets. The data sets included an Abell (1958) cluster sample out to Vmax = 22,600 km/sec, the Giovanelli and Haynes (1985) sample out to Vmax = 11,800 km/sec, the CfA sample out to Vmax = 5000 km/sec, the Thuan and Schneider (1988) dwarf sample out to Vmax = 3000 km/sec, and the Tully (1987) sample out to Vmax = 3000 km/sec. It was found that, when the topology is studied on smoothing scales significantly larger than the correlation length (i.e., smoothing length, lambda, not below 1200 km/sec), the topology is spongelike and is consistent with the standard model in which the structure seen today has grown from small fluctuations caused by random noise in the early universe. When the topology is studied on the scale of lambda of about 600 km/sec, a small shift is observed in the genus curve in the direction of a 'meatball' topology.

Spin-orbit torque in a three-dimensional topological insulator–ferromagnet heterostructure: Crossover between bulk and surface transport

KAUST Repository

Ghosh, Sumit; Manchon, Aurelien

2018-01-01

Current-driven spin-orbit torques are investigated in a heterostructure composed of a ferromagnet deposited on top of a three-dimensional topological insulator using the linear response formalism. We develop a tight-binding model of the heterostructure adopting a minimal interfacial hybridization scheme that promotes induced magnetic exchange on the topological surface states, as well as induced Rashba-like spin-orbit coupling in the ferromagnet. Therefore our model accounts for the spin Hall effect from bulk states together with inverse spin galvanic and magnetoelectric effects at the interface on equal footing. By varying the transport energy across the band structure, we uncover a crossover from surface-dominated to bulk-dominated transport regimes. We show that the spin density profile and the nature of the spin-orbit torques differ substantially in both regimes. Our results, which compare favorably with experimental observations, demonstrate that the large dampinglike torque reported recently is more likely attributed to the Berry curvature of interfacial states, while spin Hall torque remains small even in the bulk-dominated regime.

Spin-orbit torque in a three-dimensional topological insulator–ferromagnet heterostructure: Crossover between bulk and surface transport

KAUST Repository

Ghosh, Sumit

2018-04-02

Current-driven spin-orbit torques are investigated in a heterostructure composed of a ferromagnet deposited on top of a three-dimensional topological insulator using the linear response formalism. We develop a tight-binding model of the heterostructure adopting a minimal interfacial hybridization scheme that promotes induced magnetic exchange on the topological surface states, as well as induced Rashba-like spin-orbit coupling in the ferromagnet. Therefore our model accounts for the spin Hall effect from bulk states together with inverse spin galvanic and magnetoelectric effects at the interface on equal footing. By varying the transport energy across the band structure, we uncover a crossover from surface-dominated to bulk-dominated transport regimes. We show that the spin density profile and the nature of the spin-orbit torques differ substantially in both regimes. Our results, which compare favorably with experimental observations, demonstrate that the large dampinglike torque reported recently is more likely attributed to the Berry curvature of interfacial states, while spin Hall torque remains small even in the bulk-dominated regime.

The effect of van der Waal's gap expansions on the surface electronic structure of layered topological insulators

International Nuclear Information System (INIS)

Eremeev, S V; Vergniory, M G; Chulkov, E V; Menshchikova, T V; Shaposhnikov, A A

2012-01-01

On the basis of relativistic ab initio calculations, we show that an expansion of van der Waal's (vdW) spacings in layered topological insulators caused by intercalation of deposited atoms, leads to the simultaneous emergence of parabolic and M-shaped two-dimensional electron gas (2DEG) bands as well as Rashba-splitting of the former states. The expansion of vdW spacings and the emergence of the 2DEG states localized in the (sub)surface region are also accompanied by a relocation of the topological surface state to the lower quintuple layers, that can explain the absence of inter-band scattering found experimentally. (paper)

Synthesis, Crystal Structures, and Photoluminescent Properties of Two Supramolecular Architectures Based on Difunctional Ligands Containing Imidazolyl and Carboxyl Groups

Directory of Open Access Journals (Sweden)

Mei-An Zhu

2017-07-01

Full Text Available Two new supramolecular architectures, namely, [Cd(L12(H2O]n (1 and [Ni(L22(H2O]n (2, were synthesized by the reaction of corresponding metal salts of CdCl2·2.5H2O and NiCl2·6H2O with 2-(1H-imidazol-4-ylbenzoic acid (HL1 and 3-(1H-imidazol-4-ylbenzoic acid (HL2 respectively, and characterized by single-crystal X-ray diffraction, IR spectroscopy, elemental analysis and powder X-ray diffraction (PXRD. Both HL1 and HL2 ligands are deprotonated to be L1- and L2- anions that coordinate with Cd(II and Ni(II atoms to form two-dimensional (2D layer structure. Topologically, complex 1 is a 2D network with (4, 4 sql topology, while 2 is a typical 63-hcb topology net. Complex 1 exhibits intense light blue emission in the solid state at room temperature.

Current-induced switching of magnetic molecules on topological insulator surfaces

Science.gov (United States)

Locane, Elina; Brouwer, Piet W.

2017-03-01

Electrical currents at the surface or edge of a topological insulator are intrinsically spin polarized. We show that such surface or edge currents can be used to switch the orientation of a molecular magnet weakly coupled to the surface or edge of a topological insulator. For the edge of a two-dimensional topological insulator as well as for the surface of a three-dimensional topological insulator the application of a well-chosen surface or edge current can lead to a complete polarization of the molecule if the molecule's magnetic anisotropy axis is appropriately aligned with the current direction. For a generic orientation of the molecule a nonzero but incomplete polarization is obtained. We calculate the probability distribution of the magnetic states and the switching rates as a function of the applied current.

The role of spin–orbit coupling in topologically protected interface states in Dirac materials

International Nuclear Information System (INIS)

Abergel, D S L; Balatsky, Alexander V; Edge, Jonathan M

2014-01-01

We highlight the fact that two-dimensional (2D) materials with Dirac-like low energy band structures and spin–orbit coupling (SOC) will produce linearly dispersing topologically protected Jackiw–Rebbi modes at interfaces where the Dirac mass changes sign. These modes may support persistent spin or valley currents parallel to the interface, and the exact arrangement of such topologically protected currents depends crucially on the details of the SOC in the material. As examples, we discuss buckled 2D hexagonal lattices such as silicene or germanene, and transition metal dichalcogenides such as MoS 2 . (paper)

Mechanical exfoliation of two-dimensional materials

Science.gov (United States)

Gao, Enlai; Lin, Shao-Zhen; Qin, Zhao; Buehler, Markus J.; Feng, Xi-Qiao; Xu, Zhiping

2018-06-01

Two-dimensional materials such as graphene and transition metal dichalcogenides have been identified and drawn much attention over the last few years for their unique structural and electronic properties. However, their rise begins only after these materials are successfully isolated from their layered assemblies or adhesive substrates into individual monolayers. Mechanical exfoliation and transfer are the most successful techniques to obtain high-quality single- or few-layer nanocrystals from their native multi-layer structures or their substrate for growth, which involves interfacial peeling and intralayer tearing processes that are controlled by material properties, geometry and the kinetics of exfoliation. This procedure is rationalized in this work through theoretical analysis and atomistic simulations. We propose a criterion to assess the feasibility for the exfoliation of two-dimensional sheets from an adhesive substrate without fracturing itself, and explore the effects of material and interface properties, as well as the geometrical, kinetic factors on the peeling behaviors and the torn morphology. This multi-scale approach elucidates the microscopic mechanism of the mechanical processes, offering predictive models and tools for the design of experimental procedures to obtain single- or few-layer two-dimensional materials and structures.

Topological structures of adiabatic phase for multi-level quantum systems

International Nuclear Information System (INIS)

Liu Zhengxin; Zhou Xiaoting; Liu Xin; Liu Xiongjun; Chen Jingling

2007-01-01

The topological properties of adiabatic gauge fields for multi-level (three-level in particular) quantum systems are studied in detail. Similar to the result that the adiabatic gauge field for SU(2) systems (e.g. two-level quantum system or angular momentum systems, etc) has a monopole structure, the curvature 2-forms of the adiabatic holonomies for SU(3) three-level and SU(3) eight-level quantum systems are shown to have monopole-like (for all levels) or instanton-like (for the degenerate levels) structures

Evolution of two-dimensional soap froth with a single defect

International Nuclear Information System (INIS)

Levitan, B.

1994-01-01

The temporal evolution of two-dimensional soap froth, starting from a particle initial state, is studied. The initial state is a hexagonal array of bubbles in which a single defect is introduced. A cluster of transformed bubbles grows; the time dependence of the number of bubbles in this cluster in investigated and the distribution of the topological classes in the evolving part of the system is calculated. The distribution appears to approach a fixed limiting one, which differs from that obtained for the usual scaling state of the froth

Network dynamics and its relationships to topology and coupling structure in excitable complex networks

International Nuclear Information System (INIS)

Zhang Li-Sheng; Mi Yuan-Yuan; Gu Wei-Feng; Hu Gang

2014-01-01

All dynamic complex networks have two important aspects, pattern dynamics and network topology. Discovering different types of pattern dynamics and exploring how these dynamics depend on network topologies are tasks of both great theoretical importance and broad practical significance. In this paper we study the oscillatory behaviors of excitable complex networks (ECNs) and find some interesting dynamic behaviors of ECNs in oscillatory probability, the multiplicity of oscillatory attractors, period distribution, and different types of oscillatory patterns (e.g., periodic, quasiperiodic, and chaotic). In these aspects, we further explore strikingly sharp differences among network dynamics induced by different topologies (random or scale-free topologies) and different interaction structures (symmetric or asymmetric couplings). The mechanisms behind these differences are explained physically. (interdisciplinary physics and related areas of science and technology)

Cooling as a method of finding topological dislocations in lattice models

International Nuclear Information System (INIS)

Gomberoff, K.

1989-01-01

It is well known that the O(3) two-dimensional model has configurations with topological charge Q=1 and action S/sub min/=6.69. Since the exponent characterizing the renormalization-group behavior of this model is 4π such configurations invalidate the standard scaling behavior of the topological susceptibility. The analog exponent for the four-dimensional lattice SU(2) gauge model is 10.77. If there would exist configurations with Q=1 and S<10.77 in this model, they would invalidate the standard scaling behavior of its topological susceptibility. Kremer et al. have calculated the action of different configurations during cooling runs. They report that they do not find any configuration with S<12.7 and Q=1. I show that in the O(3) two-dimensional model cooling runs fail to uncover the well-known configurations with S<8. We conclude that the cooling method is not effective in uncovering the smallest action configurations in the Q=1 sector

Hall conductance and topological invariant for open systems.

Science.gov (United States)

Shen, H Z; Wang, W; Yi, X X

2014-09-24

The Hall conductivity given by the Kubo formula is a linear response of quantum transverse transport to a weak electric field. It has been intensively studied for quantum systems without decoherence, but it is barely explored for systems subject to decoherence. In this paper, we develop a formulism to deal with this issue for topological insulators. The Hall conductance of a topological insulator coupled to an environment is derived, the derivation is based on a linear response theory developed for open systems in this paper. As an application, the Hall conductance of a two-band topological insulator and a two-dimensional lattice is presented and discussed.

Extended Polymorphism of Two-Dimensional Material

NARCIS (Netherlands)

Yoshida, Masaro; Ye, Jianting; Zhang, Yijin; Imai, Yasuhiko; Kimura, Shigeru; Fujiwara, Akihiko; Nishizaki, Terukazu; Kobayashi, Norio; Nakano, Masaki; Iwasa, Yoshihiro

When controlling electronic properties of bulk materials, we usually assume that the basic crystal structure is fixed. However, in two-dimensional (2D) materials, atomic structure or to functionalize their properties. Various polymorphs can exist in transition metal dichalcogenides (TMDCs) from

Topological photonic crystals with zero Berry curvature

Science.gov (United States)

Liu, Feng; Deng, Hai-Yao; Wakabayashi, Katsunori

2018-02-01

Topological photonic crystals are designed based on the concept of Zak's phase rather than the topological invariants such as the Chern number and spin Chern number, which rely on the existence of a nonvanishing Berry curvature. Our photonic crystals (PCs) are made of pure dielectrics and sit on a square lattice obeying the C4 v point-group symmetry. Two varieties of PCs are considered: one closely resembles the electronic two-dimensional Su-Schrieffer-Heeger model, and the other continues as an extension of this analogy. In both cases, the topological transitions are induced by adjusting the lattice constants. Topological edge modes (TEMs) are shown to exist within the nontrivial photonic band gaps on the termination of those PCs. The high efficiency of these TEMs transferring electromagnetic energy against several types of disorders has been demonstrated using the finite-element method.

Percolation Analysis as a Tool to Describe the Topology of the Large Scale Structure of the Universe

Science.gov (United States)

Yess, Capp D.

1997-09-01

Percolation analysis is the study of the properties of clusters. In cosmology, it is the statistics of the size and number of clusters. This thesis presents a refinement of percolation analysis and its application to astronomical data. An overview of the standard model of the universe and the development of large scale structure is presented in order to place the study in historical and scientific context. Then using percolation statistics we, for the first time, demonstrate the universal character of a network pattern in the real space, mass distributions resulting from nonlinear gravitational instability of initial Gaussian fluctuations. We also find that the maximum of the number of clusters statistic in the evolved, nonlinear distributions is determined by the effective slope of the power spectrum. Next, we present percolation analyses of Wiener Reconstructions of the IRAS 1.2 Jy Redshift Survey. There are ten reconstructions of galaxy density fields in real space spanning the range β = 0.1 to 1.0, where β=Ω0.6/b,/ Ω is the present dimensionless density and b is the linear bias factor. Our method uses the growth of the largest cluster statistic to characterize the topology of a density field, where Gaussian randomized versions of the reconstructions are used as standards for analysis. For the reconstruction volume of radius, R≈100h-1 Mpc, percolation analysis reveals a slight 'meatball' topology for the real space, galaxy distribution of the IRAS survey. Finally, we employ a percolation technique developed for pointwise distributions to analyze two-dimensional projections of the three northern and three southern slices in the Las Campanas Redshift Survey and then give consideration to further study of the methodology, errors and application of percolation. We track the growth of the largest cluster as a topological indicator to a depth of 400 h-1 Mpc, and report an unambiguous signal, with high signal-to-noise ratio, indicating a network topology which in

Broadband Emission in Two-Dimensional Hybrid Perovskites: The Role of Structural Deformation.

Science.gov (United States)

Cortecchia, Daniele; Neutzner, Stefanie; Srimath Kandada, Ajay Ram; Mosconi, Edoardo; Meggiolaro, Daniele; De Angelis, Filippo; Soci, Cesare; Petrozza, Annamaria

2017-01-11

Only a selected group of two-dimensional (2D) lead-halide perovskites shows a peculiar broad-band photoluminescence. Here we show that the structural distortions of the perovskite lattice can determine the defectivity of the material by modulating the defect formation energies. By selecting and comparing two archetype systems, namely, (NBT) 2 PbI 4 and (EDBE)PbI 4 perovskites (NBT = n-butylammonium and EDBE = 2,2-(ethylenedioxy)bis(ethylammonium)), we find that only the latter, subject to larger deformation of the Pb-X bond length and X-Pb-X bond angles, sees the formation of V F color centers whose radiative decay ultimately leads to broadened PL. These findings highlight the importance of structural engineering to control the optoelectronic properties of this class of soft materials.

Two-Dimensional Nuclear Magnetic Resonance Structure Determination Module for Introductory Biochemistry: Synthesis and Structural Characterization of Lyso-Glycerophospholipids

Science.gov (United States)

Garrett, Teresa A.; Rose, Rebecca L.; Bell, Sidney M.

2013-01-01

In this laboratory module, introductory biochemistry students are exposed to two-dimensional [superscript 1]H-nuclear magnetic resonance of glycerophospholipids (GPLs). Working in groups of three, students enzymatically synthesized and purified a variety of 2-acyl lyso GPLs. The structure of the 2-acyl lyso GPL was verified using [superscript…

Two-dimensional confinement of heavy fermions

International Nuclear Information System (INIS)

Shishido, Hiroaki; Shibauchi, Takasada; Matsuda, Yuji; Terashima, Takahito

2010-01-01

Metallic systems with the strongest electron correlations are realized in certain rare-earth and actinide compounds whose physics are dominated by f-electrons. These materials are known as heavy fermions, so called because the effective mass of the conduction electrons is enhanced via correlation effects up to as much as several hundreds times the free electron mass. To date the electronic structure of all heavy-fermion compounds is essentially three-dimensional. Here we report on the first realization of a two-dimensional heavy-fermion system, where the dimensionality is adjusted in a controllable fashion by fabricating heterostructures using molecular beam epitaxy. The two-dimensional heavy fermion system displays striking deviations from the standard Fermi liquid low-temperature electronic properties. (author)

Three-Dimensional Dynamic Topology Optimization with Frequency Constraints Using Composite Exponential Function and ICM Method

Directory of Open Access Journals (Sweden)

Hongling Ye

2015-01-01

Full Text Available The dynamic topology optimization of three-dimensional continuum structures subject to frequency constraints is investigated using Independent Continuous Mapping (ICM design variable fields. The composite exponential function (CEF is selected to be a filter function which recognizes the design variables and to implement the changing process of design variables from “discrete” to “continuous” and back to “discrete.” Explicit formulations of frequency constraints are given based on filter functions, first-order Taylor series expansion. And an improved optimal model is formulated using CEF and the explicit frequency constraints. Dual sequential quadratic programming (DSQP algorithm is used to solve the optimal model. The program is developed on the platform of MSC Patran & Nastran. Finally, numerical examples are given to demonstrate the validity and applicability of the proposed method.

Topology and geometry of six-dimensional (1, 0) supergravity black hole horizons

International Nuclear Information System (INIS)

Akyol, M; Papadopoulos, G

2012-01-01

We show that the supersymmetric near horizon black hole geometries of six-dimensional supergravity coupled to any number of scalar and tensor multiplets are either locally AdS 3 x Σ 3 , where Σ 3 is a homology 3-sphere, or R 1,1 )xS 4 , where S 4 is a 4-manifold whose geometry depends on the hypermultiplet scalars. In both cases, we find that the tensorini multiplet scalars are constant and the associated 3-form field strengths vanish. We also demonstrate that the AdS 3 x Σ 3 horizons preserve two, four and eight supersymmetries. For horizons with four supersymmetries, Σ 3 is in addition a non-trivial circle fibration over a topological 2-sphere. The near horizon geometries preserving eight supersymmetries are locally isometric to either AdS 3 x S 3 or R 1, 1 x T 4 . Moreover, we show that the R 1,1 xS horizons preserve one, two and four supersymmetries and the geometry of S is Riemann, Kaehler and hyper-Kaehler, respectively. (paper)

Oscillations of the positive column plasma due to ionization wave propagation and two-dimensional structure of striations

International Nuclear Information System (INIS)

Golubovskii, Yu B; Kozakov, R V; Wilke, C; Behnke, J; Nekutchaev, V O

2004-01-01

Time and space resolved measurements of the plasma potential in axial and radial directions in S- and P-striations in neon are performed. The measurements in different radial positions were carried out with high spatial resolution by means of simultaneous displacement of electrodes relative to the stationary probe. The plasma potential was found to be a superposition of the potentials of ionization wave and plasma oscillations relative to the electrodes. A method of decomposition of the measured spatio-temporal structure of the potential in components associated with the plasma oscillations and ionization wave propagation is proposed. A biorthogonal decomposition of the spatio-temporal structure of the potential is performed. A comparison of the decomposition results obtained by the two methods is made. The experiments revealed a two-dimensional structure of the potential field in an ionization wave. Qualitative discussions of the reasons for the occurrence of this two-dimensional structure are presented based on the analysis of the kinetic equation and the equation for the potential

Laterally structured ripple and square phases with one and two dimensional thickness modulations in a model bilayer system.

Science.gov (United States)

Debnath, Ananya; Thakkar, Foram M; Maiti, Prabal K; Kumaran, V; Ayappa, K G

2014-10-14

Molecular dynamics simulations of bilayers in a surfactant/co-surfactant/water system with explicit solvent molecules show formation of topologically distinct gel phases depending upon the bilayer composition. At low temperatures, the bilayers transform from the tilted gel phase, Lβ', to the one dimensional (1D) rippled, Pβ' phase as the surfactant concentration is increased. More interestingly, we observe a two dimensional (2D) square phase at higher surfactant concentration which, upon heating, transforms to the gel Lβ' phase. The thickness modulations in the 1D rippled and square phases are asymmetric in two surfactant leaflets and the bilayer thickness varies by a factor of ∼2 between maximum and minimum. The 1D ripple consists of a thinner interdigitated region of smaller extent alternating with a thicker non-interdigitated region. The 2D ripple phase is made up of two superimposed square lattices of maximum and minimum thicknesses with molecules of high tilt forming a square lattice translated from the lattice formed with the thickness minima. Using Voronoi diagrams we analyze the intricate interplay between the area-per-head-group, height modulations and chain tilt for the different ripple symmetries. Our simulations indicate that composition plays an important role in controlling the formation of low temperature gel phase symmetries and rippling accommodates the increased area-per-head-group of the surfactant molecules.

Fine topology and locally Minkowskian manifolds

Science.gov (United States)

Agrawal, Gunjan; Sinha, Soami Pyari

2018-05-01

Fine topology is one of the several well-known topologies of physical and mathematical relevance. In the present paper, it is obtained that the nonempty open sets of different dimensional Minkowski spaces with the fine topology are not homeomorphic. This leads to the introduction of a new class of manifolds. It turns out that the technique developed here is also applicable to some other topologies, namely, the s-topology, space topology, f-topology, and A-topology.