The fractional quantum Hall effect
International Nuclear Information System (INIS)
Stormer, H.L.
1988-01-01
The fractional quantum Hall effect (FQHE), is the manifestation of a new, highly correlated, many-particle ground state that forms in a two-dimensional electron system at low temperatures and in high magnetic fields. It is an example of the new physics that has grown out of the tremendous recent advances in semiconductor material science, which has provided us with high-quality, lower-dimensional carrier systems. The novel electronic state exposes itself in transport experiments through quantization of the Hall resistance to an exact rational fraction of h/e, and concomitantly vanishing longitudinal resistivity. Its relevant energy scale is only a few degrees kelvin. The quantization is a consequence of the spontaneous formation of an energy gap separating the condensed ground state from its rather elusive quasiparticle excitations. The theoretical understanding of the novel quantum liquids which underlie the FQHE has predominantly emerged from an ingenious many-particle wave function strongly supported by numerous few-particle simulations. Theory has now constructed a complex model for ideal two-dimensional electron systems in the presence of high magnetic fields and makes definitive, often fascinating predictions. Experiments have successively uncovered odd-denominator fractional states reaching presently to 7/13. The application of new experimental tools to the FQHE, such as optics, microwaves, and phonon techniques promises the direct observation of such parameters as the gap energy and possibly even some of the more elusive quantities in the future. While theory and experiment in the FQHE appear to be converging, there remains considerable room for challenging surprises. This paper provides a concise overview of the FQHE. It focuses on the experimental aspects and states, but does not expand on the theoretical advances. 70 refs., 11 figs
Quantum Computing With Quasiparticles of the Fractional Quantum Hall Effect
National Research Council Canada - National Science Library
Averin, Dmitri
2001-01-01
The focus of this project was the theoretical study of quantum computation based on controlled transfer of individual quasiparticles in systems of quantum antidots in the regime of the Fractional Quantum Hall Effect (FQHE...
Theory of fractional quantum hall effect
International Nuclear Information System (INIS)
Kostadinov, I.Z.
1985-08-01
A theory of the Fractional Quantum Hall Effect is constructed based on magnetic flux fractionization, which lead to instability of the system against selfcompression. A theorem is proved stating that arbitrary potentials fail to lift a specific degeneracy of the Landau level. For the case of 1/3 fractional filling a model 3-particles interaction is constructed breaking the symmetry. The rigid 3-particles wave function plays the role of order parameter. In a BCS type of theory the gap in the single particles spectrum is produced by the 3-particles interaction. The mean field critical behaviour and critical parameters are determined as well as the Ginsburg-Landau equation coefficients. The Hall conductivity is calculated from the first principles and its temperature dependence is found. The simultaneous tunnelling of 3,5,7 etc. electrons and quantum interference effects are predicted. (author)
Fractional quantization and the quantum hall effect
International Nuclear Information System (INIS)
Guerrero, J.; Calixto, M.; Aldaya, V.
1998-01-01
Quantization with constrains is considered in a group-theoretical framework, providing a precise characterization of the set of good operators, i.e., those preserving the constrained Hilbert space, in terms of the representation of the subgroup of constraints. This machinery is applied to the quantization of the torus as symplectic manifold, obtaining that fractional quantum numbers are permitted, provided that we allow for vector valued representations. The good operators turn out to be the Wilson loops and, for certain representations of the subgroup of constraints, the modular transformations. These results are applied to the Fractional Quantum Hall Effect, where interesting implications are derived
Theory of fractional quantum Hall effect
International Nuclear Information System (INIS)
Kostadinov, I.Z.
1984-09-01
A theory of the fractional quantum Hall effect is constructed by introducing 3-particle interactions breaking the symmetry for ν=1/3 according to a degeneracy theorem proved here. An order parameter is introduced and a gap in the single particle spectrum is found. The critical temperature, critical filling number and critical behaviour are determined as well as the Ginzburg-Landau equation coefficients. A first principle calculation of the Hall current is given. 3, 5, 7 electron tunneling and Josephson interference effects are predicted. (author)
Destruction of the fractional quantum Hall effect by disorder
International Nuclear Information System (INIS)
Laughlin, R.B.
1985-07-01
It is suggested that Hall steps in the fractional quantum Hall effect are physically similar to those in the ordinary quantum Hall effect. This proposition leads to a simple scaling diagram containing a new type of fixed point, which is identified with the destruction of the fractional states by disorder. 15 refs., 3 figs
Excitons in the Fractional Quantum Hall Effect
Laughlin, R. B.
1984-09-01
Quasiparticles of charge 1/m in the Fractional Quantum Hall Effect form excitons, which are collective excitations physically similar to the transverse magnetoplasma oscillations of a Wigner crystal. A variational exciton wavefunction which shows explicitly that the magnetic length is effectively longer for quasiparticles than for electrons is proposed. This wavefunction is used to estimate the dispersion relation of these excitons and the matrix elements to generate them optically out of the ground state. These quantities are then used to describe a type of nonlinear conductivity which may occur in these systems when they are relatively clean.
The fractional quantum Hall effect goes organic
International Nuclear Information System (INIS)
Smet, Jurgen
2000-01-01
Physicists have been fascinated by the behaviour of two-dimensional electron gases for the past two decades. All of these experiments were performed on inorganic semiconductor devices, most of them based on gallium arsenide. Indeed, until recently it was thought that the subtle effects that arise due to electron-electron interactions in these devices required levels of purity that could not be achieved in other material systems. However, Hendrik Schoen, Christian Kloc and Bertram Batlogg of Bell Laboratories in the US have now observed the fractional quantum Hall effect - the most dramatic signature of electron-electron interactions - in two organic semiconductors. (U.K.)
Bimetric Theory of Fractional Quantum Hall States
Directory of Open Access Journals (Sweden)
Andrey Gromov
2017-11-01
Full Text Available We present a bimetric low-energy effective theory of fractional quantum Hall (FQH states that describes the topological properties and a gapped collective excitation, known as the Girvin-Macdonald-Platzman (GMP mode. The theory consists of a topological Chern-Simons action, coupled to a symmetric rank-2 tensor, and an action à la bimetric gravity, describing the gapped dynamics of a spin-2 mode. The theory is formulated in curved ambient space and is spatially covariant, which allows us to restrict the form of the effective action and the values of phenomenological coefficients. Using bimetric theory, we calculate the projected static structure factor up to the k^{6} order in the momentum expansion. To provide further support for the theory, we derive the long-wave limit of the GMP algebra, the dispersion relation of the GMP mode, and the Hall viscosity of FQH states. The particle-hole (PH transformation of the theory takes a very simple form, making the duality between FQH states and their PH conjugates manifest. We also comment on the possible applications to fractional Chern insulators, where closely related structures arise. It is shown that the familiar FQH observables acquire a curious geometric interpretation within the bimetric formalism.
Bimetric Theory of Fractional Quantum Hall States
Gromov, Andrey; Son, Dam Thanh
2017-10-01
We present a bimetric low-energy effective theory of fractional quantum Hall (FQH) states that describes the topological properties and a gapped collective excitation, known as the Girvin-Macdonald-Platzman (GMP) mode. The theory consists of a topological Chern-Simons action, coupled to a symmetric rank-2 tensor, and an action à la bimetric gravity, describing the gapped dynamics of a spin-2 mode. The theory is formulated in curved ambient space and is spatially covariant, which allows us to restrict the form of the effective action and the values of phenomenological coefficients. Using bimetric theory, we calculate the projected static structure factor up to the k6 order in the momentum expansion. To provide further support for the theory, we derive the long-wave limit of the GMP algebra, the dispersion relation of the GMP mode, and the Hall viscosity of FQH states. The particle-hole (PH) transformation of the theory takes a very simple form, making the duality between FQH states and their PH conjugates manifest. We also comment on the possible applications to fractional Chern insulators, where closely related structures arise. It is shown that the familiar FQH observables acquire a curious geometric interpretation within the bimetric formalism.
Geometrical Description of fractional quantum Hall quasiparticles
Park, Yeje; Yang, Bo; Haldane, F. D. M.
2012-02-01
We examine a description of fractional quantum Hall quasiparticles and quasiholes suggested by a recent geometrical approach (F. D. M. Haldane, Phys. Rev. Lett. 108, 116801 (2011)) to FQH systems, where the local excess electric charge density in the incompressible state is given by a topologically-quantized ``guiding-center spin'' times the Gaussian curvature of a ``guiding-center metric tensor'' that characterizes the local shape of the correlation hole around electrons in the fluid. We use a phenomenological energy function with two ingredients: the shear distortion energy of area-preserving distortions of the fluid, and a local (short-range) approximation to the Coulomb energy of the fluctuation of charge density associated with the Gaussian curvature. Quasiparticles and quasiholes of the 1/3 Laughlin state are modeled as ``punctures'' in the incompressible fluid which then relax by geometric distortion which generates Gaussian curvature, giving rise to the charge-density profile around the topological excitation.
Fractional Quantum Hall States in a Ge Quantum Well.
Mironov, O A; d'Ambrumenil, N; Dobbie, A; Leadley, D R; Suslov, A V; Green, E
2016-04-29
Measurements of the Hall and dissipative conductivity of a strained Ge quantum well on a SiGe/(001)Si substrate in the quantum Hall regime are reported. We analyze the results in terms of thermally activated quantum tunneling of carriers from one internal edge state to another across saddle points in the long-range impurity potential. This shows that the gaps for different filling fractions closely follow the dependence predicted by theory. We also find that the estimates of the separation of the edge states at the saddle are in line with the expectations of an electrostatic model in the lowest spin-polarized Landau level (LL), but not in the spin-reversed LL where the density of quasiparticle states is not high enough to accommodate the carriers required.
A holographic model for the fractional quantum Hall effect
Energy Technology Data Exchange (ETDEWEB)
Lippert, Matthew [Institute for Theoretical Physics, University of Amsterdam,Science Park 904, 1090GL Amsterdam (Netherlands); Meyer, René [Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo,Kashiwa, Chiba 277-8568 (Japan); Taliotis, Anastasios [Theoretische Natuurkunde, Vrije Universiteit Brussel andThe International Solvay Institutes,Pleinlaan 2, B-1050 Brussels (Belgium)
2015-01-08
Experimental data for fractional quantum Hall systems can to a large extent be explained by assuming the existence of a Γ{sub 0}(2) modular symmetry group commuting with the renormalization group flow and hence mapping different phases of two-dimensional electron gases into each other. Based on this insight, we construct a phenomenological holographic model which captures many features of the fractional quantum Hall effect. Using an SL(2,ℤ)-invariant Einstein-Maxwell-axio-dilaton theory capturing the important modular transformation properties of quantum Hall physics, we find dyonic diatonic black hole solutions which are gapped and have a Hall conductivity equal to the filling fraction, as expected for quantum Hall states. We also provide several technical results on the general behavior of the gauge field fluctuations around these dyonic dilatonic black hole solutions: we specify a sufficient criterion for IR normalizability of the fluctuations, demonstrate the preservation of the gap under the SL(2,ℤ) action, and prove that the singularity of the fluctuation problem in the presence of a magnetic field is an accessory singularity. We finish with a preliminary investigation of the possible IR scaling solutions of our model and some speculations on how they could be important for the observed universality of quantum Hall transitions.
A holographic model for the fractional quantum Hall effect
Lippert, Matthew; Meyer, René; Taliotis, Anastasios
2015-01-01
Experimental data for fractional quantum Hall systems can to a large extent be explained by assuming the existence of a Γ0(2) modular symmetry group commuting with the renormalization group flow and hence mapping different phases of two-dimensional electron gases into each other. Based on this insight, we construct a phenomenological holographic model which captures many features of the fractional quantum Hall effect. Using an -invariant Einstein-Maxwell-axio-dilaton theory capturing the important modular transformation properties of quantum Hall physics, we find dyonic diatonic black hole solutions which are gapped and have a Hall conductivity equal to the filling fraction, as expected for quantum Hall states. We also provide several technical results on the general behavior of the gauge field fluctuations around these dyonic dilatonic black hole solutions: we specify a sufficient criterion for IR normalizability of the fluctuations, demonstrate the preservation of the gap under the action, and prove that the singularity of the fluctuation problem in the presence of a magnetic field is an accessory singularity. We finish with a preliminary investigation of the possible IR scaling solutions of our model and some speculations on how they could be important for the observed universality of quantum Hall transitions.
Topologically induced fractional Hall steps in the integer quantum Hall regime of MoS 2
Firoz Islam, SK; Benjamin, Colin
2016-09-01
The quantum magnetotransport properties of a monolayer of molybdenum disulfide are derived using linear response theory. In particular, the effect of topological terms on longitudinal and Hall conductivity is analyzed. The Hall conductivity exhibits fractional steps in the integer quantum Hall regime. Further complete spin and valley polarization of the longitudinal conductivitity is seen in presence of these topological terms. Finally, the Shubnikov-de Hass oscillations are suppressed or enhanced contingent on the sign of these topological terms.
Detection of fractional solitons in quantum spin Hall systems
Fleckenstein, C.; Traverso Ziani, N.; Trauzettel, B.
2018-03-01
We propose two experimental setups that allow for the implementation and the detection of fractional solitons of the Goldstone-Wilczek type. The first setup is based on two magnetic barriers at the edge of a quantum spin Hall system for generating the fractional soliton. If then a quantum point contact is created with the other edge, the linear conductance shows evidence of the fractional soliton. The second setup consists of a single magnetic barrier covering both edges and implementing a long quantum point contact. In this case, the fractional soliton can unambiguously be detected as a dip in the conductance without the need to control the magnetization of the barrier.
Observation of the fractional quantum Hall effect in graphene.
Bolotin, Kirill I; Ghahari, Fereshte; Shulman, Michael D; Stormer, Horst L; Kim, Philip
2009-11-12
When electrons are confined in two dimensions and subject to strong magnetic fields, the Coulomb interactions between them can become very strong, leading to the formation of correlated states of matter, such as the fractional quantum Hall liquid. In this strong quantum regime, electrons and magnetic flux quanta bind to form complex composite quasiparticles with fractional electronic charge; these are manifest in transport measurements of the Hall conductivity as rational fractions of the elementary conductance quantum. The experimental discovery of an anomalous integer quantum Hall effect in graphene has enabled the study of a correlated two-dimensional electronic system, in which the interacting electrons behave like massless chiral fermions. However, owing to the prevailing disorder, graphene has so far exhibited only weak signatures of correlated electron phenomena, despite intense experimental and theoretical efforts. Here we report the observation of the fractional quantum Hall effect in ultraclean, suspended graphene. In addition, we show that at low carrier density graphene becomes an insulator with a magnetic-field-tunable energy gap. These newly discovered quantum states offer the opportunity to study correlated Dirac fermions in graphene in the presence of large magnetic fields.
Field theory of anyons and the fractional quantum Hall effect
International Nuclear Information System (INIS)
Viefers, S.F.
1997-11-01
The thesis is devoted to a theoretical study of anyons, i.e. particles with fractional statistics moving in two space dimensions, and the quantum Hall effect. The latter constitutes the only known experimental realization of anyons in that the quasiparticle excitations in the fractional quantum Hall system are believed to obey fractional statistics. First, the properties of ideal quantum gases in two dimensions and in particular the equation of state of the free anyons gas are discussed. Then, a field theory formulation of anyons in a strong magnetic field is presented and later extended to a system with several species of anyons. The relation of this model to fractional exclusion statistics, i.e. intermediate statistics introduced by a generalization of the Pauli principle, and to the low-energy excitations at the edge of the quantum Hall system is discussed. Finally, the Chern-Simons-Landau-Ginzburg theory of the fractional quantum Hall effect is studied, mainly focusing on edge effects; both the ground state and the low-energy edge excitations are examined in the simple one-component model and in an extended model which includes spin effects
Fractional quantum Hall states of atoms in optical lattices
International Nuclear Information System (INIS)
Soerensen, Anders S.; Demler, Eugene; Lukin, Mikhail D.
2005-01-01
We describe a method to create fractional quantum Hall states of atoms confined in optical lattices. We show that the dynamics of the atoms in the lattice is analogous to the motion of a charged particle in a magnetic field if an oscillating quadrupole potential is applied together with a periodic modulation of the tunneling between lattice sites. In a suitable parameter regime the ground state in the lattice is of the fractional quantum Hall type, and we show how these states can be reached by melting a Mott-insulator state in a superlattice potential. Finally, we discuss techniques to observe these strongly correlated states
A conformal field theory description of fractional quantum Hall states
Ardonne, E.
2002-01-01
In this thesis, we give a description of fractional quantum Hall states in terms of conformal field theory (CFT). As was known for a long time, the Laughlin states could be written in terms of correlators of chiral vertex operators of a c=1 CFT. It was shown by G. Moore and N. Read that more general
Spin-singlet hierarchy in the fractional quantum Hall effect
Ino, Kazusumi
1999-01-01
We show that the so-called permanent quantum Hall states are formed by the integer quantum Hall effects on the Haldane-Rezayi quantum Hall state. Novel conformal field theory description along with this picture is deduced. The odd denominator plateaux observed around $\
Quasiparticle Aggregation in the Fractional Quantum Hall Effect
Laughlin, R. B.
1984-10-10
Quasiparticles in the Fractional Quantum Hall Effect behave qualitatively like electrons confined to the lowest landau level, and can do everything electrons can do, including condense into second generation Fractional Quantum Hall ground states. I review in this paper the reasoning leading to variational wavefunctions for ground state and quasiparticles in the 1/3 effect. I then show how two-quasiparticle eigenstates are uniquely determined from symmetry, and how this leads in a natural way to variational wavefunctions for composite states which have the correct densities (2/5, 2/7, ...). I show in the process that the boson, anyon and fermion representations for the quasiparticles used by Haldane, Halperin, and me are all equivalent. I demonstrate a simple way to derive Halperin`s multiple-valued quasiparticle wavefunction from the correct single-valued electron wavefunction. (auth)
Unconventional fractional quantum Hall effect in monolayer and bilayer graphene
Jacak, Janusz; Jacak, Lucjan
2016-01-01
The commensurability condition is applied to determine the hierarchy of fractional fillings of Landau levels in monolayer and in bilayer graphene. The filling rates for fractional quantum Hall effect (FQHE) in graphene are found in the first three Landau levels in one-to-one agreement with the experimental data. The presence of even denominator filling fractions in the hierarchy for FQHE in bilayer graphene is explained. Experimentally observed hierarchy of FQHE in the first and second Landau levels in monolayer graphene and in the zeroth Landau level in bilayer graphene is beyond the conventional composite fermion interpretation but fits to the presented nonlocal topology commensurability condition. PMID:27877866
Matrix effective theories of the fractional quantum Hall effect
International Nuclear Information System (INIS)
Cappelli, Andrea; Rodriguez, Ivan D
2009-01-01
The present understanding of nonperturbative ground states in the fractional quantum Hall effect is based on effective theories of the Jain 'composite fermion' excitations. We review the approach based on matrix variables, i.e. D0 branes, originally introduced by Susskind and Polychronakos. We show that the Maxwell-Chern-Simons matrix gauge theory provides a matrix generalization of the quantum Hall effect, where the composite-fermion construction naturally follows from gauge invariance. The matrix ground states obtained by suitable projections of higher Landau levels are found to be in one-to-one correspondence with the Laughlin and Jain hierarchical states. The matrix theory possesses a physical limit for commuting matrices that could be reachable while staying in the same phase.
Vortices in superconducting films: Statistics and fractional quantum Hall effect
International Nuclear Information System (INIS)
Dziarmaga, J.
1996-01-01
We present a derivation of the Berry phase picked up during exchange of parallel vortices. This derivation is based on the Bogolubov endash de Gennes formalism. The origin of the Magnus force is also critically reanalyzed. The Magnus force can be interpreted as an interaction with the effective magnetic field. The effective magnetic field may be even of the order 10 6 T/A. We discuss a possibility of the fractional quantum Hall effect (FQHE) in vortex systems. As the real magnetic field is varied to drive changes in vortex density, the vortex density will prefer to stay at some quantized values. The mere existence of the FQHE does not depend on vortex quantum statistics, although the pattern of the plateaux does. We also discuss how the density of anyonic vortices can lower the effective strengh of the Magnus force, what might be observable in measurements of Hall resistivity. copyright 1996 The American Physical Society
Real-space imaging of fractional quantum Hall liquids
Hayakawa, Junichiro; Muraki, Koji; Yusa, Go
2013-01-01
Electrons in semiconductors usually behave like a gas--as independent particles. However, when confined to two dimensions under a perpendicular magnetic field at low temperatures, they condense into an incompressible quantum liquid. This phenomenon, known as the fractional quantum Hall (FQH) effect, is a quantum-mechanical manifestation of the macroscopic behaviour of correlated electrons that arises when the Landau-level filling factor is a rational fraction. However, the diverse microscopic interactions responsible for its emergence have been hidden by its universality and macroscopic nature. Here, we report real-space imaging of FQH liquids, achieved with polarization-sensitive scanning optical microscopy using trions (charged excitons) as a local probe for electron spin polarization. When the FQH ground state is spin-polarized, the triplet/singlet intensity map exhibits a spatial pattern that mirrors the intrinsic disorder potential, which is interpreted as a mapping of compressible and incompressible electron liquids. In contrast, when FQH ground states with different spin polarization coexist, domain structures with spontaneous quasi-long-range order emerge, which can be reproduced remarkably well from the disorder patterns using a two-dimensional random-field Ising model. Our results constitute the first reported real-space observation of quantum liquids in a class of broken symmetry state known as the quantum Hall ferromagnet.
Testing the Topological Nature of the Fractional Quantum Hall Edge
International Nuclear Information System (INIS)
Jolad, Shivakumar; Jain, Jainendra K.
2009-01-01
We carry out numerical diagonalization for much larger systems than before by restricting the fractional quantum Hall (FQH) edge excitations to a basis that is exact for a short-range interaction and very accurate for the Coulomb interaction. This enables us to perform substantial tests of the predicted universality of the edge physics. Our results suggest the possibility that the behavior of the FQH edge is intrinsically nonuniversal, even in the absence of edge reconstruction, and therefore may not bear a sharp and unique relation to the nature of the bulk FQH state
Deformed Calogero-Sutherland model and fractional quantum Hall effect
Atai, Farrokh; Langmann, Edwin
2017-01-01
The deformed Calogero-Sutherland (CS) model is a quantum integrable system with arbitrary numbers of two types of particles and reducing to the standard CS model in special cases. We show that a known collective field description of the CS model, which is based on conformal field theory (CFT), is actually a collective field description of the deformed CS model. This provides a natural application of the deformed CS model in Wen's effective field theory of the fractional quantum Hall effect (FQHE), with the two kinds of particles corresponding to electrons and quasi-hole excitations. In particular, we use known mathematical results about super-Jack polynomials to obtain simple explicit formulas for the orthonormal CFT basis proposed by van Elburg and Schoutens in the context of the FQHE.
Shot-noise evidence of fractional quasiparticle creation in a local fractional quantum Hall state.
Hashisaka, Masayuki; Ota, Tomoaki; Muraki, Koji; Fujisawa, Toshimasa
2015-02-06
We experimentally identify fractional quasiparticle creation in a tunneling process through a local fractional quantum Hall (FQH) state. The local FQH state is prepared in a low-density region near a quantum point contact in an integer quantum Hall (IQH) system. Shot-noise measurements reveal a clear transition from elementary-charge tunneling at low bias to fractional-charge tunneling at high bias. The fractional shot noise is proportional to T(1)(1-T(1)) over a wide range of T(1), where T(1) is the transmission probability of the IQH edge channel. This binomial distribution indicates that fractional quasiparticles emerge from the IQH state to be transmitted through the local FQH state. The study of this tunneling process enables us to elucidate the dynamics of Laughlin quasiparticles in FQH systems.
Superconducting Analogue of the Parafermion Fractional Quantum Hall States
Directory of Open Access Journals (Sweden)
Abolhassan Vaezi
2014-07-01
Full Text Available Read-Rezayi Z_{k} parafermion wave functions describe ν=2+(k/kM+2 fractional quantum Hall (FQH states. These states support non-Abelian excitations from which protected quantum gates can be designed. However, there is no experimental evidence for these non-Abelian anyons to date. In this paper, we study the ν=2/k FQH-superconductor heterostructure and find the superconducting analogue of the Z_{k} parafermion FQH state. Our main tool is the mapping of the FQH into coupled one-dimensional chains, each with a pair of counterpropagating modes. We show that by inducing intrachain pairing and charge preserving backscattering with identical couplings, the one-dimensional chains flow into gapless Z_{k} parafermions when k<4. By studying the effect of interchain coupling, we show that every parafermion mode becomes massive except for the two outermost ones. Thus, we achieve a fractional topological superconductor whose chiral edge state is described by a Z_{k} parafermion conformal field theory. For instance, we find that a ν=2/3 FQH in proximity to a superconductor produces a Z_{3} parafermion superconducting state. This state is topologically indistinguishable from the non-Abelian part of the ν=12/5 Read-Rezayi state. Both of these systems can host Fibonacci anyons capable of performing universal quantum computation through braiding operations.
Mechanism of plateau formation in the fractional quantum Hall effect
International Nuclear Information System (INIS)
Bruus, H.; Hansen, O.P.; Hansen, E.B.
1988-01-01
Laughlin's fractionally charged quasi-holes and quasi-electrons are assumed to be pinned, and to be subject to a force j vectorxΦ 0 vector from the transport current. A force balance argument then explains the existence of Hall plateaus. (orig.)
Fractional Quantum Hall Effect in n = 0 Landau Band of Graphene with Chern Number Matrix
Kudo, Koji; Hatsugai, Yasuhiro
2018-06-01
Fully taking into account the honeycomb lattice structure, fractional quantum Hall states of graphene are considered by a pseudopotential projected into the n = 0 Landau band. By using chirality as an internal degree of freedom, the Chern number matrices are defined and evaluated numerically. Quantum phase transition induced by changing a range of the interaction is demonstrated that is associated with chirality ferromagnetism. The chirality-unpolarized ground state is consistent with the Halperin 331 state of the bilayer quantum Hall system.
Single electron probes of fractional quantum hall states
Venkatachalam, Vivek
When electrons are confined to a two dimensional layer with a perpendicular applied magnetic field, such that the ratio of electrons to flux quanta (nu) is a small integer or simple rational value, these electrons condense into remarkable new phases of matter that are strikingly different from the metallic electron gas that exists in the absence of a magnetic field. These phases, called integer or fractional quantum Hall (IQH or FQH) states, appear to be conventional insulators in their bulk, but behave as a dissipationless metal along their edge. Furthermore, electrical measurements of such a system are largely insensitive to the detailed geometry of how the system is contacted or even how large the system is... only the order in which contacts are made appears to matter. This insensitivity to local geometry has since appeared in a number of other two and three dimensional systems, earning them the classification of "topological insulators" and prompting an enormous experimental and theoretical effort to understand their properties and perhaps manipulate these properties to create robust quantum information processors. The focus of this thesis will be two experiments designed to elucidate remarkable properties of the metallic edge and insulating bulk of certain FQH systems. To study such systems, we can use mesoscopic devices known as single electron transistors (SETs). These devices operate by watching single electrons hop into and out of a confining box and into a nearby wire (for measurement). If it is initially unfavorable for an electron to leave the box, it can be made favorable by bringing another charge nearby, modifying the energy of the confined electron and pushing it out of the box and into the nearby wire. In this way, the SET can measure nearby charges. Alternatively, we can heat up the nearby wire to make it easier for electrons to enter and leave the box. In this way, the SET is a sensitive thermometer. First, by operating the SET as an
Fragility of the fractional quantum spin Hall effect in quantum gases
International Nuclear Information System (INIS)
Fialko, O; Brand, J; Zülicke, U
2014-01-01
We consider the effect of contact interaction in a prototypical quantum spin Hall system of pseudo-spin-1/2 particles. A strong effective magnetic field with opposite directions for the two spin states restricts two-dimensional particle motion to the lowest Landau level. While interaction between same-spin particles leads to incompressible correlated states at fractional filling factors as known from the fractional quantum Hall effect, these states are destabilized by interactions between opposite spin particles. Exact results for two particles with opposite spin reveal a quasi-continuous spectrum of extended states with a large density of states at low energy. This has implications for the prospects of realizing the fractional quantum spin Hall effect in electronic or ultra-cold atom systems. Numerical diagonalization is used to extend the two-particle results to many bosonic particles and trapped systems. The interplay between an external trapping potential and spin-dependent interactions is shown to open up new possibilities for engineering exotic correlated many-particle states with ultra-cold atoms. (paper)
The enigma of the ν=2+3/8 fractional quantum Hall effect
DEFF Research Database (Denmark)
Hutasoit, Jimmy; nrc762, nrc762; Mukherjee, Sutirtha
2017-01-01
The fractional quantum Hall effect at ν=2+3/8, which has been definitively observed, is one of the last fractions for which no viable explanation has so far been demonstrated. Our detailed study suggests that it belongs to a new class of exotic states described by the Bonderson-Slingerland wave...
Effective-field-theory model for the fractional quantum Hall effect
International Nuclear Information System (INIS)
Zhang, S.C.; Hansson, T.H.; Kivelson, S.
1989-01-01
Starting directly from the microscopic Hamiltonian, we derive a field-theory model for the fractional quantum hall effect. By considering an approximate coarse-grained version of the same model, we construct a Landau-Ginzburg theory similar to that of Girvin. The partition function of the model exhibits cusps as a function of density and the Hall conductance is quantized at filling factors ν = (2k-1)/sup -1/ with k an arbitrary integer. At these fractions the ground state is incompressible, and the quasiparticles and quasiholes have fractional charge and obey fractional statistics. Finally, we show that the collective density fluctuations are massive
Quantum simulation of conductivity plateaux and fractional quantum Hall effect using ultracold atoms
International Nuclear Information System (INIS)
Barberán, Nuria; García-March, Miguel Angel; Taron, Josep; Dagnino, Daniel; Trombettoni, Andrea; Lewenstein, Maciej
2015-01-01
We analyze the role of impurities in the fractional quantum Hall effect using a highly controllable system of ultracold atoms. We investigate the mechanism responsible for the formation of plateaux in the resistivity/conductivity as a function of the applied magnetic field in the lowest Landau level regime. To this aim, we consider an impurity immersed in a small cloud of an ultracold quantum Bose gas subjected to an artificial magnetic field. We consider scenarios corresponding to experimentally realistic systems with gauge fields induced by rotation of the trapping parabolic potential. Systems of this kind are adequate to simulate quantum Hall effects in ultracold atom setups. We use exact diagonalization for few atoms and to emulate transport equations, we analyze the time evolution of the system under a periodic perturbation. We provide a theoretical proposal to detect the up-to-now elusive presence of strongly correlated states related to fractional filling factors in the context of ultracold atoms. We analyze the conditions under which these strongly correlated states are associated with the presence of the resistivity/conductivity plateaux. Our main result is the presence of a plateau in a region, where the transfer between localized and non-localized particles takes place, as a necessary condition to maintain a constant value of the resistivity/conductivity as the magnetic field increases. (paper)
Analytic calculations of trial wave functions of the fractional quantum Hall effect on the sphere
Energy Technology Data Exchange (ETDEWEB)
Souza Batista, C.L. de [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); Dingping Li [Perugia Univ. (Italy). Dipt. di Fisica
1996-07-01
We present a framework for the analytic calculations of the hierarchical wave functions and the composite fermion wave functions in the fractional quantum Hall effect on the sphere by using projective coordinates. Then we calculate the overlaps between these two wave functions at various fillings and small numbers of electrons. We find that the overlaps are most equal to one. This gives a further evidence that two theories of the fractional quantum Hall effect, the hierarchical theory, are physically equivalent. (author). 31 refs., 2 tabs.
Fabry-Perot Interferometry in the Integer and Fractional Quantum Hall Regimes
McClure, Douglas; Chang, Willy; Kou, Angela; Marcus, Charles; Pfeiffer, Loren; West, Ken
2011-03-01
We present measurements of electronic Fabry-Perot interferometers in the integer and fractional quantum Hall regimes. Two classes of resistance oscillations may be seen as a function of magnetic field and gate voltage, as we have previously reported. In small interferometers in the integer regime, oscillations of the type associated with Coulomb interaction are ubiquitous, while those consistent with single-particle Aharonov-Bohm interference are seen to co-exist in some configurations. The amplitude scaling of both types with temperature and device size is consistent with a theoretical model. Oscillations are further observed in the fractional quantum Hall regime. Here the dependence of the period on the filling factors in the constrictions and bulk of the interferometer can shed light on the effective charge of the interfering quasiparticles, but care is needed to distinguish these oscillations from those associated with integer quantum Hall states. We acknowledge funding from Microsoft Project Q and IBM.
On the conductance sum rule for the hierarchical edge states of the fractional quantum hall effect
International Nuclear Information System (INIS)
Ma Zhongshui; Chen Yixin; Su Zhaobin.
1993-09-01
The conductance sum rule for the hierarchical edge channel currents of a Fractional Quantum Hall Effect state is derived analytically within the Haldane-Halperin hierarchy scheme. We provide also an intuitive interpretation for the hierarchical drift velocities of the edge excitations. (author). 12 refs
The role of localization within the vortex picture of the fractional quantum Hall effect
International Nuclear Information System (INIS)
Bruus, H.; Hansen, O.P.; Hansen, E.B.
1988-01-01
Plateau formation in the fractional quantum Hall effect is shown to arise because, by pinning of vortices in the incompressible electron liquid, the canonical filling factor can be stationarily maintained in the interconnected region between the vortices. The crucial role of localization is demonstrated by considering the idealized limit where pinning centres are absent. (orig.)
Hořava-Lifshitz gravity and effective theory of the fractional quantum Hall effect
Energy Technology Data Exchange (ETDEWEB)
Wu, Chaolun [Kadanoff Center for Theoretical Physics and Enrico Fermi Institute, University of Chicago,Chicago, Illinois 60637 (United States); Wu, Shao-Feng [Department of Physics, Shanghai University,Shanghai 200444 (China); Kadanoff Center for Theoretical Physics and Enrico Fermi Institute, University of Chicago,Chicago, Illinois 60637 (United States)
2015-01-22
We show that Hořava-Lifshitz gravity theory can be employed as a covariant framework to build an effective field theory for the fractional quantum Hall effect that respects all the spacetime symmetries such as non-relativistic diffeomorphism invariance and anisotropic Weyl invariance as well as the gauge symmetry. The key to this formalism is a set of correspondence relations that maps all the field degrees of freedom in the Hořava-Lifshitz gravity theory to external background (source) fields among others in the effective action of the quantum Hall effect, according to their symmetry transformation properties. We originally derive the map as a holographic dictionary, but its form is independent of the existence of holographic duality. This paves the way for the application of Hořava-Lifshitz holography on fractional quantum Hall effect. Using the simplest holographic Chern-Simons model, we compute the low energy effective action at leading orders and show that it captures universal electromagnetic and geometric properties of quantum Hall states, including the Wen-Zee shift, Hall viscosity, angular momentum density and their relations. We identify the shift function in Hořava-Lifshitz gravity theory as minus of guiding center velocity and conjugate to guiding center momentum. This enables us to distinguish guiding center angular momentum density from the internal one, which is the sum of Landau orbit spin and intrinsic (topological) spin of the composite particles. Our effective action shows that Hall viscosity is minus half of the internal angular momentum density and proportional to Wen-Zee shift, and Hall bulk viscosity is half of the guiding center angular momentum density.
Higher fractions theory of fractional hall effect
International Nuclear Information System (INIS)
Kostadinov, I.Z.; Popov, V.N.
1985-07-01
A theory of fractional quantum Hall effect is generalized to higher fractions. N-particle model interaction is used and the gap is expressed through n-particles wave function. The excitation spectrum in general and the mean field critical behaviour are determined. The Hall conductivity is calculated from first principles. (author)
Directory of Open Access Journals (Sweden)
Netanel H. Lindner
2012-10-01
Full Text Available We study the non-Abelian statistics characterizing systems where counterpropagating gapless modes on the edges of fractional quantum Hall states are gapped by proximity coupling to superconductors and ferromagnets. The most transparent example is that of a fractional quantum spin Hall state, in which electrons of one spin direction occupy a fractional quantum Hall state of ν=1/m, while electrons of the opposite spin occupy a similar state with ν=-1/m. However, we also propose other examples of such systems, which are easier to realize experimentally. We find that each interface between a region on the edge coupled to a superconductor and a region coupled to a ferromagnet corresponds to a non-Abelian anyon of quantum dimension sqrt[2m]. We calculate the unitary transformations that are associated with the braiding of these anyons, and we show that they are able to realize a richer set of non-Abelian representations of the braid group than the set realized by non-Abelian anyons based on Majorana fermions. We carry out this calculation both explicitly and by applying general considerations. Finally, we show that topological manipulations with these anyons cannot realize universal quantum computation.
Framing anomaly in the effective theory of the fractional quantum Hall effect.
Gromov, Andrey; Cho, Gil Young; You, Yizhi; Abanov, Alexander G; Fradkin, Eduardo
2015-01-09
We consider the geometric part of the effective action for the fractional quantum Hall effect (FQHE). It is shown that accounting for the framing anomaly of the quantum Chern-Simons theory is essential to obtain the correct gravitational linear response functions. In the lowest order in gradients, the linear response generating functional includes Chern-Simons, Wen-Zee, and gravitational Chern-Simons terms. The latter term has a contribution from the framing anomaly which fixes the value of thermal Hall conductivity and contributes to the Hall viscosity of the FQH states on a sphere. We also discuss the effects of the framing anomaly on linear responses for non-Abelian FQH states.
International Nuclear Information System (INIS)
El-Arabi, N. M.
1993-01-01
Transport phenomena in two dimensional semiconductors have revealed unusual properties. In this thesis these systems are considered and discussed. The theories explain the Integral Quantum Hall Effect (IQHE) and the Fractional Quantum Hall Effect (FQHE). The thesis is composed of five chapters. The first and the second chapters lay down the theory of the IQHE, the third and fourth consider the theory of the FQHE. Chapter five deals with the statistics of particles in two dimension. (author). Refs
DEFF Research Database (Denmark)
Coimbatore Balram, Ajit; Jain, Jainendra
2017-01-01
The particle-hole (PH) symmetry of {\\em electrons} is an exact symmetry of the electronic Hamiltonian confined to a specific Landau level, and its interplay with the formation of composite fermions has attracted much attention of late. This article investigates an emergent symmetry...... in the fractional quantum Hall effect, namely the PH symmetry of {\\em composite fermions}, which relates states at composite fermion filling factors $\
Robust integer and fractional helical modes in the quantum Hall effect
Ronen, Yuval; Cohen, Yonatan; Banitt, Daniel; Heiblum, Moty; Umansky, Vladimir
2018-04-01
Electronic systems harboring one-dimensional helical modes, where spin and momentum are locked, have lately become an important field of their own. When coupled to a conventional superconductor, such systems are expected to manifest topological superconductivity; a unique phase hosting exotic Majorana zero modes. Even more interesting are fractional helical modes, yet to be observed, which open the route for realizing generalized parafermions. Possessing non-Abelian exchange statistics, these quasiparticles may serve as building blocks in topological quantum computing. Here, we present a new approach to form protected one-dimensional helical edge modes in the quantum Hall regime. The novel platform is based on a carefully designed double-quantum-well structure in a GaAs-based system hosting two electronic sub-bands; each tuned to the quantum Hall effect regime. By electrostatic gating of different areas of the structure, counter-propagating integer, as well as fractional, edge modes with opposite spins are formed. We demonstrate that, due to spin protection, these helical modes remain ballistic over large distances. In addition to the formation of helical modes, this platform can serve as a rich playground for artificial induction of compounded fractional edge modes, and for construction of edge-mode-based interferometers.
Quasi-particle properties from tunneling in the v = 5/2 fractional quantum Hall state.
Radu, Iuliana P; Miller, J B; Marcus, C M; Kastner, M A; Pfeiffer, L N; West, K W
2008-05-16
Quasi-particles with fractional charge and statistics, as well as modified Coulomb interactions, exist in a two-dimensional electron system in the fractional quantum Hall (FQH) regime. Theoretical models of the FQH state at filling fraction v = 5/2 make the further prediction that the wave function can encode the interchange of two quasi-particles, making this state relevant for topological quantum computing. We show that bias-dependent tunneling across a narrow constriction at v = 5/2 exhibits temperature scaling and, from fits to the theoretical scaling form, extract values for the effective charge and the interaction parameter of the quasi-particles. Ranges of values obtained are consistent with those predicted by certain models of the 5/2 state.
Pikus, F. G.; Efros, A. L.
1993-06-01
A two-dimensional electron liquid (TDEL), subjected to a smooth random potential, is studied in the regime of the fractional quantum Hall effect. An analytical theory of the nonlinear screening is presented for the case when the fractional gap is much less than the magnitude of the unscreened random potential. In this ``narrow-gap approximation'' (NGA), we calculate the electron density distribution function, the fraction of the TDEL which is in the incompressible state, and the thermodynamic density of states. The magnetocapacitance is calculated to compare with the recent experiments. The NGA is found to be not accurate enough to describe the data. The results for larger fractional gaps are obtained by computer modeling. To fit the recent experimental data we have also taken into account the anyon-anyon interaction in the vicinity of a fractional singularity.
Hyperspherical Slater determinant approach to few-body fractional quantum Hall states
Energy Technology Data Exchange (ETDEWEB)
Yan, Bin, E-mail: yanbin@purdue.edu; Wooten, Rachel E.; Daily, Kevin M.; Greene, Chris H.
2017-05-15
In a recent study (Daily et al., 2015), a hyperspherical approach has been developed to study few-body fractional quantum Hall states. This method has been successfully applied to the exploration of few boson and fermion problems in the quantum Hall region, as well as the study of inter-Landau level collective excitations (Rittenhouse et al., 2016; Wooten et al., 2016). However, the hyperspherical method as it is normally implemented requires a subsidiary (anti-)symmetrization process, which limits its computational effectiveness. The present work overcomes these difficulties and extends the power of this method by implementing a representation of the hyperspherical many-body basis space in terms of Slater determinants of single particle eigenfunctions. A clear connection between the hyperspherical representation and the conventional single particle picture is presented, along with a compact operator representation of the theoretical framework. - Highlights: • A hyperspherical method has been implemented to study the quantum Hall effect. • The hyperspherical many-body basis space is represented with Slater determinants. • Example numerical studies of the 4- and 8-electron systems are presented.
Post, Evert Jan
1999-05-01
This essay presents conclusive evidence of the impermissibility of Copenhagen's single system interpretation of the Schroedinger process. The latter needs to be viewed as a tool exclusively describing phase and orientation randomized ensembles and is not be used for isolated single systems. Asymptotic closeness of single system and ensemble behavior and the rare nature of true single system manifestations have prevented a definitive identification of this Copenhagen deficiency over the past three quarter century. Quantum uncertainty so becomes a basic trade mark of phase and orientation disordered ensembles. The ensuing void of usable single system tools opens a new inquiry for tools without statistical connotations. Three, in part already known, period integrals here identified as flux, charge and action counters emerge as diffeo-4 invariant tools fully compatible with the demands of the general theory of relativity. The discovery of the quantum Hall effect has been instrumental in forcing a distinction between ensemble disorder as in the normal Hall effect versus ensemble order in the plateau states. Since the order of the latter permits a view of the plateau states as a macro- or meso-scopic single system, the period integral description applies, yielding a straightforward unified description of integer and fractional quantum Hall effects.
Evidence of a fractional quantum Hall nematic phase in a microscopic model
Regnault, N.; Maciejko, J.; Kivelson, S. A.; Sondhi, S. L.
2017-07-01
At small momenta, the Girvin-MacDonald-Platzman (GMP) mode in the fractional quantum Hall (FQH) effect can be identified with gapped nematic fluctuations in the isotropic FQH liquid. This correspondence would be exact as the GMP mode softens upon approach to the putative point of a quantum phase transition to a FQH nematic. Motivated by these considerations as well as by suggestive evidence of an FQH nematic in tilted field experiments, we have sought evidence of such a nematic FQHE in a microscopic model of interacting electrons in the lowest Landau level at filling factor 1/3. Using a family of anisotropic Laughlin states as trial wave functions, we find a continuous quantum phase transition between the isotropic Laughlin liquid and the FQH nematic. Results of numerical exact diagonalization also suggest that rotational symmetry is spontaneously broken, and that the phase diagram of the model contains both a nematic and a stripe phase.
International Nuclear Information System (INIS)
Ezawa, Z.F.; Iwazaki, A.
1991-01-01
It is shown that Chern-Simons gauge theories describe both the fractional-quantum-Hall-effect (FQHE) hierarchy and anyon superconductivity, simply by field-theoretically extracting the effects of vortex excitations. Vortices correspond to Laughlin's quasiparticles or bound states of anyons. Both of these phenomena are explained by the condensations of these vortices. We clarify why the anyon systems become incompressible (FQHE) or compressible (anyon superconductivity) depending on the statistics. It is to be emphasized that we can derive an effective Lagrangian describing fully the FQHE hierarchy from a basic Chern-Simons gauge theory
International Nuclear Information System (INIS)
JOHNSON, B.L.; MOON, JEONG-SUN; RENO, JOHN L.; SIMMONS, JERRY A.
1999-01-01
The propagation direction of fractional quantum Hall effect (FQHE) edge states has been investigated experimentally via the symmetry properties of the multi-terminal capacitances of a two dimensional electron gas. Although strong asymmetries with respect to zero magnetic field appear, no asymmetries with respect to even denominator Landau level filling factor ν are seen. This indicates that current-carrying FQHE edge states propagate in the same direction as integer QHE edge states. In addition, anomalous capacitance features, indicative of enhanced bulk conduction, are observed at ν = 1/2 and 3/2
Time and angle resolved phonon absorption in the fractional quantum hall regime
International Nuclear Information System (INIS)
Devitt, A.M.
2000-09-01
The work described in this thesis is a study of the phonon absorption by a two-dimensional electron system (2DES) in the fractional quantum Hall regime and also at ν = 1/2. The fractional quantum Hall effect arises in 2DES's in high magnetic fields and is characterised by the quantisation of the transverse or Hall resistance and the vanishing longitudinal conductivity. The filling factor denotes the number of filled Landau levels and the quantum Hall effect occurs when this ratio is at certain rational odd denominator filling factors. The phenomenology of the effect arises due to the existence of an energy gap between the ground state and the lowest excited state. This energy gap is characterised by a deep minimum, or minima, at finite in-plane wavevector. Acoustic phonon absorption is expected to probe the energy gap at wavevectors close to or at the minimum in the dispersion curve. The experiments reported here incorporate the use of a thin film heater to produce a pulse of phonons of which a fraction are absorbed by the 2DES. A fast amplifier and signal averaging board enable detection of small signals due to absorption of phonons. The technique used allows time resolution of the phonon signal which typically takes place over a period of 10 μs or so. The time resolution enables different phonon modes to be studied. By altering the position of the heater relative to the 2DES angular resolution is also possible. The phonon absorption at several different filling factors has been investigated and the energy gaps found are in reasonable agreement with theoretical predictions. The absorption at ν 1/2 has also been investigated. Here the composite fermions are expected to have a well defined Fermi wavevector. The absorption at ν = 1/2 and the fractional quantum Hall states is found to be qualitatively and quantitatively different. We see that the change in electron temperature atν = 1/2 is much less than at ν = 1/3 due to the larger heat capacity. At ν = 1
Exotic Non-Abelian Topological Defects in Lattice Fractional Quantum Hall States
Liu, Zhao; Möller, Gunnar; Bergholtz, Emil J.
2017-09-01
We investigate extrinsic wormholelike twist defects that effectively increase the genus of space in lattice versions of multicomponent fractional quantum Hall systems. Although the original band structure is distorted by these defects, leading to localized midgap states, we find that a new lowest flat band representing a higher genus system can be engineered by tuning local single-particle potentials. Remarkably, once local many-body interactions in this new band are switched on, we identify various Abelian and non-Abelian fractional quantum Hall states, whose ground-state degeneracy increases with the number of defects, i.e, with the genus of space. This sensitivity of topological degeneracy to defects provides a "proof of concept" demonstration that genons, predicted by topological field theory as exotic non-Abelian defects tied to a varying topology of space, do exist in realistic microscopic models. Specifically, our results indicate that genons could be created in the laboratory by combining the physics of artificial gauge fields in cold atom systems with already existing holographic beam shaping methods for creating twist defects.
Imaging the Conductance of Integer and Fractional Quantum Hall Edge States
Directory of Open Access Journals (Sweden)
Nikola Pascher
2014-01-01
Full Text Available We measure the conductance of a quantum point contact while the biased tip of a scanning probe microscope induces a depleted region in the electron gas underneath. At a finite magnetic field, we find plateaus in the real-space maps of the conductance as a function of tip position at integer (ν=1, 2, 3, 4, 6, 8 and fractional (ν=1/3, 2/3, 5/3, 4/5 values of transmission. They resemble theoretically predicted compressible and incompressible stripes of quantum Hall edge states. The scanning tip allows us to shift the constriction limiting the conductance in real space over distances of many microns. The resulting stripes of integer and fractional filling factors are rugged on scales of a few hundred nanometers, i.e., on a scale much smaller than the zero-field elastic mean free path of the electrons. Our experiments demonstrate that microscopic inhomogeneities are relevant even in high-quality samples and lead to locally strongly fluctuating widths of incompressible regions even down to their complete suppression for certain tip positions. The macroscopic quantization of the Hall resistance measured experimentally in a nonlocal contact configuration survives in the presence of these inhomogeneities, and the relevant local energy scale for the ν=2 state turns out to be independent of tip position.
Numerical studies of the fractional quantum Hall effect in systems with tunable interactions
International Nuclear Information System (INIS)
Papić, Z; Bhatt, R N; Abanin, D A; Barias, Y
2012-01-01
The discovery of the fractional quantum Hall effect in GaAs-based semiconductor devices has lead to new advances in condensed matter physics, in particular the possibility for exotic, topological phases of matter that possess fractional, and even non-Abelian, statistics of quasiparticles. One of the main limitations of the experimental systems based on GaAs has been the lack of tunability of the effective interactions between two-dimensional electrons, which made it difficult to stabilize some of the more fragile states, or induce phase transitions in a controlled manner. Here we review the recent studies that have explored the effects of tunability of the interactions offered by alternative two-dimensional systems, characterized by non-trivial Berry phases and including graphene, bilayer graphene and topological insulators. The tunability in these systems is achieved via external fields that change the mass gap, or by screening via dielectric plate in the vicinity of the device. Our study points to a number of different ways to manipulate the effective interactions, and engineer phase transitions between quantum Hall liquids and compressible states in a controlled manner.
Non-Abelian fractional quantum Hall states for hard-core bosons in one dimension
Paredes, Belén
2012-05-01
I present a family of one-dimensional bosonic liquids analogous to non-Abelian fractional quantum Hall states. A new quantum number is introduced to characterize these liquids, the chiral momentum, which differs from the usual angular or linear momentum in one dimension. As their two-dimensional counterparts, these liquids minimize a k-body hard-core interaction with the minimum total chiral momentum. They exhibit global order, with a hidden organization of the particles in k identical copies of a one-dimensional Laughlin state. For k=2 the state is a p-wave paired phase corresponding to the Pfaffian quantum Hall state. By imposing conservation of the total chiral momentum, an exact parent Hamiltonian is derived which involves long-range tunneling and interaction processes with an amplitude decaying with the chord distance. This family of non-Abelian liquids is shown to be in formal correspondence with a family of spin-(k)/(2) liquids which are total singlets made out of k indistinguishable resonating valence bond states. The corresponding spin Hamiltonians are obtained.
Helical edge states and fractional quantum Hall effect in a graphene electron-hole bilayer.
Sanchez-Yamagishi, Javier D; Luo, Jason Y; Young, Andrea F; Hunt, Benjamin M; Watanabe, Kenji; Taniguchi, Takashi; Ashoori, Raymond C; Jarillo-Herrero, Pablo
2017-02-01
Helical 1D electronic systems are a promising route towards realizing circuits of topological quantum states that exhibit non-Abelian statistics. Here, we demonstrate a versatile platform to realize 1D systems made by combining quantum Hall (QH) edge states of opposite chiralities in a graphene electron-hole bilayer at moderate magnetic fields. Using this approach, we engineer helical 1D edge conductors where the counterpropagating modes are localized in separate electron and hole layers by a tunable electric field. These helical conductors exhibit strong non-local transport signals and suppressed backscattering due to the opposite spin polarizations of the counterpropagating modes. Unlike other approaches used for realizing helical states, the graphene electron-hole bilayer can be used to build new 1D systems incorporating fractional edge states. Indeed, we are able to tune the bilayer devices into a regime hosting fractional and integer edge states of opposite chiralities, paving the way towards 1D helical conductors with fractional quantum statistics.
Particle-hole symmetry and composite fermions in fractional quantum Hall states
Nguyen, Dung Xuan; Golkar, Siavash; Roberts, Matthew M.; Son, Dam Thanh
2018-05-01
We study fractional quantum Hall states at filling fractions in the Jain sequences using the framework of composite Dirac fermions. Synthesizing previous work, we write an effective field theory consistent with all symmetry requirements, including Galilean invariance and particle-hole symmetry. Employing a Fermi-liquid description, we demonstrate the appearance of the Girvin-Macdonald-Platzman algebra and compute the dispersion relation of neutral excitations and various response functions. Our results satisfy requirements of particle-hole symmetry. We show that while the dispersion relation obtained from the modified random-phase approximation (MRPA) of the Halperin-Lee-Read (HLR) theory is particle-hole symmetric, correlation functions obtained from this scheme are not. The results of the Dirac theory are shown to be consistent with the Haldane bound on the projected structure factor, while those of the MPRA of the HLR theory violate it.
Quantum hall effect. A perspective
International Nuclear Information System (INIS)
Aoki, Hideo
2006-01-01
Novel concepts and phenomena are emerging recently in the physics of quantum Hall effect. This article gives an overview, which starts from the fractional quantum Hall system viewed as an extremely strongly correlated system, and move on to present various phenomena involving internal degrees of freedom (spin and layer), non-equilibrium and optical properties, and finally the spinoff to anomalous Hall effect and the rotating Bose-Einstein condensate. (author)
Spectral sum rules and magneto-roton as emergent graviton in fractional quantum Hall effect
Energy Technology Data Exchange (ETDEWEB)
Golkar, Siavash; Nguyen, Dung X.; Son, Dam T. [Enrico Fermi Institute, James Franck Institute and Department of Physics,University of Chicago, Chicago, Illinois 60637 (United States)
2016-01-05
We consider gapped fractional quantum Hall states on the lowest Landau level when the Coulomb energy is much smaller than the cyclotron energy. We introduce two spectral densities, ρ{sub T}(ω) and ρ̄{sub T}(ω), which are proportional to the probabilities of absorption of circularly polarized gravitons by the quantum Hall system. We prove three sum rules relating these spectral densities with the shift S, the q{sup 4} coefficient of the static structure factor S{sub 4}, and the high-frequency shear modulus of the ground state μ{sub ∞}, which is precisely defined. We confirm an inequality, first suggested by Haldane, that S{sub 4} is bounded from below by |S−1|/8. The Laughlin wavefunction saturates this bound, which we argue to imply that systems with ground state wavefunctions close to Laughlin’s absorb gravitons of predominantly one circular polarization. We consider a nonlinear model where the sum rules are saturated by a single magneto-roton mode. In this model, the magneto-roton arises from the mixing between oscillations of an internal metric and the hydrodynamic motion. Implications for experiments are briefly discussed.
Hao, Tian
2017-02-22
The Hall effects, especially the integer, fractional and anomalous quantum Hall effects, have been addressed using Eyring's rate process theory and free volume concept. The basic assumptions are that the conduction process is a common rate controlled "reaction" process that can be described with Eyring's absolute rate process theory; the mobility of electrons should be dependent on the free volume available for conduction electrons. The obtained Hall conductivity is clearly quantized as with prefactors related to both the magnetic flux quantum number and the magnetic quantum number via the azimuthal quantum number, with and without an externally applied magnetic field. This article focuses on two dimensional (2D) systems, but the approaches developed in this article can be extended to 3D systems.
Structure of edge-state inner products in the fractional quantum Hall effect
Fern, R.; Bondesan, R.; Simon, S. H.
2018-04-01
We analyze the inner products of edge state wave functions in the fractional quantum Hall effect, specifically for the Laughlin and Moore-Read states. We use an effective description for these inner products given by a large-N expansion ansatz proposed in a recent work by J. Dubail, N. Read, and E. Rezayi [Phys. Rev. B 86, 245310 (2012), 10.1103/PhysRevB.86.245310]. As noted by these authors, the terms in this ansatz can be constrained using symmetry, a procedure we perform to high orders. We then check this conjecture by calculating the overlaps exactly for small system sizes and compare the numerics with our high-order expansion. We find the effective description to be very accurate.
Probing bulk physics in the 5/2 fractional quantum Hall effect using the Corbino geometry
Schmidt, Benjamin; Bennaceur, Keyan; Bilodeau, Simon; Gaucher, Samuel; Lilly, Michael; Reno, John; Pfeiffer, Loren; West, Ken; Reulet, Bertrand; Gervais, Guillaume
We present two- and four-point Corbino geometry transport measurements in the second Landau level in GaAs/AlGaAs heterostructures. By avoiding edge transport, we are able to directly probe the physics of the bulk quasiparticles in fractional quantum Hall (FQH) states including 5/2. Our highest-quality sample shows stripe and bubble phases in high Landau levels, and most importantly well-resolved FQH minima in the second Landau level. We report Arrhenius-type fits to the activated conductance, and find that σ0 agrees well with theory and existing Hall geometry data in the first Landau level, but not in the second Landau level. We will discuss the advantages the Corbino geometry could bring to various experiments designed to detect the non-Abelian entropy at 5/2, and our progress towards realizing those schemes. The results of these experiments could complement interferometry and other edge-based measurements by providing direct evidence for non-Abelian behaviour of the bulk quasiparticles. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under Contract DE-AC04-94AL8500.
International Nuclear Information System (INIS)
Tomimatsu, Toru; Shirai, Shota; Hashimoto, Katsushi; Sato, Ken; Hirayama, Yoshiro
2015-01-01
Electric-field-induced nuclear resonance (NER: nuclear electric resonance) involving quantum Hall states (QHSs) was studied at various filling factors by exploiting changes in nuclear spins polarized at quantum Hall breakdown. Distinct from the magnetic dipole interaction in nuclear magnetic resonance, the interaction of the electric-field gradient with the electric quadrupole moment plays the dominant role in the NER mechanism. The magnitude of the NER signal strongly depends on whether electronic states are localized or extended. This indicates that NER is sensitive to the screening capability of the electric field associated with QHSs
International Nuclear Information System (INIS)
Ferrari, R.; I.N.F.N., Trento
1994-01-01
The formalism introduced in a previous paper is used for discussing the Coulomb interaction of many electrons moving in two space-dimensions in the presence of a strong magnetic field. The matrix element of the coulomb interaction is evaluated in the new basis, whose states are invariant under discrete translations. This paper is devoted to the case of low filling factor, thus the authors limit themselves to the lowest Landau level and to spins all oriented along the magnetic field. For the case of filling factor ν f = 1/u they give an Ansatz on the state of many electrons which provides a good approximated solution of the Hartree-Fock equation. For general filling factor ν f = u'/u a trial state is given which converges very rapidly to a solution of the self-consistent equation. They generalize the Hartree-Fock equation by considering some correlation: all quantum states are allowed for the u' electrons with the same translation quantum numbers. Numerical results are given for the mean energy and the energy bands, for some values of the filling factor (ν f = 1/2, 1/3, 2/3, 1/4, 3/4, 1/5, 2/5, 3/5, 4/5). The results agree numerically with the Charge Density Wave approach. The boundary conditions are shown to be very important: only large systems (degeneracy of Landau level over 200) are not affected by the boundaries. Therefore results obtained on small scale systems are somewhat unreliable. The relevance of the results for the Fractional Quantum Hall Effect is briefly discussed
Edge modes in the fractional quantum Hall effect without extra edge fermions
Lima, G. L. S.; Dias, S. A.
2011-05-01
We show that the Chern-Simons-Landau-Ginsburg theory that describes the quantum Hall effect on a bounded sample is anomaly free and thus does not require the addition of extra chiral fermions on the boundary to restore local gauge invariance.
Structure of quasiparticles and their fusion algebra in fractional quantum Hall states
Barkeshli, Maissam; Wen, Xiao-Gang
2009-05-01
It was recently discovered that fractional quantum Hall (FQH) states can be characterized quantitatively by the pattern of zeros that describe how the ground-state wave function goes to zero when electrons are brought close together. Quasiparticles in the FQH states can be described in a similar quantitative way by the pattern of zeros that result when electrons are brought close to the quasiparticles. In this paper, we combine the pattern of zeros approach and the conformal field theory (CFT) approach to calculate the topological properties of quasiparticles. We discuss how the quasiparticles in FQH states naturally form representations of a magnetic translation algebra, with members of a representation differing from each other by Abelian quasiparticles. We find that this structure dramatically simplifies topological properties of the quasiparticles, such as their fusion rules, charges, and scaling dimensions, and has consequences for the ground state degeneracy of FQH states on higher genus surfaces. We find constraints on the pattern of zeros of quasiparticles that can fuse together, which allow us to derive the fusion rules of quasiparticles from their pattern of zeros, at least in the case of the (generalized and composite) parafermion states. We also calculate from CFT the number of quasiparticle types in the generalized and composite parafermion states, which confirm the result obtained previously through a completely different approach.
Structure of quasiparticles and their fusion algebra in fractional quantum Hall states
International Nuclear Information System (INIS)
Barkeshli, Maissam; Wen Xiaogang
2009-01-01
It was recently discovered that fractional quantum Hall (FQH) states can be characterized quantitatively by the pattern of zeros that describe how the ground-state wave function goes to zero when electrons are brought close together. Quasiparticles in the FQH states can be described in a similar quantitative way by the pattern of zeros that result when electrons are brought close to the quasiparticles. In this paper, we combine the pattern of zeros approach and the conformal field theory (CFT) approach to calculate the topological properties of quasiparticles. We discuss how the quasiparticles in FQH states naturally form representations of a magnetic translation algebra, with members of a representation differing from each other by Abelian quasiparticles. We find that this structure dramatically simplifies topological properties of the quasiparticles, such as their fusion rules, charges, and scaling dimensions, and has consequences for the ground state degeneracy of FQH states on higher genus surfaces. We find constraints on the pattern of zeros of quasiparticles that can fuse together, which allow us to derive the fusion rules of quasiparticles from their pattern of zeros, at least in the case of the (generalized and composite) parafermion states. We also calculate from CFT the number of quasiparticle types in the generalized and composite parafermion states, which confirm the result obtained previously through a completely different approach.
The Quasi-Electron Shell Structure of the Fractional Quantum Hall Effect
Haxton, Wick; Haxton, Daniel
2015-04-01
The fractional quantum Hall effect (FQHE) formulated on a sphere resembles the nuclear shell model, with the desired translationally invariant states having total angular momentum zero. This property was exploited by Ginocchio and Haxton (GH) to derive a new set of scalar operators and a first-Landau-level representation of the full set of hierarchy states (fillings 1/3, 2/5, 3/7, etc.), with overlaps identical to those of Jain, who used unphysical higher Landau levels excitations followed by numerical projection. We demonstrate that the GH operators produce an appealing description of the FQHE as shells filled by non-interacting quasi-electrons, or composite fermions. These are explicitly constructed, and their planar forms are also found. The evolution of the shells and their quasi-electrons is quite unusual. The connections with electron correlations and Laughlin's variational arguments are described. We discuss how ``new states'' found experimentally at fillings such as 4/11 and 5/13 fit into this scheme. Work support in part by the US DOE Offices of Nuclear Physics and Basic Energy Sciences.
Q-balls of quasi-particles in a (2,0)-theory model of the fractional quantum Hall effect
Ganor, O.J.; Hong, Y.P.; Moore, N.; Sun, H.Y.; Tan, H.S.; Torres-Chicon, N.R.
2015-01-01
A toy model of the fractional quantum Hall effect appears as part of the low-energy description of the Coulomb branch of the A(1) (2, 0)-theory formulated on (S-1 x R-2)/Z(k), where the generator of Z(k) acts as a combination of translation on S-1 and rotation by 2 pi/k on R-2. At low energy the
International Nuclear Information System (INIS)
Pan, W.; Tsui, D.C.; Pan, W.; Xia, J.; Shvarts, V.; Adams, D.E.; Xia, J.; Shvarts, V.; Adams, D.E.; Stormer, H.L.; Stormer, H.L.; Pfeiffer, L.N.; Baldwin, K.W.; West, K.W.
1999-01-01
We report ultralow temperature experiments on the obscure fractional quantum Hall effect at Landau level filling factor ν=5/2 in a very high-mobility specimen of μ=1.7x10 7 cm 2 /V s . We achieve an electron temperature as low as ∼4 mK , where we observe vanishing R xx and, for the first time, a quantized Hall resistance, R xy =h/(5/2)e 2 to within 2ppm. R xy at the neighboring odd-denominator states ν=7/3 and 8/3 is also quantized. The temperature dependences of the R xx minima at these fractional fillings yield activation energy gaps Δ 5/2 =0.11 , Δ 7/3 =0.10 , and Δ 8/3 =0.055 K . copyright 1999 The American Physical Society
Post, E J
1999-01-01
This essay presents conclusive evidence of the impermissibility of Copenhagen's single system interpretation of the Schroedinger process. The latter needs to be viewed as a tool exclusively describing phase and orientation randomized ensembles and is not be used for isolated single systems. Asymptotic closeness of single system and ensemble behavior and the rare nature of true single system manifestations have prevented a definitive identification of this Copenhagen deficiency over the past three quarter century. Quantum uncertainty so becomes a basic trade mark of phase and orientation disordered ensembles. The ensuing void of usable single system tools opens a new inquiry for tools without statistical connotations. Three, in part already known, period integrals here identified as flux, charge and action counters emerge as diffeo-4 invariant tools fully compatible with the demands of the general theory of relativity. The discovery of the quantum Hall effect has been instrumental in forcing a distinction betw...
International Nuclear Information System (INIS)
Ma Zhongshui; Su Zhaobin.
1992-09-01
By applying the Dirac quantization method, we build the constraint that all electrons are in the lowest Landau level into the Chern-Simons field theory approach for the fractional quantum Hall system and show that the constraint can be transmuted from hierarchy to hierarchy. For a finite system, we derive that the action for each hierarchy can be split into two parts: a surface part provides the action for the edge excitations while the remaining part is precisely the bulk action for the next hierarchy. An the action for the edge could be decoupled from the bulk only at the hierarchy filling. (author). 16 refs
Nguyen, Dung Xuan; Gromov, Andrey; Son, Dam Thanh
2018-05-01
We perform a detailed comparison of the Dirac composite fermion and the recently proposed bimetric theory for a quantum Hall Jain states near half filling. By tuning the composite Fermi liquid to the vicinity of a nematic phase transition, we find that the two theories are equivalent to each other. We verify that the single mode approximation for the response functions and the static structure factor becomes reliable near the phase transition. We show that the dispersion relation of the nematic mode near the phase transition can be obtained from the Dirac brackets between the components of the nematic order parameter. The dispersion is quadratic at low momenta and has a magnetoroton minimum at a finite momentum, which is not related to any nearby inhomogeneous phase.
Effective field theory and tunneling currents in the fractional quantum Hall effect
International Nuclear Information System (INIS)
Bieri, Samuel; Fröhlich, Jürg
2012-01-01
We review the construction of a low-energy effective field theory and its state space for “abelian” quantum Hall fluids. The scaling limit of the incompressible fluid is described by a Chern–Simons theory in 2+1 dimensions on a manifold with boundary. In such a field theory, gauge invariance implies the presence of anomalous chiral modes localized on the edge of the sample. We assume a simple boundary structure, i.e., the absence of a reconstructed edge. For the bulk, we consider a multiply connected planar geometry. We study tunneling processes between two boundary components of the fluid and calculate the tunneling current to lowest order in perturbation theory as a function of dc bias voltage. Particular attention is paid to the special cases when the edge modes propagate at the same speed, and when they exhibit two significantly distinct propagation speeds. We distinguish between two “geometries” of interference contours corresponding to the (electronic) Fabry–Perot and Mach–Zehnder interferometers, respectively. We find that the interference term in the current is absent when exactly one hole in the fluid corresponding to one of the two edge components involved in the tunneling processes lies inside the interference contour (i.e., in the case of a Mach–Zehnder interferometer). We analyze the dependence of the tunneling current on the state of the quantum Hall fluid and on the external magnetic flux through the sample. - Highlights: ► We review and extend on the field theoretic construction of the FQHE. ► We calculate tunneling currents between different edge components of a sample. ► We find an absence of interference terms in the currents for some sample geometries. ► No observable Aharonov–Bohm effect is found as the magnetic field is varied. ► Deformation of the edge leads to observable Aharonov–Bohm effect in the currents.
Fractional statistics and fractional quantized Hall effect
International Nuclear Information System (INIS)
Tao, R.; Wu, Y.S.
1985-01-01
The authors suggest that the origin of the odd-denominator rule observed in the fractional quantized Hall effect (FQHE) may lie in fractional statistics which govern quasiparticles in FQHE. A theorem concerning statistics of clusters of quasiparticles implies that fractional statistics do not allow coexistence of a large number of quasiparticles at fillings with an even denominator. Thus, no Hall plateau can be formed at these fillings, regardless of the presence of an energy gap. 15 references
Quantum critical Hall exponents
Lütken, C A
2014-01-01
We investigate a finite size "double scaling" hypothesis using data from an experiment on a quantum Hall system with short range disorder [1-3]. For Hall bars of width w at temperature T the scaling form is w(-mu)T(-kappa), where the critical exponent mu approximate to 0.23 we extract from the data is comparable to the multi-fractal exponent alpha(0) - 2 obtained from the Chalker-Coddington (CC) model [4]. We also use the data to find the approximate location (in the resistivity plane) of seven quantum critical points, all of which closely agree with the predictions derived long ago from the modular symmetry of a toroidal sigma-model with m matter fields [5]. The value nu(8) = 2.60513 ... of the localisation exponent obtained from the m = 8 model is in excellent agreement with the best available numerical value nu(num) = 2.607 +/- 0.004 derived from the CC-model [6]. Existing experimental data appear to favour the m = 9 model, suggesting that the quantum Hall system is not in the same universality class as th...
Q-balls of quasi-particles in a (2, 0)-theory model of the fractional quantum Hall effect
Ganor, Ori J.; Hong, Yoon Pyo; Moore, Nathan; Sun, Hao-Yu; Tan, Hai Siong; Torres-Chicon, Nesty R.
2015-09-01
A toy model of the fractional quantum Hall effect appears as part of the low-energy description of the Coulomb branch of the A 1 (2 , 0)-theory formulated on ({S}^1× {{R}}^2)/{{Z}}_k , where the generator of {{Z}}_k acts as a combination of translation on S 1 and rotation by 2 π/k on {{R}}^2 . At low energy the configuration is described in terms of a 4+1D Super-Yang-Mills theory on a cone ({{R}}^2/{{Z}}_k) with additional 2+1D degrees of freedom at the tip of the cone that include fractionally charged particles. These fractionally charged "quasi-particles" are BPS strings of the (2 , 0)-theory wrapped on short cycles. We analyze the large k limit, where a smooth cigar-geometry provides an alternative description. In this framework a W-boson can be modeled as a bound state of k quasi-particles. The W-boson becomes a Q-ball, and it can be described as a soliton solution of Bogomolnyi monopole equations on a certain auxiliary curved space. We show that axisymmetric solutions of these equations correspond to singular maps from AdS 3 to AdS 2, and we present some numerical results and an asymptotic expansion.
Elementary theory of quantum Hall effect
Directory of Open Access Journals (Sweden)
Keshav N. Shrivastava
2008-04-01
Full Text Available The Hall effect is the generation of a current perpendicular to both the direction of the applied electric as well as magnetic field in a metal or in a semiconductor. It is used to determine the concentration of electrons. The quantum Hall effect with integer quantization was discovered by von Klitzing and fractionally charged states were found by Tsui, Stormer and Gossard. Robert Laughlin explained the quantization of Hall current by using “flux quantization” and introduced incompressibility to obtain the fractional charge. We have developed the theory of the quantum Hall effect by using the theory of angular momentum. Our predicted fractions are in accord with those measured. We emphasize our explanation of the observed phenomena. We use spin to explain the fractional charge and hence we discover spin-charge locking.
Composite fermions in the quantum Hall effect
International Nuclear Information System (INIS)
Johnson, B.L.; Kirczenow, G.
1997-01-01
The quantum Hall effect and associated quantum transport phenomena in low-dimensional systems have been the focus of much attention for more than a decade. Recent theoretical development of interesting quasiparticles - 'composite fermions' - has led to significant advances in understanding and predicting the behaviour of two-dimensional electron systems under high transverse magnetic fields. Composite fermions may be viewed as fermions carrying attached (fictitious) magnetic flux. Here we review models of the integer and fractional quantum Hall effects, including the development of a unified picture of the integer and fractional effects based upon composite fermions. The composite fermion picture predicts remarkable new physics: the formation of a Fermi surface at high magnetic fields, and anomalous ballistic transport, thermopower, and surface acoustic wave behaviour. The specific theoretical predictions of the model, as well as the body of experimental evidence for these phenomena are reviewed. We also review recent edge-state models for magnetotransport in low-dimensional devices based on the composite fermion picture. These models explain the fractional quantum Hall effect and transport phenomena in nanoscale devices in a unified framework that also includes edge state models of the integer quantum Hall effect. The features of the composite fermion edge-state model are compared and contrasted with those of other recent edge-state models of the fractional quantum Hall effect. (author)
Energy Technology Data Exchange (ETDEWEB)
Clark, R.G.; Ford, R.A.; Haynes, S.R.; Ryan, J.F.; Turberfield, A.J.; Wright, P.A. (Clarendon Lab., Univ. of Oxford (UK)); Williams, F.I.B.; Deville, G.; Glattli, D.C. (CEN de Saclay, 91 - Gif-sur-Yvette (France)); Mallett, J.R.; Oswald, P.M.W. (Clarendon Lab., Univ. of Oxford (UK) Katholieke Univ. Leuven (Belgium)); Burgt, M. van der; Herlach, F. (Katholieke Univ. Leuven (Belgium)); Foxon, C.T.; Harris, J.J. (Philips Research Labs., Redhill (UK))
1991-02-01
Our recent optical detection of the integer and fractional quantum Hall effects in GaAs, by intrinsic band-gap photoluminescence at dilution refrigerator temperatures, is reviewed. This work has been extended to the extreme quantum limit where a photoluminescence peak develops close to Landau level filling factor {nu}=1/5 which correlates both with the onset of threshold behaviour in current-voltage characteristics of the two-dimensional electron system and a resonant radio-frequency absorption; the latter are quantitatively accounted for by a model of crystalline electronic structure broken up into domains. Preliminary mK transport experiments in intense, pulsed magnetic fields are also described, which establish a basis to access the electron solid phase transition in a hitherto unattainable region of the (B,T) plane. (orig.).
Magnetoresistance in quantum Hall metals due to Pancharatnam ...
Indian Academy of Sciences (India)
Abstract. We derive the trial Hall resistance formula for the quantum Hall metals to address both the integer and fractional quantum Hall effects. Within the degenerate (and crossed) Landau levels, and in the presence of changing magnetic field strength, one can invoke two physical processes responsible for the electron ...
Quantum Hall effect in quantum electrodynamics
International Nuclear Information System (INIS)
Penin, Alexander A.
2009-01-01
We consider the quantum Hall effect in quantum electrodynamics and find a deviation from the quantum-mechanical prediction for the Hall conductivity due to radiative antiscreening of electric charge in an external magnetic field. A weak dependence of the universal von Klitzing constant on the magnetic field strength, which can possibly be observed in a dedicated experiment, is predicted
Quantum Hall Electron Nematics
MacDonald, Allan
In 2D electron systems hosted by crystals with hexagonal symmetry, electron nematic phases with spontaneously broken C3 symmetry are expected to occur in the quantum Hall regime when triplets of Landau levels associated with three different Fermi surface pockets are partially filled. The broken symmetry state is driven by intravalley Coulombic exchange interactions that favor spontaneously polarized valley occupations. I will discuss three different examples of 2D electron systems in which this type of broken symmetry state is expected to occur: i) the SnTe (111) surface, ii) the Bi (111) surface. and iii) unbalanced bilayer graphene. This type of quantum Hall electron nematic state has so far been confirmed only in the Bi (111) case, in which the anisotropic quasiparticle wavefunctions of the broken symmetry state were directly imaged. In the SnTe case the nematic state phase boundary is controlled by a competition between intravalley Coulomb interactions and intervalley scattering processes that increase in relative strength with magnetic field. An in-plane Zeeman field alters the phase diagram by lifting the three-fold Landau level degeneracy, yielding a ground state energy with 2 π/3 periodicity as a function of Zeeman-field orientation angle. I will comment on the possibility of observing similar states in the absence of a magnetic field. Supported by DOE Division of Materials Sciences and Engineering Grant DE-FG03-02ER45958.
Gauge invariance and fractional quantized Hall effect
International Nuclear Information System (INIS)
Tao, R.; Wu, Y.S.
1984-01-01
It is shown that gauge invariance arguments imply the possibility of fractional quantized Hall effect; the Hall conductance is accurately quantized to a rational value. The ground state of a system showing the fractional quantized Hall effect must be degenerate; the non-degenerate ground state can only produce the integral quantized Hall effect. 12 references
Zamaere, Christine Berkesch; Griffeth, Stephen; Sam, Steven V.
2014-08-01
We show that for Jack parameter α = -( k + 1)/( r - 1), certain Jack polynomials studied by Feigin-Jimbo-Miwa-Mukhin vanish to order r when k + 1 of the coordinates coincide. This result was conjectured by Bernevig and Haldane, who proposed that these Jack polynomials are model wavefunctions for fractional quantum Hall states. Special cases of these Jack polynomials include the wavefunctions of Laughlin and Read-Rezayi. In fact, along these lines we prove several vanishing theorems known as clustering properties for Jack polynomials in the mathematical physics literature, special cases of which had previously been conjectured by Bernevig and Haldane. Motivated by the method of proof, which in the case r = 2 identifies the span of the relevant Jack polynomials with the S n -invariant part of a unitary representation of the rational Cherednik algebra, we conjecture that unitary representations of the type A Cherednik algebra have graded minimal free resolutions of Bernstein-Gelfand-Gelfand type; we prove this for the ideal of the ( k + 1)-equals arrangement in the case when the number of coordinates n is at most 2 k + 1. In general, our conjecture predicts the graded S n -equivariant Betti numbers of the ideal of the ( k + 1)-equals arrangement with no restriction on the number of ambient dimensions.
International Nuclear Information System (INIS)
Ciftja, O.
1999-01-01
The microscopic approach for studying the half-filled state of the fractional quantum Hall effect is based on the idea of proposing a trial Fermi wave function of the Jastrow-Slater form, which is then fully projected onto the lowest Landau level. A simplified starting point is to drop the projection operator and to consider an unprojected wave function. A recent study claims that such a wave function approximated in a Jastrow form may still constitute a good starting point on the study of the half-filled state. In this paper we formalize the effective hypernetted-chain approximation and apply it to the unprojected Fermi wave function, which describes the even-denominator-filling states. We test the above approximation by using the Fermi hypernetted-chain theory, which constitutes the natural choice for the present case. Our results suggest that the approximation of the Slater determinant of plane waves as a Jastrow wave function may not be a very accurate approximation. We conclude that the lowest Landau-level projection operator cannot be neglected if one wants a better quantitative understanding of the phenomena. copyright 1999 The American Physical Society
International Nuclear Information System (INIS)
Joynt, R.J.
1982-01-01
A general investigation of the electronic structure of two dimensional systems is undertaken with a view towards understanding the quantum Hall effect. The work is limited to the case of a strong perpendicular magnetic field, with a disordered potential and an externally applied electric field. The electrons are treated as noninteracting. First, the scattering theory of the system is worked out. The surprising result is found that a wavepacket will reform after scattering from an isolated potential. Also it will tend to be accelerated in the neighborhood of the scatterer if the potential has bound states. Fredholm theory can then be used to show that the extended states carry an additional current which compensates for the zero current of the bound states. Together, these give the quantized conductance. The complementary case of a smooth random potential is treated by a path-integral approach which exploits the analogies to the classical equations of motion. The Green's function can be calculated approximately, which gives the general character of both the bound and extended states. Also the ratio of these two types of states can be computed for a given potential. The charge density is uniform in first approximation, and the Hall conductance is quantized. Higher-order corrections for more rapidly fluctuating potential are calculated. The most general conditions under which the conductance is quantized are discussed. Because of the peculiar scattering properties of the system, numerical solution of the Schroedinger equation is of interest, both to confirm the analytical results, and for pedagogical reasons. The stability and convergence problems inherent in the computer solution of the problem are analyzed. Results for some model scattering potentials are presented
Hall viscosity of hierarchical quantum Hall states
Fremling, M.; Hansson, T. H.; Suorsa, J.
2014-03-01
Using methods based on conformal field theory, we construct model wave functions on a torus with arbitrary flat metric for all chiral states in the abelian quantum Hall hierarchy. These functions have no variational parameters, and they transform under the modular group in the same way as the multicomponent generalizations of the Laughlin wave functions. Assuming the absence of Berry phases upon adiabatic variations of the modular parameter τ, we calculate the quantum Hall viscosity and find it to be in agreement with the formula, given by Read, which relates the viscosity to the average orbital spin of the electrons. For the filling factor ν =2/5 Jain state, which is at the second level in the hierarchy, we compare our model wave function with the numerically obtained ground state of the Coulomb interaction Hamiltonian in the lowest Landau level, and find very good agreement in a large region of the complex τ plane. For the same example, we also numerically compute the Hall viscosity and find good agreement with the analytical result for both the model wave function and the numerically obtained Coulomb wave function. We argue that this supports the notion of a generalized plasma analogy that would ensure that wave functions obtained using the conformal field theory methods do not acquire Berry phases upon adiabatic evolution.
The quantum Hall effect helicity
Energy Technology Data Exchange (ETDEWEB)
Shrivastava, Keshav N., E-mail: keshav1001@yahoo.com [Department of Physics, University of Malaya, Kuala Lumpur 50603 (Malaysia); School of Physics, University of Hyderabad, Hyderabad 500046 (India)
2015-04-16
The quantum Hall effect in semiconductor heterostructures is explained by two signs in the angular momentum j=l±s and g=(2j+1)/(2l+1) along with the Landau factor (n+1/2). These modifications in the existing theories explain all of the fractional charges. The helicity which is the sign of the product of the linear momentum with the spin p.s plays an important role for the understanding of the data at high magnetic fields. In particular it is found that particles with positive sign in the spin move in one direction and those with negative sign move in another direction which explains the up and down stream motion of the particles.
Yang, Kun
2017-12-01
We consider an interface separating the Moore-Read state and Halperin 331 state in a half-filled Landau level, which can be realized in a double quantum well system with varying interwell tunneling and/or interaction strengths. In the presence of electron tunneling and strong Coulomb interactions across the interface, we find that all charge modes localize and the only propagating mode left is a chiral Majorana fermion mode. Methods to probe this neutral mode are proposed. A quantum phase transition between the Moore-Read and Halperin 331 states is described by a network of such Majorana fermion modes. In addition to a direct transition, they may also be separated by a phase in which the Majorana fermions are delocalized, realizing an incompressible state which exhibits quantum Hall charge transport and bulk heat conduction.
Directory of Open Access Journals (Sweden)
Kiryl Pakrouski
2015-04-01
Full Text Available Interesting non-Abelian states, e.g., the Moore-Read Pfaffian and the anti-Pfaffian, offer candidate descriptions of the ν=5/2 fractional quantum Hall state. But, the significant controversy surrounding the nature of the ν=5/2 state has been hampered by the fact that the competition between these and other states is affected by small parameter changes. To study the phase diagram of the ν=5/2 state, we numerically diagonalize a comprehensive effective Hamiltonian describing the fractional quantum Hall effect of electrons under realistic conditions in GaAs semiconductors. The effective Hamiltonian takes Landau-level mixing into account to lowest order perturbatively in κ, the ratio of the Coulomb energy scale to the cyclotron gap. We also incorporate the nonzero width w of the quantum-well and subband mixing. We find the ground state in both the torus and spherical geometries as a function of κ and w. To sort out the nontrivial competition between candidate ground states, we analyze the following four criteria: its overlap with trial wave functions, the magnitude of energy gaps, the sign of the expectation value of an order parameter for particle-hole symmetry breaking, and the entanglement spectrum. We conclude that the ground state is in the universality class of the Moore-Read Pfaffian state, rather than the anti-Pfaffian, for κ<κ_{c}(w, where κ_{c}(w is a w-dependent critical value 0.6≲κ_{c}(w≲1. We observe that both Landau-level mixing and nonzero width suppress the excitation gap, but Landau-level mixing has a larger effect in this regard. Our findings have important implications for the identification of non-Abelian fractional quantum Hall states.
Umucalılar, R. O.; Carusotto, I.
2017-11-01
We investigate theoretically a driven dissipative model of strongly interacting photons in a nonlinear optical cavity in the presence of a synthetic magnetic field. We show the possibility of using a frequency-dependent incoherent pump to create a strongly correlated ν =1 /2 bosonic Laughlin state of light: Due to the incompressibility of the Laughlin state, fluctuations in the total particle number and excitation of edge modes can be tamed by imposing a suitable external potential profile for photons. We further propose angular-momentum-selective spectroscopy of the emitted light as a tool to obtain unambiguous signatures of the microscopic physics of the quantum Hall liquid of light.
Theory of the quantum hall effects in lattice systems
International Nuclear Information System (INIS)
Kliros, G.S.
1990-06-01
The Fractional Quantum Hall Effect is identified as an Integral Quantum Hall Effect of electrons on a lattice with an even number of statistical flux quanta. A variational wavefunction in terms of the Hofstadter lattice eigenstates is proposed. (author). 21 refs
Critical current in the Integral Quantum Hall Effect
International Nuclear Information System (INIS)
Kostadinov, I.Z.
1985-11-01
A multiparticle theory of the Integral Quantum Hall Effect (IQHE) was constructed operating with pairs wave function as an order parameter. The IQHE is described with bosonic macroscopic states while the fractional QHE with fermionic ones. The calculation of the critical current and Hall conductivity temperature dependence is presented. (author)
Graphene and the universality of the quantum Hall effect
DEFF Research Database (Denmark)
Tzalenchuk, A.; Janssen, T. J.B.M.; Kazakova, O.
2013-01-01
The quantum Hall effect allows the standard for resistance to be defined in terms of the elementary charge and Planck's constant alone. The effect comprises the quantization of the Hall resistance in two-dimensional electron systems in rational fractions of RK=h/e2=25812.8074434(84) Ω (Mohr P. J....... the unconventional quantum Hall effect and then present in detail the route, which led to the most precise quantum Hall resistance universality test ever performed.......The quantum Hall effect allows the standard for resistance to be defined in terms of the elementary charge and Planck's constant alone. The effect comprises the quantization of the Hall resistance in two-dimensional electron systems in rational fractions of RK=h/e2=25812.8074434(84) Ω (Mohr P. J....... et al., Rev. Mod. Phys., 84 (2012) 1527), the resistance quantum. Despite 30 years of research into the quantum Hall effect, the level of precision necessary for metrology, a few parts per billion, has been achieved only in silicon and III-V heterostructure devices. In this lecture we show...
Fractional statistics and fractional quantized Hall effect. Revision
International Nuclear Information System (INIS)
Tao, R.; Wu, Y.S.
1984-01-01
We suggest that the origin of the odd denominator rule observed in the fractional quantized Hall effect (FQHE) may lie in fractional statistics which governs quasiparticles in FQHE. A theorem concerning statistics of clusters of quasiparticles implies that fractional statistics does not allow coexistence of a large number of quasiparticles at fillings with an even denominator. Thus no Hall plateau can be formed at these fillings, regardless of the presence of an energy gap. 15 references
Quantum Hall Effect: proposed multi-electron tunneling experiment
International Nuclear Information System (INIS)
Kostadinov, I.Z.
1985-11-01
Here we propose a tunneling experiment for the fractional and Integral Quantum Hall Effect. It may demonstrate multi-electron tunneling and may provide information about the nature of the macroscopic quantum states of 2D electronic liquid or solid. (author)
Coulomb blockade in hierarchical quantum Hall droplets
International Nuclear Information System (INIS)
Cappelli, Andrea; Georgiev, Lachezar S; Zemba, Guillermo R
2009-01-01
The degeneracy of energy levels in a quantum dot of Hall fluid, leading to conductance peaks, can be readily derived from the partition functions of conformal field theory. Their complete expressions can be found for Hall states with both Abelian and non-Abelian statistics, upon adapting known results for the annulus geometry. We analyze the Abelian states with hierarchical filling fractions, ν = m/(mp ± 1), and find a non-trivial pattern of conductance peaks. In particular, each one of them occurs with a characteristic multiplicity, which is due to the extended symmetry of the m-folded edge. Experimental tests of the multiplicity can shed more light on the dynamics of this composite edge. (fast track communication)
Nobel Prize in physics 1985: Quantum Hall effect
International Nuclear Information System (INIS)
Herrmann, R.
1986-01-01
The conditions (like very strong magnetic fields, ultralow temperatures, and occurrence of a two-dimensional electron gas in microelectronic structures) for the measurement of the quantum Hall effect are explained. Two possible measuring methods are described. Measuring results for p-Si-MOSFET, GaAs/AlGaAs heterojuntions and grain boundaries in InSb crystals are reported. Differences between normal (integer) and fractional quantum Hall effect are discussed. One of the important consequences is that by means of the quantum Hall effect the value h/e 2 can be determined with very high accuracy. In 1985 Klaus von Klitzing was awarded the Nobel Prize for his work on the quantum Hall effect
Studies of quantum dots in the quantum Hall regime
Goldmann, Eyal
We present two studies of quantum dots in the quantum Hall regime. In the first study, presented in Chapter 3, we investigate the edge reconstruction phenomenon believed to occur when the quantum dot filling fraction is n≲1 . Our approach involves the examination of large dots (≤40 electrons) using a partial diagonalization technique in which the occupancies of the deep interior orbitals are frozen. To interpret the results of this calculation, we evaluate the overlap between the diagonalized ground state and a set of trial wavefunctions which we call projected necklace (PN) states. A PN state is simply the angular momentum projection of a maximum density droplet surrounded by a ring of localized electrons. Our calculations reveal that PN states have up to 99% overlap with the diagonalized ground states, and are lower in energy than the states identified in Chamon and Wen's study of the edge reconstruction. In the second study, presented in Chapter 4, we investigate quantum dots in the fractional quantum Hall regime using a Hartree formulation of composite fermion theory. We find that under appropriate conditions, the chemical potential of the dots oscillates periodically with B due to the transfer of composite fermions between quasi-Landau bands. This effect is analogous the addition spectrum oscillations which occur in quantum dots in the integer quantum Hall regime. Period f0 oscillations are found in sharply confined dots with filling factors nu = 2/5 and nu = 2/3. Period 3 f0 oscillations are found in a parabolically confined nu = 2/5 dot. More generally, we argue that the oscillation period of dots with band pinning should vary continuously with B, whereas the period of dots without band pinning is f0 .
Laskin, Nick
2018-01-01
Fractional quantum mechanics is a recently emerged and rapidly developing field of quantum physics. This is the first monograph on fundamentals and physical applications of fractional quantum mechanics, written by its founder. The fractional Schrödinger equation and the fractional path integral are new fundamental physical concepts introduced and elaborated in the book. The fractional Schrödinger equation is a manifestation of fractional quantum mechanics. The fractional path integral is a new mathematical tool based on integration over Lévy flights. The fractional path integral method enhances the well-known Feynman path integral framework. Related topics covered in the text include time fractional quantum mechanics, fractional statistical mechanics, fractional classical mechanics and the α-stable Lévy random process. The book is well-suited for theorists, pure and applied mathematicians, solid-state physicists, chemists, and others working with the Schrödinger equation, the path integral technique...
International Nuclear Information System (INIS)
Lindelof, P.E.; Bruus, H.; Taboryski, R.; Soerensen, C.B.
1989-01-01
An inverted and a normal GaAs/AlGaAs interface grown back to back in a socalled selectively doped double heterostructure (SD DH) has been studied in magnetic fields up to 12 tesla and at temperatures down to 0.3 K. The longitudinal resistance goes to zero at minima of the Shubnikov-de Haas oscillations. The Hall resistivity is found to exhibit the quantum Hall effect. By etching the surface of the double heterostructure wafer we create an unbalance in the density of electrons in the two parallel two-dimensional electronic sheets. Although we in this way create only a modest change in the electron densities, we observe a significant change in the Shubnikov-de Haas oscillations, which can be interpreted as a beat between the oscillations of two electron layers with different densities. At the same time we observe a significant variation of the width of the quantum Hall steps. The most astonishing feature of our results is a clear quantum Hall plateou at 1/2 filling in each of the two parallel layers observed at temperatures below 1 K at a magnetic field above 10 T. Weak localization was also studied and such experiments are consistent with two parallel and independent two-dimensional electronic layers. (orig.)
The quantum Hall effects: Philosophical approach
Lederer, P.
2015-05-01
The Quantum Hall Effects offer a rich variety of theoretical and experimental advances. They provide interesting insights on such topics as gauge invariance, strong interactions in Condensed Matter physics, emergence of new paradigms. This paper focuses on some related philosophical questions. Various brands of positivism or agnosticism are confronted with the physics of the Quantum Hall Effects. Hacking's views on Scientific Realism, Chalmers' on Non-Figurative Realism are discussed. It is argued that the difficulties with those versions of realism may be resolved within a dialectical materialist approach. The latter is argued to provide a rational approach to the phenomena, theory and ontology of the Quantum Hall Effects.
Direct comparison of fractional and integer quantized Hall resistance
Ahlers, Franz J.; Götz, Martin; Pierz, Klaus
2017-08-01
We present precision measurements of the fractional quantized Hall effect, where the quantized resistance {{R}≤ft[ 1/3 \\right]} in the fractional quantum Hall state at filling factor 1/3 was compared with a quantized resistance {{R}[2]} , represented by an integer quantum Hall state at filling factor 2. A cryogenic current comparator bridge capable of currents down to the nanoampere range was used to directly compare two resistance values of two GaAs-based devices located in two cryostats. A value of 1-(5.3 ± 6.3) 10-8 (95% confidence level) was obtained for the ratio ({{R}≤ft[ 1/3 \\right]}/6{{R}[2]} ). This constitutes the most precise comparison of integer resistance quantization (in terms of h/e 2) in single-particle systems and of fractional quantization in fractionally charged quasi-particle systems. While not relevant for practical metrology, such a test of the validity of the underlying physics is of significance in the context of the upcoming revision of the SI.
Mesoscopic effects in the quantum Hall regime
Indian Academy of Sciences (India)
. When band mixing between multiple Landau levels is present, mesoscopic effects cause a crossover from a sequence of quantum Hall transitions for weak disorder to classical behavior for strong disorder. This behavior may be of relevance ...
Novel optical probe for quantum Hall system
Indian Academy of Sciences (India)
to explore Landau levels of a two-dimensional electron gas (2DEG) in modulation doped ... Keywords. Surface photovoltage spectroscopy; quantum Hall effect; Landau levels; edge states. ... An optical fibre carries light from tunable diode laser.
Quantum Theory of Conducting Matter Superconductivity and Quantum Hall Effect
Fujita, Shigeji; Godoy, Salvador
2009-01-01
Explains major superconducting properties including zero resistance, Meissner effect, sharp phase change, flux quantization, excitation energy gap, and Josephson effects using quantum statistical mechanical calculations. This book covers the 2D superconductivity and the quantum Hall effects
Properties of Nonabelian Quantum Hall States
Simon, Steven H.
2004-03-01
The quantum statistics of particles refers to the behavior of a multiparticle wavefunction under adiabatic interchange of two identical particles. While a three dimensional world affords the possibilities of Bosons or Fermions, the two dimensional world has more exotic possibilities such as Fractional and Nonabelian statistics (J. Frölich, in ``Nonperturbative Quantum Field Theory", ed, G. t'Hooft. 1988). The latter is perhaps the most interesting where the wavefunction obeys a ``nonabelian'' representation of the braid group - meaning that braiding A around B then B around C is not the same as braiding B around C then A around B. This property enables one to think about using these exotic systems for robust topological quantum computation (M. Freedman, A. Kitaev, et al, Bull Am Math Soc 40, 31 (2003)). Surprisingly, it is thought that quasiparticles excitations with such nonabelian statistics may actually exist in certain quantum Hall states that have already been observed. The most likely such candidate is the quantum Hall ν=5/2 state(R. L. Willett et al, Phys. Rev. Lett. 59, 1776-1779 (1987)), thought to be a so-called Moore-Read Pfaffian state(G. Moore and N. Read, Nucl Phys. B360 362 (1991)), which can be thought of as a p-wave paired superconducting state of composite fermions(M. Greiter, X. G. Wen, and F. Wilczek, PRL 66, 3205 (1991)). Using this superconducting analogy, we use a Chern-Simons field theory approach to make a number of predictions as to what experimental signatures one should expect for this state if it really is this Moore-Read state(K. Foster, N. Bonesteel, and S. H. Simon, PRL 91 046804 (2003)). We will then discuss how the nonabelian statistics can be explored in detail using a quantum monte-carlo approach (Y. Tserkovnyak and S. H. Simon, PRL 90 106802 (2003)), (I. Finkler, Y. Tserkovnyak, and S. H. Simon, work in progress.) that allows one to explicitly drag one particle around another and observe the change in the wavefunctions
The quantum Hall effect in quantum dot systems
International Nuclear Information System (INIS)
Beltukov, Y M; Greshnov, A A
2014-01-01
It is proposed to use quantum dots in order to increase the temperatures suitable for observation of the integer quantum Hall effect. A simple estimation using Fock-Darwin spectrum of a quantum dot shows that good part of carriers localized in quantum dots generate the intervals of plateaus robust against elevated temperatures. Numerical calculations employing local trigonometric basis and highly efficient kernel polynomial method adopted for computing the Hall conductivity reveal that quantum dots may enhance peak temperature for the effect by an order of magnitude, possibly above 77 K. Requirements to potentials, quality and arrangement of the quantum dots essential for practical realization of such enhancement are indicated. Comparison of our theoretical results with the quantum Hall measurements in InAs quantum dot systems from two experimental groups is also given
The fractional quantum Hall effect
International Nuclear Information System (INIS)
Stoermer, H.L.
1999-01-01
The article is a translation of the lecture on the title topic, delivered on the occasion of the Noble Prize awarding ceremony in 1998. The outline is completed with the author's autobiography. (P.A.)
Infinite symmetry in the quantum Hall effect
Directory of Open Access Journals (Sweden)
Lütken C.A.
2014-04-01
Full Text Available The new states of matter and concomitant quantum critical phenomena revealed by the quantum Hall effect appear to be accompanied by an emergent modular symmetry. The extreme rigidity of this infinite symmetry makes it easy to falsify, but two decades of experiments have failed to do so, and the location of quantum critical points predicted by the symmetry is in increasingly accurate agreement with scaling experiments. The symmetry severely constrains the structure of the effective quantum field theory that encodes the low energy limit of quantum electrodynamics of 1010 charges in two dirty dimensions. If this is a non-linear σ-model the target space is a torus, rather than the more familiar sphere. One of the simplest toroidal models gives a critical (correlation length exponent that agrees with the value obtained from numerical simulations of the quantum Hall effect.
Local Thermometry of Neutral Modes on the Quantum Hall Edge
Hart, Sean; Venkatachalam, Vivek; Pfeiffer, Loren; West, Ken; Yacoby, Amir
2012-02-01
A system of electrons in two dimensions and strong magnetic fields can be tuned to create a gapped 2D system with one dimensional channels along the edge. Interactions among these edge modes can lead to independent transport of charge and heat, even in opposite directions. Measuring the chirality and transport properties of these charge and heat modes can reveal otherwise hidden structure in the edge. Here, we heat the outer edge of such a quantum Hall system using a quantum point contact. By placing quantum dots upstream and downstream along the edge of the heater, we can measure both the chemical potential and temperature of that edge to study charge and heat transport, respectively. We find that charge is transported exclusively downstream, but heat can be transported upstream when the edge has additional structure related to fractional quantum Hall physics.
Localization in a quantum spin Hall system.
Onoda, Masaru; Avishai, Yshai; Nagaosa, Naoto
2007-02-16
The localization problem of electronic states in a two-dimensional quantum spin Hall system (that is, a symplectic ensemble with topological term) is studied by the transfer matrix method. The phase diagram in the plane of energy and disorder strength is exposed, and demonstrates "levitation" and "pair annihilation" of the domains of extended states analogous to that of the integer quantum Hall system. The critical exponent nu for the divergence of the localization length is estimated as nu congruent with 1.6, which is distinct from both exponents pertaining to the conventional symplectic and the unitary quantum Hall systems. Our analysis strongly suggests a different universality class related to the topology of the pertinent system.
Quantum energy teleportation in a quantum Hall system
Energy Technology Data Exchange (ETDEWEB)
Yusa, Go; Izumida, Wataru; Hotta, Masahiro [Department of Physics, Tohoku University, Sendai 980-8578 (Japan)
2011-09-15
We propose an experimental method for a quantum protocol termed quantum energy teleportation (QET), which allows energy transportation to a remote location without physical carriers. Using a quantum Hall system as a realistic model, we discuss the physical significance of QET and estimate the order of energy gain using reasonable experimental parameters.
Guterding, Daniel; Jeschke, Harald O; Valentí, Roser
2016-05-17
Electronic states with non-trivial topology host a number of novel phenomena with potential for revolutionizing information technology. The quantum anomalous Hall effect provides spin-polarized dissipation-free transport of electrons, while the quantum spin Hall effect in combination with superconductivity has been proposed as the basis for realizing decoherence-free quantum computing. We introduce a new strategy for realizing these effects, namely by hole and electron doping kagome lattice Mott insulators through, for instance, chemical substitution. As an example, we apply this new approach to the natural mineral herbertsmithite. We prove the feasibility of the proposed modifications by performing ab-initio density functional theory calculations and demonstrate the occurrence of the predicted effects using realistic models. Our results herald a new family of quantum anomalous Hall and quantum spin Hall insulators at affordable energy/temperature scales based on kagome lattices of transition metal ions.
Quantum Hall Conductivity and Topological Invariants
Reyes, Andres
2001-04-01
A short survey of the theory of the Quantum Hall effect is given emphasizing topological aspects of the quantization of the conductivity and showing how topological invariants can be derived from the hamiltonian. We express these invariants in terms of Chern numbers and show in precise mathematical terms how this relates to the Kubo formula.
Pseudospin anisotropy classification of quantum Hall ferromagnets
Czech Academy of Sciences Publication Activity Database
Jungwirth, Tomáš; MacDonald, A. H.
2000-01-01
Roč. 63, č. 3 (2000), s. 035305-1 - 035305-9 ISSN 0163-1829 R&D Projects: GA ČR GA202/98/0085 Institutional research plan: CEZ:AV0Z1010914 Keywords : quantum Hall ferromagnets * anisotropy Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 3.065, year: 2000
Josephson tunneling in bilayer quantum Hall system
International Nuclear Information System (INIS)
Ezawa, Z.F.; Tsitsishvili, G.; Sawada, A.
2012-01-01
A Bose–Einstein condensation is formed by composite bosons in the quantum Hall state. A composite boson carries the fundamental charge (−e). We investigate Josephson tunneling of such charges in the bilayer quantum Hall system at the total filling ν=1. We show the existence of the critical current for the tunneling current to be coherent and dissipationless. Our results explain recent experiments due to [L. Tiemann, Y. Yoon, W. Dietsche, K. von Klitzing, W. Wegscheider, Phys. Rev. B 80 (2009) 165120] and due to [Y. Yoon, L. Tiemann, S. Schmult, W. Dietsche, K. von Klitzing, Phys. Rev. Lett. 104 (2010) 116802]. We predict also how the critical current changes as the sample is tilted in the magnetic field. -- Highlights: ► Composite bosons undergo Bose–Einstein condensation to form the bilayer quantum Hall state. ► A composite boson is a single electron bound to a flux quantum and carries one unit charge. ► Quantum coherence develops due to the condensation. ► Quantum coherence drives the supercurrent in each layer and the tunneling current. ► There exists the critical input current so that the tunneling current is coherent and dissipationless.
Observation of the Zero Hall Plateau in a Quantum Anomalous Hall Insulator
Energy Technology Data Exchange (ETDEWEB)
Feng, Yang; Feng, Xiao; Ou, Yunbo; Wang, Jing; Liu, Chang; Zhang, Liguo; Zhao, Dongyang; Jiang, Gaoyuan; Zhang, Shou-Cheng; He, Ke; Ma, Xucun; Xue, Qi-Kun; Wang, Yayu
2015-09-16
We report experimental investigations on the quantum phase transition between the two opposite Hall plateaus of a quantum anomalous Hall insulator. We observe a well-defined plateau with zero Hall conductivity over a range of magnetic field around coercivity when the magnetization reverses. The features of the zero Hall plateau are shown to be closely related to that of the quantum anomalous Hall effect, but its temperature evolution exhibits a significant difference from the network model for a conventional quantum Hall plateau transition. We propose that the chiral edge states residing at the magnetic domain boundaries, which are unique to a quantum anomalous Hall insulator, are responsible for the novel features of the zero Hall plateau.
Synthetic Topological Qubits in Conventional Bilayer Quantum Hall Systems
Directory of Open Access Journals (Sweden)
Maissam Barkeshli
2014-11-01
Full Text Available The idea of topological quantum computation is to build powerful and robust quantum computers with certain macroscopic quantum states of matter called topologically ordered states. These systems have degenerate ground states that can be used as robust “topological qubits” to store and process quantum information. In this paper, we propose a new experimental setup that can realize topological qubits in a simple bilayer fractional quantum Hall system with proper electric gate configurations. Our proposal is accessible with current experimental techniques, involves well-established topological states, and, moreover, can realize a large class of topological qubits, generalizing the Majorana zero modes studied in recent literature to more computationally powerful possibilities. We propose three tunneling and interferometry experiments to detect the existence and nonlocal topological properties of the topological qubits.
Large quantum rings in the ν > 1 quantum Hall regime
International Nuclear Information System (INIS)
Raesaenen, E; Aichinger, M
2009-01-01
We study computationally the ground-state properties of large quantum rings in the filling-factor ν>1 quantum Hall regime. We show that the arrangement of electrons into different Landau levels leads to clear signatures in the total energies as a function of the magnetic field. In this context, we discuss possible approximations for the filling factor ν in the system. We are able to characterize integer-ν states in quantum rings in an analogy with conventional quantum Hall droplets. We also find a partially spin-polarized state between ν = 2 and 3. Despite the specific topology of a quantum ring, this state is strikingly reminiscent of the recently found ν = 5/2 state in a quantum dot.
Large quantum rings in the ν > 1 quantum Hall regime.
Räsänen, E; Aichinger, M
2009-01-14
We study computationally the ground-state properties of large quantum rings in the filling-factor ν>1 quantum Hall regime. We show that the arrangement of electrons into different Landau levels leads to clear signatures in the total energies as a function of the magnetic field. In this context, we discuss possible approximations for the filling factor ν in the system. We are able to characterize integer-ν states in quantum rings in an analogy with conventional quantum Hall droplets. We also find a partially spin-polarized state between ν = 2 and 3. Despite the specific topology of a quantum ring, this state is strikingly reminiscent of the recently found ν = 5/2 state in a quantum dot.
Single-electron quantum tomography in quantum Hall edge channels
International Nuclear Information System (INIS)
Grenier, Ch; Degiovanni, P; Herve, R; Bocquillon, E; Parmentier, F D; Placais, B; Berroir, J M; Feve, G
2011-01-01
We propose a quantum tomography protocol to measure single-electron coherence in quantum Hall edge channels, and therefore access for the first time the wavefunction of single-electron excitations propagating in ballistic quantum conductors. Its implementation would open the way to quantitative studies of single-electron decoherence and would provide a quantitative tool for analyzing single- to few-electron sources. We show how this protocol could be implemented using ultrahigh-sensitivity noise measurement schemes.
Quantum Hall effect in epitaxial graphene with permanent magnets.
Parmentier, F D; Cazimajou, T; Sekine, Y; Hibino, H; Irie, H; Glattli, D C; Kumada, N; Roulleau, P
2016-12-06
We have observed the well-kown quantum Hall effect (QHE) in epitaxial graphene grown on silicon carbide (SiC) by using, for the first time, only commercial NdFeB permanent magnets at low temperature. The relatively large and homogeneous magnetic field generated by the magnets, together with the high quality of the epitaxial graphene films, enables the formation of well-developed quantum Hall states at Landau level filling factors v = ±2, commonly observed with superconducting electro-magnets. Furthermore, the chirality of the QHE edge channels can be changed by a top gate. These results demonstrate that basic QHE physics are experimentally accessible in graphene for a fraction of the price of conventional setups using superconducting magnets, which greatly increases the potential of the QHE in graphene for research and applications.
Quantum Hall effect in epitaxial graphene with permanent magnets
Parmentier, F. D.; Cazimajou, T.; Sekine, Y.; Hibino, H.; Irie, H.; Glattli, D. C.; Kumada, N.; Roulleau, P.
2016-12-01
We have observed the well-kown quantum Hall effect (QHE) in epitaxial graphene grown on silicon carbide (SiC) by using, for the first time, only commercial NdFeB permanent magnets at low temperature. The relatively large and homogeneous magnetic field generated by the magnets, together with the high quality of the epitaxial graphene films, enables the formation of well-developed quantum Hall states at Landau level filling factors v = ±2, commonly observed with superconducting electro-magnets. Furthermore, the chirality of the QHE edge channels can be changed by a top gate. These results demonstrate that basic QHE physics are experimentally accessible in graphene for a fraction of the price of conventional setups using superconducting magnets, which greatly increases the potential of the QHE in graphene for research and applications.
The quantum Hall's effect: A quantum electrodynamic phenomenon
International Nuclear Information System (INIS)
Arbab, A. I.
2012-01-01
We have applied Maxwell's equations to study the physics of quantum Hall's effect. The electromagnetic properties of this system are obtained. The Hall's voltage, V H = 2πħ 2 n s /em, where n s is the electron number density, for a 2-dimensional system, and h = 2πħ is the Planck's constant, is found to coincide with the voltage drop across the quantum capacitor. Consideration of the cyclotronic motion of electrons is found to give rise to Hall's resistance. Ohmic resistances in the horizontal and vertical directions have been found to exist before equilibrium state is reached. At a fundamental level, the Hall's effect is found to be equivalent to a resonant LCR circuit with L H = 2π m/e 2 n s and C H = me 2 /2πħ 2 n s satisfying the resonance condition with resonant frequency equal to the inverse of the scattering (relaxation) time, τ s . The Hall's resistance is found to be R H = √L H /C H . The Hall's resistance may be connected with the impedance that the electron wave experiences when it propagates in the 2-dimensional gas. (condensed matter: electronic structure, electrical, magnetic, and optical properties)
Experiments on Quantum Hall Topological Phases in Ultra Low Temperatures
International Nuclear Information System (INIS)
Du, Rui-Rui
2015-01-01
This project is to cool electrons in semiconductors to extremely low temperatures and to study new states of matter formed by low-dimensional electrons (or holes). At such low temperatures (and with an intense magnetic field), electronic behavior differs completely from ordinary ones observed at room temperatures or regular low temperature. Studies of electrons at such low temperatures would open the door for fundamental discoveries in condensed matter physics. Present studies have been focused on topological phases in the fractional quantum Hall effect in GaAs/AlGaAs semiconductor heterostructures, and the newly discovered (by this group) quantum spin Hall effect in InAs/GaSb materials. This project consists of the following components: 1) Development of efficient sample cooling techniques and electron thermometry: Our goal is to reach 1 mK electron temperature and reasonable determination of electron temperature; 2) Experiments at ultra-low temperatures: Our goal is to understand the energy scale of competing quantum phases, by measuring the temperature-dependence of transport features. Focus will be placed on such issues as the energy gap of the 5/2 state, and those of 12/5 (and possible 13/5); resistive signature of instability near 1/2 at ultra-low temperatures; 3) Measurement of the 5/2 gaps in the limit of small or large Zeeman energies: Our goal is to gain physics insight of 5/2 state at limiting experimental parameters, especially those properties concerning the spin polarization; 4) Experiments on tuning the electron-electron interaction in a screened quantum Hall system: Our goal is to gain understanding of the formation of paired fractional quantum Hall state as the interaction pseudo-potential is being modified by a nearby screening electron layer; 5) Experiments on the quantized helical edge states under a strong magnetic field and ultralow temperatures: our goal is to investigate both the bulk and edge states in a quantum spin Hall insulator under
Strong quasi-particle tunneling study in the paired quantum Hall states
Nomura, Kentaro; Yoshioka, Daijiro
2001-01-01
The quasi-particle tunneling phenomena in the paired fractional quantum Hall states are studied. A single point-contact system is first considered. Because of relevancy of the quasi-particle tunneling term, the strong tunneling regime should be investigated. Using the instanton method it is shown that the strong quasi-particle tunneling regime is described as the weak electron tunneling regime effectively. Expanding to the network model the paired quantum Hall liquid to insulator transition i...
Valley-chiral quantum Hall state in graphene superlattice structure
Tian, H. Y.; Tao, W. W.; Wang, J.; Cui, Y. H.; Xu, N.; Huang, B. B.; Luo, G. X.; Hao, Y. H.
2016-05-01
We theoretically investigate the quantum Hall effect in a graphene superlattice (GS) system, in which the two valleys of graphene are coupled together. In the presence of a perpendicular magnetic field, an ordinary quantum Hall effect is found with the sequence σxy=ν e^2/h(ν=0,+/-1,+/-2,\\cdots) . At the zeroth Hall platform, a valley-chiral Hall state stemming from the single K or K' valley is found and it is localized only on one sample boundary contributing to the longitudinal conductance but not to the Hall conductivity. Our findings may shed light on the graphene-based valleytronics applications.
OPTICS. Quantum spin Hall effect of light.
Bliokh, Konstantin Y; Smirnova, Daria; Nori, Franco
2015-06-26
Maxwell's equations, formulated 150 years ago, ultimately describe properties of light, from classical electromagnetism to quantum and relativistic aspects. The latter ones result in remarkable geometric and topological phenomena related to the spin-1 massless nature of photons. By analyzing fundamental spin properties of Maxwell waves, we show that free-space light exhibits an intrinsic quantum spin Hall effect—surface modes with strong spin-momentum locking. These modes are evanescent waves that form, for example, surface plasmon-polaritons at vacuum-metal interfaces. Our findings illuminate the unusual transverse spin in evanescent waves and explain recent experiments that have demonstrated the transverse spin-direction locking in the excitation of surface optical modes. This deepens our understanding of Maxwell's theory, reveals analogies with topological insulators for electrons, and offers applications for robust spin-directional optical interfaces. Copyright © 2015, American Association for the Advancement of Science.
On-Chip Microwave Quantum Hall Circulator
Directory of Open Access Journals (Sweden)
A. C. Mahoney
2017-01-01
Full Text Available Circulators are nonreciprocal circuit elements that are integral to technologies including radar systems, microwave communication transceivers, and the readout of quantum information devices. Their nonreciprocity arises from the interference of microwaves over the centimeter scale of the signal wavelength, in the presence of bulky magnetic media that breaks time-reversal symmetry. Here, we realize a completely passive on-chip microwave circulator with size 1/1000th the wavelength by exploiting the chiral, “slow-light” response of a two-dimensional electron gas in the quantum Hall regime. For an integrated GaAs device with 330 μm diameter and about 1-GHz center frequency, a nonreciprocity of 25 dB is observed over a 50-MHz bandwidth. Furthermore, the nonreciprocity can be dynamically tuned by varying the voltage at the port, an aspect that may enable reconfigurable passive routing of microwave signals on chip.
Bulk Versus Edge in the Quantum Hall Effect
Kao, Y. -C.; Lee, D. -H.
1996-01-01
The manifestation of the bulk quantum Hall effect on edge is the chiral anomaly. The chiral anomaly {\\it is} the underlying principle of the ``edge approach'' of quantum Hall effect. In that approach, $\\sxy$ should not be taken as the conductance derived from the space-local current-current correlation function of the pure one-dimensional edge problem.
Hong, Changki; Park, Jinhong; Chung, Yunchul; Choi, Hyungkook; Umansky, Vladimir
2017-11-01
Transmission through a quantum point contact (QPC) in the quantum Hall regime usually exhibits multiple resonances as a function of gate voltage and high nonlinearity in bias. Such behavior is unpredictable and changes sample by sample. Here, we report the observation of a sharp transition of the transmission through an open QPC at finite bias, which was observed consistently for all the tested QPCs. It is found that the bias dependence of the transition can be fitted to the Fermi-Dirac distribution function through universal scaling. The fitted temperature matches quite nicely to the electron temperature measured via shot-noise thermometry. While the origin of the transition is unclear, we propose a phenomenological model based on our experimental results that may help to understand such a sharp transition. Similar transitions are observed in the fractional quantum Hall regime, and it is found that the temperature of the system can be measured by rescaling the quasiparticle energy with the effective charge (e*=e /3 ). We believe that the observed phenomena can be exploited as a tool for measuring the electron temperature of the system and for studying the quasiparticle charges of the fractional quantum Hall states.
Gate-Controlled Transmission of Quantum Hall Edge States in Bilayer Graphene.
Li, Jing; Wen, Hua; Watanabe, Kenji; Taniguchi, Takashi; Zhu, Jun
2018-02-02
The edge states of the quantum Hall and fractional quantum Hall effect of a two-dimensional electron gas carry key information of the bulk excitations. Here we demonstrate gate-controlled transmission of edge states in bilayer graphene through a potential barrier with tunable height. The backscattering rate is continuously varied from 0 to close to 1, with fractional quantized values corresponding to the sequential complete backscattering of individual modes. Our experiments demonstrate the feasibility to controllably manipulate edge states in bilayer graphene, thus opening the door to more complex experiments.
Gate-Controlled Transmission of Quantum Hall Edge States in Bilayer Graphene
Li, Jing; Wen, Hua; Watanabe, Kenji; Taniguchi, Takashi; Zhu, Jun
2018-02-01
The edge states of the quantum Hall and fractional quantum Hall effect of a two-dimensional electron gas carry key information of the bulk excitations. Here we demonstrate gate-controlled transmission of edge states in bilayer graphene through a potential barrier with tunable height. The backscattering rate is continuously varied from 0 to close to 1, with fractional quantized values corresponding to the sequential complete backscattering of individual modes. Our experiments demonstrate the feasibility to controllably manipulate edge states in bilayer graphene, thus opening the door to more complex experiments.
Unconventional quantum Hall effect in Floquet topological insulators
Tahir, M.
2016-07-27
We study an unconventional quantum Hall effect for the surface states of ultrathin Floquet topological insulators in a perpendicular magnetic field. The resulting band structure is modified by photon dressing and the topological property is governed by the low-energy dynamics of a single surface. An exchange of symmetric and antisymmetric surface states occurs by reversing the lights polarization. We find a novel quantum Hall state in which the zeroth Landau level undergoes a phase transition from a trivial insulator state, with Hall conductivity αyx = 0 at zero Fermi energy, to a Hall insulator state with αyx = e2/2h. These findings open new possibilities for experimentally realizing nontrivial quantum states and unusual quantum Hall plateaus at (±1/2,±3/2,±5/2, ...)e2/h. © 2016 IOP Publishing Ltd Printed in the UK.
Unconventional quantum Hall effect in Floquet topological insulators
Tahir, M.; Vasilopoulos, P.; Schwingenschlö gl, Udo
2016-01-01
We study an unconventional quantum Hall effect for the surface states of ultrathin Floquet topological insulators in a perpendicular magnetic field. The resulting band structure is modified by photon dressing and the topological property is governed by the low-energy dynamics of a single surface. An exchange of symmetric and antisymmetric surface states occurs by reversing the lights polarization. We find a novel quantum Hall state in which the zeroth Landau level undergoes a phase transition from a trivial insulator state, with Hall conductivity αyx = 0 at zero Fermi energy, to a Hall insulator state with αyx = e2/2h. These findings open new possibilities for experimentally realizing nontrivial quantum states and unusual quantum Hall plateaus at (±1/2,±3/2,±5/2, ...)e2/h. © 2016 IOP Publishing Ltd Printed in the UK.
Quantum Hall Ferroelectrics and Nematics in Multivalley Systems
Sodemann, Inti; Zhu, Zheng; Fu, Liang
2017-10-01
We study broken symmetry states at integer Landau-level fillings in multivalley quantum Hall systems whose low-energy dispersions are anisotropic. When the Fermi surface of individual pockets lacks twofold rotational symmetry, like in bismuth (111) [Feldman et al. , Observation of a Nematic Quantum Hall Liquid on the Surface of Bismuth, Science 354, 316 (2016), 10.1126/science.aag1715] and in Sn1 -xPbxSe (001) [Dziawa et al., Topological Crystalline Insulator States in Pb1 -xSnxSe , Nat. Mater. 11, 1023 (2012), 10.1038/nmat3449] surfaces, interactions tend to drive the formation of quantum Hall ferroelectric states. We demonstrate that the dipole moment in these states has an intimate relation to the Fermi surface geometry of the parent metal. In quantum Hall nematic states, like those arising in AlAs quantum wells, we demonstrate the existence of unusually robust Skyrmion quasiparticles.
Quantum Hall states of atomic Bose gases: Density profiles in single-layer and multilayer geometries
International Nuclear Information System (INIS)
Cooper, N. R.; Lankvelt, F. J. M. van; Reijnders, J. W.; Schoutens, K.
2005-01-01
We describe the density profiles of confined atomic Bose gases in the high-rotation limit, in single-layer and multilayer geometries. We show that, in a local-density approximation, the density in a single layer shows a landscape of quantized steps due to the formation of incompressible liquids, which are analogous to fractional quantum Hall liquids for a two-dimensional electron gas in a strong magnetic field. In a multilayered setup we find different phases, depending on the strength of the interlayer tunneling t. We discuss the situation where a vortex lattice in the three-dimensional condensate (at large tunneling) undergoes quantum melting at a critical tunneling t c 1 . For tunneling well below t c 1 one expects weakly coupled or isolated layers, each exhibiting a landscape of quantum Hall liquids. After expansion, this gives a radial density distribution with characteristic features (cusps) that provide experimental signatures of the quantum Hall liquids
A review of the quantum Hall effects in MgZnO/ZnO heterostructures
Falson, Joseph; Kawasaki, Masashi
2018-05-01
This review visits recent experimental efforts on high mobility two-dimensional electron systems (2DES) hosted at the Mg x Zn1-x O/ZnO heterointerface. We begin with the growth of these samples, and highlight the key characteristics of ozone-assisted molecular beam epitaxy required for their production. The transport characteristics of these structures are found to rival that of traditional semiconductor material systems, as signified by the high electron mobility (μ > 1000 000 cm2 Vs‑1) and rich quantum Hall features. Owing to a large effective mass and small dielectric constant, interaction effects are an order of magnitude stronger in comparison with the well studied GaAs-based 2DES. The strong correlation physics results in robust Fermi-liquid renormalization of the effective mass and spin susceptibility of carriers, which in turn dictates the parameter space for the quantum Hall effect. Finally, we explore the quantum Hall effect with a particular emphasis on the spin degree of freedom of carriers, and how their large spin splitting allows control of the ground states encountered at ultra-low temperatures within the fractional quantum Hall regime. We discuss in detail the physics of even-denominator fractional quantum Hall states, whose observation and underlying character remain elusive and exotic.
Higher (odd dimensional quantum Hall effect and extended dimensional hierarchy
Directory of Open Access Journals (Sweden)
Kazuki Hasebe
2017-07-01
Full Text Available We demonstrate dimensional ladder of higher dimensional quantum Hall effects by exploiting quantum Hall effects on arbitrary odd dimensional spheres. Non-relativistic and relativistic Landau models are analyzed on S2k−1 in the SO(2k−1 monopole background. The total sub-band degeneracy of the odd dimensional lowest Landau level is shown to be equal to the winding number from the base-manifold S2k−1 to the one-dimension higher SO(2k gauge group. Based on the chiral Hopf maps, we clarify the underlying quantum Nambu geometry for odd dimensional quantum Hall effect and the resulting quantum geometry is naturally embedded also in one-dimension higher quantum geometry. An origin of such dimensional ladder connecting even and odd dimensional quantum Hall effects is illuminated from a viewpoint of the spectral flow of Atiyah–Patodi–Singer index theorem in differential topology. We also present a BF topological field theory as an effective field theory in which membranes with different dimensions undergo non-trivial linking in odd dimensional space. Finally, an extended version of the dimensional hierarchy for higher dimensional quantum Hall liquids is proposed, and its relationship to quantum anomaly and D-brane physics is discussed.
Physics Nobel Prize Goes to Tsui, Stormer and Laughlin for the Fractional Quantum Hall Effect
International Nuclear Information System (INIS)
Schwarzschild, Bertram
1998-01-01
This year's Nobel Prize in Physics is shared by Robert Laughlin (Stanford), Horst Stormer (Columbia University and Bell Laboratories) and Daniel Tsui (Princeton), for their roles in the discovery and explanation of the fractional quantum Hall effect. In 1982, when Stormer and Tsui were experimenters at Bell Labs, they and their colleague Arthur Gossard discovered this totally unexpected quantum effect in the transport properties of two‐dimensional electron gases at low temperature in strong magnetic fields.’ (See PHYSICS TODAY, July 1983, page 19.)
Physics Nobel Prize Goes to Tsui, Stormer and Laughlin for the Fractional Quantum Hall Effect
Energy Technology Data Exchange (ETDEWEB)
Schwarzschild, Bertram
1998-12-15
This year's Nobel Prize in Physics is shared by Robert Laughlin (Stanford), Horst Stormer (Columbia University and Bell Laboratories) and Daniel Tsui (Princeton), for their roles in the discovery and explanation of the fractional quantum Hall effect. In 1982, when Stormer and Tsui were experimenters at Bell Labs, they and their colleague Arthur Gossard discovered this totally unexpected quantum effect in the transport properties of two‐dimensional electron gases at low temperature in strong magnetic fields.’ (See PHYSICS TODAY, July 1983, page 19.)
Complex scattering dynamics and the quantum Hall effects
International Nuclear Information System (INIS)
Trugman, S.A.
1994-01-01
We review both classical and quantum potential scattering in two dimensions in a magnetic field, with applications to the quantum Hall effect. Classical scattering is complex, due to the approach of scattering states to an infinite number of dynamically bound states. Quantum scattering follows the classical behavior rather closely, exhibiting sharp resonances in place of the classical bound states. Extended scatterers provide a quantitative explanation for the breakdown of the QHE at a comparatively small Hall voltage as seen by Kawaji et al., and possibly for noise effects
Complex dynamics of the integer quantum Hall effect
International Nuclear Information System (INIS)
Trugman, S.A.; Nicopoulos, V.N.; Florida Univ., Gainesville, FL
1991-01-01
We investigate both classical and quantum potential scattering in two dimensions in a magnetic field, with applications to the integer quantum Hall effect. Classical scattering is complex, due in one case to the approach of scattering states to an infinite number of bound states. We show that bound states are generic, and occur for all but extremely smooth scattering potentials (|rvec ∇| → 0). Quantum scattering follows the classical behavior rather closely, exhibiting sharp resonances rather than classical bound states. Extended scatterers provide an explanation for the breakdown of the QHE at a comparatively small Hall voltage. 16 refs., 14 figs
Anisotropic intrinsic spin Hall effect in quantum wires
International Nuclear Information System (INIS)
Cummings, A W; Akis, R; Ferry, D K
2011-01-01
We use numerical simulations to investigate the spin Hall effect in quantum wires in the presence of both Rashba and Dresselhaus spin-orbit coupling. We find that the intrinsic spin Hall effect is highly anisotropic with respect to the orientation of the wire, and that the nature of this anisotropy depends strongly on the electron density and the relative strengths of the Rashba and Dresselhaus spin-orbit couplings. In particular, at low densities, when only one subband of the quantum wire is occupied, the spin Hall effect is strongest for electron momentum along the [1-bar 10] axis, which is the opposite of what is expected for the purely 2D case. In addition, when more than one subband is occupied, the strength and anisotropy of the spin Hall effect can vary greatly over relatively small changes in electron density, which makes it difficult to predict which wire orientation will maximize the strength of the spin Hall effect. These results help to illuminate the role of quantum confinement in spin-orbit-coupled systems, and can serve as a guide for future experimental work on the use of quantum wires for spin-Hall-based spintronic applications. (paper)
Modular invariance, universality and crossover in the quantum Hall effect
International Nuclear Information System (INIS)
Dolan, Brian P.
1999-01-01
An analytic form for the conductivity tensor in crossover between two quantum Hall plateaux is derived, which appears to be in good agreement with existing experimental data. The derivation relies on an assumed symmetry between quantum Hall states, a generalisation of the law of corresponding states from rational filling factors to complex conductivity, which has a mathematical expression in terms of an action of the modular group on the upper-half complex conductivity plane. This symmetry implies universality in quantum Hall crossovers. The assumption that the β-function for the complex conductivity is a complex analytic function, together with some experimental constraints, results in an analytic expression for the crossover, as a function of the external magnetic field
Field theory approach to quantum hall effect
International Nuclear Information System (INIS)
Cabo, A.; Chaichian, M.
1990-07-01
The Fradkin's formulation of statistical field theory is applied to the Coulomb interacting electron gas in a magnetic field. The electrons are confined to a plane in normal 3D-space and also interact with the physical 3D-electromagnetic field. The magnetic translation group (MTG) Ward identities are derived. Using them it is shown that the exact electron propagator is diagonalized in the basis of the wave functions of the free electron in a magnetic field whenever the MTG is unbroken. The general tensor structure of the polarization operator is obtained and used to show that the Chern-Simons action always describes the Hall effect properties of the system. A general proof of the Streda formula for the Hall conductivity is presented. It follows that the coefficient of the Chern-Simons terms in the long-wavelength approximation is exactly given by this relation. Such a formula, expressing the Hall conductivity as a simple derivative, in combination with diagonal form of the full propagator allows to obtain a simple expressions for the filling factor and the Hall conductivity. Indeed, these results, after assuming that the chemical potential lies in a gap of the density of states, lead to the conclusion that the Hall conductivity is given without corrections by σ xy = νe 2 /h where ν is the filling factor. In addition it follows that the filling factor is independent of the magnetic field if the chemical potential remains in the gap. (author). 21 ref, 1 fig
Interaction Induced Quantum Valley Hall Effect in Graphene
Directory of Open Access Journals (Sweden)
E. C. Marino
2015-03-01
Full Text Available We use pseudo-quantum electrodynamics in order to describe the full electromagnetic interaction of the p electrons in graphene in a consistent 2D formulation. We first consider the effect of this interaction in the vacuum polarization tensor or, equivalently, in the current correlator. This allows us to obtain the T→0 conductivity after a smooth zero-frequency limit is taken in Kubo’s formula. Thereby, we obtain the usual expression for the minimal conductivity plus corrections due to the interaction that bring it closer to the experimental value. We then predict the onset of an interaction-driven spontaneous quantum valley Hall effect below an activation temperature of the order of 2 K. The transverse (Hall valley conductivity is evaluated exactly and shown to coincide with the one in the usual quantum Hall effect. Finally, by considering the effects of pseudo-quantum electrodynamics, we show that the electron self-energy is such that a set of P- and T-symmetric gapped electron energy eigenstates are dynamically generated, in association with the quantum valley Hall effect.
A programmable quantum current standard from the Josephson and the quantum Hall effects
Energy Technology Data Exchange (ETDEWEB)
Poirier, W., E-mail: wilfrid.poirier@lne.fr; Lafont, F.; Djordjevic, S.; Schopfer, F.; Devoille, L. [Quantum metrology group, Laboratoire National de métrologie et d' Essais, 29 avenue Roger Hennequin, 78197 Trappes (France)
2014-01-28
We propose a way to realize a programmable quantum current standard (PQCS) from the Josephson voltage standard and the quantum Hall resistance standard (QHR) exploiting the multiple connection technique provided by the quantum Hall effect (QHE) and the exactness of the cryogenic current comparator. The PQCS could lead to breakthroughs in electrical metrology like the realization of a programmable quantum current source, a quantum ampere-meter, and a simplified closure of the quantum metrological triangle. Moreover, very accurate universality tests of the QHE could be performed by comparing PQCS based on different QHRs.
Quantum hall conductivity in a Landau type model with a realistic geometry II
International Nuclear Information System (INIS)
Chandelier, F.; Georgelin, Y.; Masson, T.; Wallet, J.-C.
2004-01-01
We use a mathematical framework that we introduced in a previous paper to study geometrical and quantum mechanical aspects of a Hall system with finite size and general boundary conditions. Geometrical structures control possibly the integral or fractional quantization of the Hall conductivity depending on the value of NB/2π (N is the number of charge carriers and B is the magnetic field). When NB/2π is irrational, we show that monovaluated wave functions can be constructed only on the graph of a free group with two generators. When NB/2π is rational, the relevant space becomes a punctured Riemann surface. We finally discuss our results from a phenomenological viewpoint
Parity Anomaly and Spin Transmutation in Quantum Spin Hall Josephson Junctions.
Peng, Yang; Vinkler-Aviv, Yuval; Brouwer, Piet W; Glazman, Leonid I; von Oppen, Felix
2016-12-23
We study the Josephson effect in a quantum spin Hall system coupled to a localized magnetic impurity. As a consequence of the fermion parity anomaly, the spin of the combined system of impurity and spin-Hall edge alternates between half-integer and integer values when the superconducting phase difference across the junction advances by 2π. This leads to characteristic differences in the splittings of the spin multiplets by exchange coupling and single-ion anisotropy at phase differences, for which time-reversal symmetry is preserved. We discuss the resulting 8π-periodic (or Z_{4}) fractional Josephson effect in the context of recent experiments.
The quantum Hall effect at 5/2 filling factor
International Nuclear Information System (INIS)
Willett, R L
2013-01-01
Experimental discovery of a quantized Hall state at 5/2 filling factor presented an enigmatic finding in an established field of study that has remained an open issue for more than twenty years. In this review we first examine the experimental requirements for observing this state and outline the initial theoretical implications and predictions. We will then follow the chronology of experimental studies over the years and present the theoretical developments as they pertain to experiments, directed at sets of issues. These topics will include theoretical and experimental examination of the spin properties at 5/2; is the state spin polarized? What properties of the higher Landau levels promote development of the 5/2 state, what other correlation effects are observed there, and what are their interactions with the 5/2 state? The 5/2 state is not a robust example of the fractional quantum Hall effect: what experimental and material developments have allowed enhancement of the effect? Theoretical developments from initial pictures have promoted the possibility that 5/2 excitations are exceptional; do they obey non-abelian statistics? The proposed experiments to determine this and their executions in various forms will be presented: this is the heart of this review. Experimental examination of the 5/2 excitations through interference measurements will be reviewed in some detail, focusing on recent results that demonstrate consistency with the picture of non-abelian charges. The implications of this in the more general physics picture is that the 5/2 excitations, shown to be non-abelian, should exhibit the properties of Majorana operators. This will be the topic of the last review section. (review article)
Quantum Hall conductivity in a Landau type model with a realistic geometry
International Nuclear Information System (INIS)
Chandelier, F.; Georgelin, Y.; Masson, T.; Wallet, J.-C.
2003-01-01
In this paper, we revisit some quantum mechanical aspects related to the quantum Hall effect. We consider a Landau type model, paying a special attention to the experimental and geometrical features of quantum Hall experiments. The resulting formalism is then used to compute explicitly the Hall conductivity from a Kubo formula
Admittance of multiterminal quantum Hall conductors at kilohertz frequencies
International Nuclear Information System (INIS)
Hernández, C.; Consejo, C.; Chaubet, C.; Degiovanni, P.
2014-01-01
We present an experimental study of the low frequency admittance of quantum Hall conductors in the [100 Hz, 1 MHz] frequency range. We show that the frequency dependence of the admittance of the sample strongly depends on the topology of the contacts connections. Our experimental results are well explained within the Christen and Büttiker approach for finite frequency transport in quantum Hall edge channels taking into account the influence of the coaxial cables capacitance. In the Hall bar geometry, we demonstrate that there exists a configuration in which the cable capacitance does not influence the admittance measurement of the sample. In this case, we measure the electrochemical capacitance of the sample and observe its dependence on the filling factor
Admittance of multiterminal quantum Hall conductors at kilohertz frequencies
Energy Technology Data Exchange (ETDEWEB)
Hernández, C. [Departamento de Física, Universidad Militar Nueva Granada, Carrera 11 101-80 Bogotá D.C. (Colombia); Consejo, C.; Chaubet, C., E-mail: christophe.chaubet@univ-montp2.fr [Université Montpellier 2, Laboratoire Charles Coulomb UMR5221, F-34095 Montpellier, France and CNRS, Laboratoire Charles Coulomb UMR5221, F-34095 Montpellier (France); Degiovanni, P. [Université de Lyon, Fédération de Physique Andrée Marie Ampère, CNRS, Laboratoire de Physique de l' Ecole Normale Supérieure de Lyon, 46 allée d' Italie, 69364 Lyon Cedex 07 (France)
2014-03-28
We present an experimental study of the low frequency admittance of quantum Hall conductors in the [100 Hz, 1 MHz] frequency range. We show that the frequency dependence of the admittance of the sample strongly depends on the topology of the contacts connections. Our experimental results are well explained within the Christen and Büttiker approach for finite frequency transport in quantum Hall edge channels taking into account the influence of the coaxial cables capacitance. In the Hall bar geometry, we demonstrate that there exists a configuration in which the cable capacitance does not influence the admittance measurement of the sample. In this case, we measure the electrochemical capacitance of the sample and observe its dependence on the filling factor.
Zero field Quantum Hall Effect in QED3
International Nuclear Information System (INIS)
Raya, K; Sánchez-Madrigal, S; Raya, A
2013-01-01
We study analytic structure of the fermion propagator in the Quantum Electrodynamics in 2+1 dimensions (QED3) in the Landau gauge, both in perturbation theory and nonperturbatively, by solving the corresponding Schwinger-Dyson equation in rainbow approximation. In the chiral limit, we found many nodal solutions, which could be interpreted as vacuum excitations. Armed with these solutions, we use the Kubo formula and calculate the filling factor for the zero field Quantum Hall Effect
Algebraic quantization, good operators and fractional quantum numbers
International Nuclear Information System (INIS)
Aldaya, V.; Calixto, M.; Guerrero, J.
1996-01-01
The problems arising when quantizing systems with periodic boundary conditions are analysed, in an algebraic (group-) quantization scheme, and the failure of the Ehrenfest theorem is clarified in terms of the already defined notion of good (and bad) operators. The analysis of constrained Heisenberg-Weyl groups according to this quantization scheme reveals the possibility for quantum operators without classical analogue and for new quantum (fractional) numbers extending those allowed for Chern classes in traditional Geometric Quantization. This study is illustrated with the examples of the free particle on the circumference and the charged particle in a homogeneous magnetic field on the torus, both examples featuring anomalous operators, non-equivalent quantization and the latter, fractional quantum numbers. These provide the rationale behind flux quantization in superconducting rings and Fractional Quantum Hall Effect, respectively. (orig.)
Spin-singlet quantum Hall states and Jack polynomials with a prescribed symmetry
International Nuclear Information System (INIS)
Estienne, Benoit; Bernevig, B. Andrei
2012-01-01
We show that a large class of bosonic spin-singlet Fractional Quantum Hall model wavefunctions and their quasihole excitations can be written in terms of Jack polynomials with a prescribed symmetry. Our approach describes new spin-singlet quantum Hall states at filling fraction ν=(2k)/(2r-1) and generalizes the (k,r) spin-polarized Jack polynomial states. The NASS and Halperin spin-singlet states emerge as specific cases of our construction. The polynomials express many-body states which contain configurations obtained from a root partition through a generalized squeezing procedure involving spin and orbital degrees of freedom. The corresponding generalized Pauli principle for root partitions is obtained, allowing for counting of the quasihole states. We also extract the central charge and quasihole scaling dimension, and propose a conjecture for the underlying CFT of the (k,r) spin-singlet Jack states.
Imaging of Coulomb-Driven Quantum Hall Edge States
Lai, Keji; Kundhikanjana, Worasom; Kelly, Michael A.; Shen, Zhi-Xun; Shabani, Javad; Shayegan, Mansour
2011-01-01
The edges of a two-dimensional electron gas (2DEG) in the quantum Hall effect (QHE) regime are divided into alternating metallic and insulating strips, with their widths determined by the energy gaps of the QHE states and the electrostatic Coulomb
Composite fermions a unified view of the quantum Hall regime
1998-01-01
One of the most exciting recent developments to have emerged from the quantum Hall effect is the subject of composite fermions. This important volume gives a self-contained, comprehensive description of the subject, including fundamentals, more advanced theoretical work, and results from experimental observations of composite fermions.
Magnus force on quantum Hall skyrmions and vortices
International Nuclear Information System (INIS)
Dhar, S.; Basu, B.; Bandyopadhyay, P.
2003-01-01
We have discussed here the Magnus force acting on the vortices and skyrmions in the quantum Hall systems. We have found that it is generated by the chirality of the system which is associated with the Berry phase and is same for both the cases
The quantum anomalous Hall effect on a star lattice with spin-orbit coupling and an exchange field
International Nuclear Information System (INIS)
Chen Mengsu; Wan Shaolong
2012-01-01
We study a star lattice with Rashba spin-orbit coupling and an exchange field and find that there is a quantum anomalous Hall effect in this system, and that there are five energy gaps at Dirac points and quadratic band crossing points. We calculate the Berry curvature distribution and obtain the Hall conductivity (Chern number ν) quantized as integers, and find that ν =- 1,2,1,1,2 when the Fermi level lies in these five gaps. Our model can be viewed as a general quantum anomalous Hall system and, in limit cases, can give what the honeycomb lattice and kagome lattice give. We also find that there is a nearly flat band with ν = 1 which may provide an opportunity for realizing the fractional quantum anomalous Hall effect. Finally, the chiral edge states on a zigzag star lattice are given numerically, to confirm the topological property of this system. (paper)
Gate-controlled tunneling of quantum Hall edge states in bilayer graphene
Zhu, Jun; Li, Jing; Wen, Hua
Controlled tunneling of integer and fractional quantum Hall edge states provides a powerful tool to probe the physics of 1D systems and exotic particle statistics. Experiments in GaAs 2DEGs employ either a quantum point contact or a line junction tunnel barrier. It is generally difficult to independently control the filling factors νL and νR on the two sides of the barrier. Here we show that in bilayer graphene both νL and νR as well as their Landau level structures can be independently controlled using a dual-split-gate structure. In addition, the height of the line-junction tunnel barrier implemented in our experiments is tunable via a 5th gate. By measuring the tunneling resistance across the junction RT we examine the equilibration of the edge states in a variety of νL/νR scenarios and under different barrier heights. Edge states from both sides are fully mixed in the case of a low barrier. As the barrier height increases, we observe plateaus in RT that correspond to sequential complete backscattering of edge states. Gate-controlled manipulation of edge states offers a new angle to the exploration of quantum Hall magnetism and fractional quantum Hall effect in bilayer graphene.
AC conductivity of a quantum Hall line junction
International Nuclear Information System (INIS)
Agarwal, Amit; Sen, Diptiman
2009-01-01
We present a microscopic model for calculating the AC conductivity of a finite length line junction made up of two counter- or co-propagating single mode quantum Hall edges with possibly different filling fractions. The effect of density-density interactions and a local tunneling conductance (σ) between the two edges is considered. Assuming that σ is independent of the frequency ω, we derive expressions for the AC conductivity as a function of ω, the length of the line junction and other parameters of the system. We reproduce the results of Sen and Agarwal (2008 Phys. Rev. B 78 085430) in the DC limit (ω→0), and generalize those results for an interacting system. As a function of ω, the AC conductivity shows significant oscillations if σ is small; the oscillations become less prominent as σ increases. A renormalization group analysis shows that the system may be in a metallic or an insulating phase depending on the strength of the interactions. We discuss the experimental implications of this for the behavior of the AC conductivity at low temperatures.
Dynamical quantum Hall effect in the parameter space.
Gritsev, V; Polkovnikov, A
2012-04-24
Geometric phases in quantum mechanics play an extraordinary role in broadening our understanding of fundamental significance of geometry in nature. One of the best known examples is the Berry phase [M.V. Berry (1984), Proc. Royal. Soc. London A, 392:45], which naturally emerges in quantum adiabatic evolution. So far the applicability and measurements of the Berry phase were mostly limited to systems of weakly interacting quasi-particles, where interference experiments are feasible. Here we show how one can go beyond this limitation and observe the Berry curvature, and hence the Berry phase, in generic systems as a nonadiabatic response of physical observables to the rate of change of an external parameter. These results can be interpreted as a dynamical quantum Hall effect in a parameter space. The conventional quantum Hall effect is a particular example of the general relation if one views the electric field as a rate of change of the vector potential. We illustrate our findings by analyzing the response of interacting spin chains to a rotating magnetic field. We observe the quantization of this response, which we term the rotational quantum Hall effect.
Quantum Hall Valley Nematics: From Field Theories to Microscopic Models
Parameswaran, Siddharth
The interplay between quantum Hall ordering and spontaneously broken ``internal'' symmetries in two-dimensional electron systems with spin or pseudospin degrees of freedom gives rise to a variety of interesting phenomena, including novel phases, phase transitions, and topological excitations. I will discuss a theory of broken-symmetry quantum Hall states, applicable to a class of multivalley systems, where the symmetry at issue is a point-group element that combines a spatial rotation with a permutation of valley indices. I will explore its ramifications for the phase diagram of a variety of experimental systems, such as AlAs and Si quantum wells and the surface states of bismuth. I will also discuss unconventional transport phenomena in these phases in the presence of quenched randomness, and the possible mechanisms of selection between degenerate broken-symmetry phases in clean systems. I acknowledge support from NSF DMR-1455366.
Effect of quantum tunneling on spin Hall magnetoresistance.
Ok, Seulgi; Chen, Wei; Sigrist, Manfred; Manske, Dirk
2017-02-22
We present a formalism that simultaneously incorporates the effect of quantum tunneling and spin diffusion on the spin Hall magnetoresistance observed in normal metal/ferromagnetic insulator bilayers (such as Pt/Y 3 Fe 5 O 12 ) and normal metal/ferromagnetic metal bilayers (such as Pt/Co), in which the angle of magnetization influences the magnetoresistance of the normal metal. In the normal metal side the spin diffusion is known to affect the landscape of the spin accumulation caused by spin Hall effect and subsequently the magnetoresistance, while on the ferromagnet side the quantum tunneling effect is detrimental to the interface spin current which also affects the spin accumulation. The influence of generic material properties such as spin diffusion length, layer thickness, interface coupling, and insulating gap can be quantified in a unified manner, and experiments that reveal the quantum feature of the magnetoresistance are suggested.
Signatures of lattice geometry in quantum and topological Hall effect
International Nuclear Information System (INIS)
Göbel, Börge; Mook, Alexander; Mertig, Ingrid; Henk, Jürgen
2017-01-01
The topological Hall effect (THE) of electrons in skyrmion crystals (SkXs) is strongly related to the quantum Hall effect (QHE) on lattices. This relation suggests to revisit the QHE because its Hall conductivity can be unconventionally quantized. It exhibits a jump and changes sign abruptly if the Fermi level crosses a van Hove singularity. In this Paper, we investigate the unconventional QHE features by discussing band structures, Hall conductivities, and topological edge states for square and triangular lattices; their origin are Chern numbers of bands in the SkX (THE) or of the corresponding Landau levels (QHE). Striking features in the energy dependence of the Hall conductivities are traced back to the band structure without magnetic field whose properties are dictated by the lattice geometry. Based on these findings, we derive an approximation that allows us to determine the energy dependence of the topological Hall conductivity on any two-dimensional lattice. The validity of this approximation is proven for the honeycomb lattice. We conclude that SkXs lend themselves for experiments to validate our findings for the THE and—indirectly—the QHE. (paper)
Mini array of quantum Hall devices based on epitaxial graphene
International Nuclear Information System (INIS)
Novikov, S.; Lebedeva, N.; Hämäläinen, J.; Iisakka, I.; Immonen, P.; Manninen, A. J.; Satrapinski, A.
2016-01-01
Series connection of four quantum Hall effect (QHE) devices based on epitaxial graphene films was studied for realization of a quantum resistance standard with an up-scaled value. The tested devices showed quantum Hall plateaux R H,2 at a filling factor v = 2 starting from a relatively low magnetic field (between 4 T and 5 T) when the temperature was 1.5 K. The precision measurements of quantized Hall resistance of four QHE devices connected by triple series connections and external bonding wires were done at B = 7 T and T = 1.5 K using a commercial precision resistance bridge with 50 μA current through the QHE device. The results showed that the deviation of the quantized Hall resistance of the series connection of four graphene-based QHE devices from the expected value of 4×R H,2 = 2 h/e 2 was smaller than the relative standard uncertainty of the measurement (<1 × 10 −7 ) limited by the used resistance bridge.
Quantum hall fluid on fuzzy two dimensional sphere
International Nuclear Information System (INIS)
Luo Xudong; Peng Dantao
2004-01-01
After reviewing the Haldane's description about the quantum Hall effect on the fuzzy two-sphere S 2 , authors construct the noncommutative algebra on the fuzzy sphere S 2 and the Moyal structure of the Hilbert space. By constructing noncommutative Chern-Simons theory of the incompressible Hall fluid on the fuzzy sphere and solving the Gaussian constraint with quasiparticle source, authors find the Calogero matrix on S 2 and the complete set of the Laughlin wave function for the lowest Landau level, and this wave function is expressed by the generalized Jack polynomials in terms of spinor coordinates. (author)
Measured Early Lateral Energy Fractions in Concert Halls and Opera Houses
BARRON, M.
2000-04-01
In the 30 years since early lateral reflections were first suggested as important for concert halls, spatial impression and source broadening have become almost universally accepted as essential characteristics of halls with good acoustics. Two objective measures of source broadening have been proposed. Measured values of the best defined of these measures, the early lateral energy fraction (LF), are considered here. Results from two independent measurement surveys are discussed. Comparisons of LF values by hall show a significant link between hall mean LF and hall width. There is however considerable overlap between measured LF values in different halls so the relevance of describing halls by their mean early lateral energy fraction values is questionable. The behaviour of LF values within auditoria is discussed for different concert hall plan forms and within opera houses. A measure of source broadening including sound level is proposed and results considered in the context of auditorium design.
Quantum Hall effect on Riemann surfaces
Tejero Prieto, Carlos
2009-06-01
We study the family of Landau Hamiltonians compatible with a magnetic field on a Riemann surface S by means of Fourier-Mukai and Nahm transforms. Starting from the geometric formulation of adiabatic charge transport on Riemann surfaces, we prove that Hall conductivity is proportional to the intersection product on the first homology group of S and therefore it is quantized. Finally, by using the theory of determinant bundles developed by Bismut, Gillet and Soul, we compute the adiabatic curvature of the spectral bundles defined by the holomorphic Landau levels. We prove that it is given by the polarization of the jacobian variety of the Riemann surface, plus a term depending on the relative analytic torsion.
Quantum Hall effect on Riemann surfaces
International Nuclear Information System (INIS)
Tejero Prieto, Carlos
2009-01-01
We study the family of Landau Hamiltonians compatible with a magnetic field on a Riemann surface S by means of Fourier-Mukai and Nahm transforms. Starting from the geometric formulation of adiabatic charge transport on Riemann surfaces, we prove that Hall conductivity is proportional to the intersection product on the first homology group of S and therefore it is quantized. Finally, by using the theory of determinant bundles developed by Bismut, Gillet and Soul, we compute the adiabatic curvature of the spectral bundles defined by the holomorphic Landau levels. We prove that it is given by the polarization of the jacobian variety of the Riemann surface, plus a term depending on the relative analytic torsion.
Nonadiabatic effects in the Quantum Hall regime
International Nuclear Information System (INIS)
Page, D.A.; Brown, E.
1993-01-01
The authors consider the effect of a finite electric field on the states of a Bloch electron in two dimensions, with a uniform magnetic field present. They make use of the concept of electric time translation symmetry and treat the electric and magnetic fields symmetrically in a time dependent formalism. In addition to a wave vector k, the states are characterized by a frequency specifying the behavior under electric time translations. An effective Hamiltonian is employed to obtain the splitting of an isolated Bloch band into open-quotes frequencyclose quotes subbands. The time-averaged velocity and energy of the states are expressed in terms of the frequency dispersion. The relationship to the Stark ladder eigenstates in a scalar potential representation of the electric field is examined. This is seen to justify the use of the averaged energy in determining occupation of the states. In the weak electric field (adiabatic) limit, an expression is recovered for the quantized Hall conductivity of a magnetic subband as a topological invariant. A numerical procedure is outlined and results obtained over a range of electric field strengths. A transition between strong and weak field regimes is seen, with level repulsions between the frequencies playing an important role. The numerical results show how the magnetic subband structure and quantized Hall conductivity emerge as the electric field becomes weaker. In this regime, the behavior can be understood by comparison to the predictions of the adiabatic approximation. The latter predicts crossings in the frequencies at certain locations in wave vector space. Nonadiabatic effects are seen to produce gaps in the frequency spectrum at these locations. 35 refs., 14 figs
Induced Superconductivity in the Quantum Spin Hall Edge
Ren, Hechen; Hart, Sean; Wagner, Timo; Leubner, Philipp; Muehlbauer, Mathias; Bruene, Christoph; Buhmann, Hartmut; Molenkamp, Laurens; Yacoby, Amir
2014-03-01
Two-dimensional topological insulators have a gapped bulk and helical edge states, making it a quantum spin Hall insulator. Combining such edge states with superconductivity can be an excellent platform for observing and manipulating localized Majorana fermions. In the context of condensed matter, these are emergent electronic states that obey non-Abelian statistics and hence support fault-tolerant quantum computing. To realize such theoretical constructions, an essential step is to show these edge channels are capable of carrying coherent supercurrent. In our experiment, we fabricate Josephson junctions with HgTe/HgCdTe quantum wells, a two-dimensional material that becomes a quantum spin Hall insulator when the quantum well is thicker than 6.3 nm and the bulk density is depleted. In this regime, we observe supercurrents whose densities are confined to the edges of the junctions, with edge widths ranging from 180 nm to 408 nm. To verify the topological nature of these edges, we measure identical junctions with HgTe/HgCdTe quantum wells thinner than 6.3 nm and observe only uniform supercurrent density across the junctions. This research is supported by Microsoft Corporation Project Q, the NSF DMR-1206016, the DOE SCGF Program, the German Research Foundation, and EU ERC-AG program.
A constricted quantum Hall system as a beam-splitter: understanding ballistic transport on the edge
International Nuclear Information System (INIS)
Lal, Siddhartha
2007-09-01
We study transport in a model of a quantum Hall edge system with a gate-voltage controlled constriction. A finite backscattered current at finite edge-bias is explained from a Landauer- Buttiker analysis as arising from the splitting of edge current caused by the difference in the filling fractions of the bulk (ν 1 ) and constriction(ν 2 ) quantum Hall fluid regions. We develop a hydrodynamic theory for bosonic edge modes inspired by this model. The constriction region splits the incident long-wavelength chiral edge density-wave excitations among the transmitting and reflecting edge states encircling it. These findings provide satisfactory explanations for several puzzling recent experimental results. These results are confirmed by computing various correlators and chiral linear conductances of the system. In this way, our results find excellent agreement with some of the recent puzzling experimental results for the cases of ν 1 = 1/3, 1. (author)
Contactless measurement of alternating current conductance in quantum Hall structures
Energy Technology Data Exchange (ETDEWEB)
Drichko, I. L.; Diakonov, A. M.; Malysh, V. A.; Smirnov, I. Yu.; Ilyinskaya, N. D.; Usikova, A. A. [A. F. Ioffe Physical-Technical Institute of the Russian Academy of Sciences, 194021 St. Petersburg (Russian Federation); Galperin, Y. M. [Department of Physics, University of Oslo, P.O. Box 1048 Blindern, 0316 Oslo (Norway); A. F. Ioffe Physical-Technical Institute of the Russian Academy of Sciences, 194021 St. Petersburg (Russian Federation); Kummer, M.; Känel, H. von [Laboratorium für Festkörperphysik ETH Zürich, CH-8093 Zürich (Switzerland)
2014-10-21
We report a procedure to determine the frequency-dependent conductance of quantum Hall structures in a broad frequency domain. The procedure is based on the combination of two known probeless methods—acoustic spectroscopy and microwave spectroscopy. By using the acoustic spectroscopy, we study the low-frequency attenuation and phase shift of a surface acoustic wave in a piezoelectric crystal in the vicinity of the electron (hole) layer. The electronic contribution is resolved using its dependence on a transverse magnetic field. At high frequencies, we study the attenuation of an electromagnetic wave in a coplanar waveguide. To quantitatively calibrate these data, we use the fact that in the quantum-Hall-effect regime the conductance at the maxima of its magnetic field dependence is determined by extended states. Therefore, it should be frequency independent in a broad frequency domain. The procedure is verified by studies of a well-characterized p-SiGe/Ge/SiGe heterostructure.
Error modelling of quantum Hall array resistance standards
Marzano, Martina; Oe, Takehiko; Ortolano, Massimo; Callegaro, Luca; Kaneko, Nobu-Hisa
2018-04-01
Quantum Hall array resistance standards (QHARSs) are integrated circuits composed of interconnected quantum Hall effect elements that allow the realization of virtually arbitrary resistance values. In recent years, techniques were presented to efficiently design QHARS networks. An open problem is that of the evaluation of the accuracy of a QHARS, which is affected by contact and wire resistances. In this work, we present a general and systematic procedure for the error modelling of QHARSs, which is based on modern circuit analysis techniques and Monte Carlo evaluation of the uncertainty. As a practical example, this method of analysis is applied to the characterization of a 1 MΩ QHARS developed by the National Metrology Institute of Japan. Software tools are provided to apply the procedure to other arrays.
From rotating atomic rings to quantum Hall states.
Roncaglia, M; Rizzi, M; Dalibard, J
2011-01-01
Considerable efforts are currently devoted to the preparation of ultracold neutral atoms in the strongly correlated quantum Hall regime. However, the necessary angular momentum is very large and in experiments with rotating traps this means spinning frequencies extremely near to the deconfinement limit; consequently, the required control on parameters turns out to be too stringent. Here we propose instead to follow a dynamic path starting from the gas initially confined in a rotating ring. The large moment of inertia of the ring-shaped fluid facilitates the access to large angular momenta, corresponding to giant vortex states. The trapping potential is then adiabatically transformed into a harmonic confinement, which brings the interacting atomic gas in the desired quantum-Hall regime. We provide numerical evidence that for a broad range of initial angular frequencies, the giant-vortex state is adiabatically connected to the bosonic ν = 1/2 Laughlin state.
Edge states in quantum Hall effect in graphene
International Nuclear Information System (INIS)
Gusynin, V.P.; Miransky, V.A.; Sharapov, S.G.; Shovkovy, I.A.
2008-01-01
We review recent results concerning the spectrum of edge states in the quantum Hall effect in graphene. In particular, special attention is paid to the derivation of the conditions under which gapless edge states exist in the spectrum of graphene with 'zigzag' and 'armchair' edges. It is found that in the case of a half-plane or a ribbon with zigzag edges, there are gapless edge states only when a spin gap dominates over a Dirac mass gap. In the case of a half-plane with an armchair edge, the existence of the gapless edge states depends on the specific type of Dirac mass gaps. The implications of these results for the dynamics in the quantum Hall effect in graphene are discussed
Levitation and percolation in quantum Hall systems with correlated disorder
Song, Hui; Maruyama, Isao; Hatsugai, Yasuhiro
2007-01-01
We investigate the integer quantum Hall system in a two dimensional lattice model with spatially correlated disorder by using the efficient method to calculate the Chern number proposed by Fukui et al. [J. Phys. Soc. Jpn. 74, 1674 (2005)]. Distribution of charge density indicates that the extended states at the center of each Landau band have percolating current paths, which are topologically equivalent to the edge states that exist in a system with boundaries. As increasing the strength of d...
Tunneling between edge states in a quantum spin Hall system.
Ström, Anders; Johannesson, Henrik
2009-03-06
We analyze a quantum spin Hall device with a point contact connecting two of its edges. The contact supports a net spin tunneling current that can be probed experimentally via a two-terminal resistance measurement. We find that the low-bias tunneling current and the differential conductance exhibit scaling with voltage and temperature that depend nonlinearly on the strength of the electron-electron interaction.
Two-dimensional Ising physics in quantum Hall ferromagnets
Czech Academy of Sciences Publication Activity Database
Jungwirth, Tomáš; MacDonald, A. H.; Rezayi, E. H.
2002-01-01
Roč. 12, - (2002), s. 1-7 ISSN 1386-9477 R&D Projects: GA ČR GA202/01/0754; GA MŠk OC 514.10 Institutional research plan: CEZ:AV0Z1010914 Keywords : quantum Hall ferromagnets * higher Landau levels * domain walls Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.107, year: 2002
The integer quantum hall effect revisited
Energy Technology Data Exchange (ETDEWEB)
Michalakis, Spyridon [Los Alamos National Laboratory; Hastings, Matthew [Q STATION, CALIFORNIA
2009-01-01
For T - L x L a finite subset of Z{sup 2}, let H{sub o} denote a Hamiltonian on T with periodic boundary conditions and finite range, finite strength intetactions and a unique ground state with a nonvanishing spectral gap. For S {element_of} T, let q{sub s} denote the charge at site s and assume that the total charge Q = {Sigma}{sub s {element_of} T} q{sub s} is conserved. Using the local charge operators q{sub s}, we introduce a boundary magnetic flux in the horizontal and vertical direction and allow the ground state to evolve quasiadiabatically around a square of size one magnetic flux, in flux space. At the end of the evolution we obtain a trivial Berry phase, which we compare, via a method reminiscent of Stokes Theorem. to the Berry phase obtained from an evolution around an exponentially small loop near the origin. As a result, we show, without any averaging assumption, that the Hall conductance is quantized in integer multiples of e{sup 2}/h up to exponentially small corrections of order e{sup -L/{zeta}}, where {zeta}, is a correlation length that depends only on the gap and the range and strength of the interactions.
Mani, Arjun; Benjamin, Colin
2016-04-13
On the surface of 2D topological insulators, 1D quantum spin Hall (QSH) edge modes occur with Dirac-like dispersion. Unlike quantum Hall (QH) edge modes, which occur at high magnetic fields in 2D electron gases, the occurrence of QSH edge modes is due to spin-orbit scattering in the bulk of the material. These QSH edge modes are spin-dependent, and chiral-opposite spins move in opposing directions. Electronic spin has a larger decoherence and relaxation time than charge. In view of this, it is expected that QSH edge modes will be more robust to disorder and inelastic scattering than QH edge modes, which are charge-dependent and spin-unpolarized. However, we notice no such advantage accrues in QSH edge modes when subjected to the same degree of contact disorder and/or inelastic scattering in similar setups as QH edge modes. In fact we observe that QSH edge modes are more susceptible to inelastic scattering and contact disorder than QH edge modes. Furthermore, while a single disordered contact has no effect on QH edge modes, it leads to a finite charge Hall current in the case of QSH edge modes, and thus a vanishing of the pure QSH effect. For more than a single disordered contact while QH states continue to remain immune to disorder, QSH edge modes become more susceptible--the Hall resistance for the QSH effect changes sign with increasing disorder. In the case of many disordered contacts with inelastic scattering included, while quantization of Hall edge modes holds, for QSH edge modes a finite charge Hall current still flows. For QSH edge modes in the inelastic scattering regime we distinguish between two cases: with spin-flip and without spin-flip scattering. Finally, while asymmetry in sample geometry can have a deleterious effect in the QSH case, it has no impact in the QH case.
International Nuclear Information System (INIS)
Mani, Arjun; Benjamin, Colin
2016-01-01
On the surface of 2D topological insulators, 1D quantum spin Hall (QSH) edge modes occur with Dirac-like dispersion. Unlike quantum Hall (QH) edge modes, which occur at high magnetic fields in 2D electron gases, the occurrence of QSH edge modes is due to spin–orbit scattering in the bulk of the material. These QSH edge modes are spin-dependent, and chiral-opposite spins move in opposing directions. Electronic spin has a larger decoherence and relaxation time than charge. In view of this, it is expected that QSH edge modes will be more robust to disorder and inelastic scattering than QH edge modes, which are charge-dependent and spin-unpolarized. However, we notice no such advantage accrues in QSH edge modes when subjected to the same degree of contact disorder and/or inelastic scattering in similar setups as QH edge modes. In fact we observe that QSH edge modes are more susceptible to inelastic scattering and contact disorder than QH edge modes. Furthermore, while a single disordered contact has no effect on QH edge modes, it leads to a finite charge Hall current in the case of QSH edge modes, and thus a vanishing of the pure QSH effect. For more than a single disordered contact while QH states continue to remain immune to disorder, QSH edge modes become more susceptible—the Hall resistance for the QSH effect changes sign with increasing disorder. In the case of many disordered contacts with inelastic scattering included, while quantization of Hall edge modes holds, for QSH edge modes a finite charge Hall current still flows. For QSH edge modes in the inelastic scattering regime we distinguish between two cases: with spin-flip and without spin-flip scattering. Finally, while asymmetry in sample geometry can have a deleterious effect in the QSH case, it has no impact in the QH case. (paper)
Paired quantum Hall states on noncommutative two-tori
Energy Technology Data Exchange (ETDEWEB)
Marotta, Vincenzo [Dipartimento di Scienze Fisiche, Universita di Napoli ' Federico II' and INFN, Sezione di Napoli, Compl. universitario M. Sant' Angelo, Via Cinthia, 80126 Napoli (Italy); Naddeo, Adele, E-mail: naddeo@sa.infn.i [CNISM, Unita di Ricerca di Salerno and Dipartimento di Fisica ' E. R. Caianiello' , Universita degli Studi di Salerno, Via Salvador Allende, 84081 Baronissi (Italy)
2010-08-01
By exploiting the notion of Morita equivalence for field theories on noncommutative tori and choosing rational values of the noncommutativity parameter theta (in appropriate units), a one-to-one correspondence between an Abelian noncommutative field theory (NCFT) and a non-Abelian theory of twisted fields on ordinary space can be established. Starting from this general result, we focus on the conformal field theory (CFT) describing a quantum Hall fluid (QHF) at paired states fillings nu=m/(pm+2) Cristofano et al. (2000) , recently obtained by means of m-reduction procedure, and show that it is the Morita equivalent of a NCFT. In this way we extend the construction proposed in Marotta and Naddeo (2008) for the Jain series nu=m/(2pm+1) . The case m=2 is explicitly discussed and the role of noncommutativity in the physics of quantum Hall bilayers is emphasized. Our results represent a step forward the construction of a new effective low energy description of certain condensed matter phenomena and help to clarify the relationship between noncommutativity and quantum Hall fluids.
Nematic and Valley Ordering in Anisotropic Quantum Hall Systems
Parameswaran, S. A.; Abanin, D. A.; Kivelson, S. A.; Sondhi, S. L.
2010-03-01
We consider a multi-valley two dimensional electron system in the quantum Hall effect (QHE) regime. We focus on QHE states that arise due to spontaneous breaking of the valley symmetry by the Coulomb interactions. We show that the anisotropy of the Fermi surface in each valley, which is generally present in such systems, favors states where all the electrons reside in one of the valleys. In a clean system, the valley ordering occurs via a finite temperature Ising-like phase transition, which, owing to the Fermi surface anisotropy, is accompanied by the onset of nematic order. In a disordered system, domains of opposite polarization are formed, and therefore long-range valley order is destroyed, however, the resulting state is still compressible. We discuss the transport properties in ordered and disordered regimes, and point out the possible relation of our results to recent experiments in AlAs [1]. [1] Y. P. Shkolnikov, S. Misra, N. C. Bishop, E. P. De Poortere, and M. Shayegan, Observation of Quantum Hall ``Valley Skyrmions", Phys. Rev. Lett. 95, 068809 (2005)[2] D.A. Abanin, S.A. Parameswaran, S.A. Kivelson and S.L. Sondhi, Nematic and Valley Ordering in Anisotropic Quantum Hall Systems, to be published.
ADHM and the 4d quantum Hall effect
Barns-Graham, Alec; Dorey, Nick; Lohitsiri, Nakarin; Tong, David; Turner, Carl
2018-04-01
Yang-Mills instantons are solitonic particles in d = 4 + 1 dimensional gauge theories. We construct and analyse the quantum Hall states that arise when these particles are restricted to the lowest Landau level. We describe the ground state wavefunctions for both Abelian and non-Abelian quantum Hall states. Although our model is purely bosonic, we show that the excitations of this 4d quantum Hall state are governed by the Nekrasov partition function of a certain five dimensional supersymmetric gauge theory with Chern-Simons term. The partition function can also be interpreted as a variant of the Hilbert series of the instanton moduli space, counting holomorphic sections rather than holomorphic functions. It is known that the Hilbert series of the instanton moduli space can be rewritten using mirror symmetry of 3d gauge theories in terms of Coulomb branch variables. We generalise this approach to include the effect of a five dimensional Chern-Simons term. We demonstrate that the resulting Coulomb branch formula coincides with the corresponding Higgs branch Molien integral which, in turn, reproduces the standard formula for the Nekrasov partition function.
An edge index for the quantum spin-Hall effect
International Nuclear Information System (INIS)
Prodan, Emil
2009-01-01
Quantum spin-Hall systems are topological insulators displaying dissipationless spin currents flowing at the edges of the samples. In contradistinction to the quantum Hall systems where the charge conductance of the edge modes is quantized, the spin conductance is not and it remained an open problem to find the observable whose edge current is quantized. In this paper, we define a particular observable and the edge current corresponding to this observable. We show that this current is quantized and that the quantization is given by the index of a certain Fredholm operator. This provides a new topological invariant that is shown to take the generic values 0 and 2, in line with the Z 2 topological classification of time-reversal invariant systems. The result gives an effective tool for the investigation of the edge structure in quantum spin-Hall systems. Based on a reasonable assumption, we also show that the edge conducting channels are not destroyed by a random edge. (fast track communication)
Magnon Spin Hall Magnetoresistance of a Gapped Quantum Paramagnet
Ulloa, Camilo; Duine, R. A.
2018-04-01
Motivated by recent experimental work, we consider spin transport between a normal metal and a gapped quantum paramagnet. We model the latter as the magnonic Mott-insulating phase of an easy-plane ferromagnetic insulator. We evaluate the spin current mediated by the interface exchange coupling between the ferromagnet and the adjacent normal metal. For the strongly interacting magnons that we consider, this spin current gives rise to a spin Hall magnetoresistance that strongly depends on the magnitude of the magnetic field, rather than its direction. This Letter may motivate electrical detection of the phases of quantum magnets and the incorporation of such materials into spintronic devices.
Valley polarized quantum Hall effect and topological insulator phase transitions in silicene
Tahir, M.; Schwingenschlö gl, Udo
2013-01-01
encountered for graphene, in particular the zero band gap and weak spin orbit interaction. We demonstrate a valley polarized quantum Hall effect and topological insulator phase transitions. We use the Kubo formalism to discuss the Hall conductivity and address
Giant anisotropic magnetoresistance in a quantum anomalous Hall insulator
Kandala, Abhinav; Richardella, Anthony; Kempinger, Susan; Liu, Chao-Xing; Samarth, Nitin
2015-01-01
When a three-dimensional ferromagnetic topological insulator thin film is magnetized out-of-plane, conduction ideally occurs through dissipationless, one-dimensional (1D) chiral states that are characterized by a quantized, zero-field Hall conductance. The recent realization of this phenomenon, the quantum anomalous Hall effect, provides a conceptually new platform for studies of 1D transport, distinct from the traditionally studied quantum Hall effects that arise from Landau level formation. An important question arises in this context: how do these 1D edge states evolve as the magnetization is changed from out-of-plane to in-plane? We examine this question by studying the field-tilt-driven crossover from predominantly edge-state transport to diffusive transport in Crx(Bi,Sb)2−xTe3 thin films. This crossover manifests itself in a giant, electrically tunable anisotropic magnetoresistance that we explain by employing a Landauer–Büttiker formalism. Our methodology provides a powerful means of quantifying dissipative effects in temperature and chemical potential regimes far from perfect quantization. PMID:26151318
Experimental probes of emergent symmetries in the quantum Hall system
Lutken, C A
2011-01-01
Experiments studying renormalization group flows in the quantum Hall system provide significant evidence for the existence of an emergent holomorphic modular symmetry Gamma(0)(2). We briefly review this evidence and show that, for the lowest temperatures, the experimental determination of the position of the quantum critical points agrees to the parts per mille level with the prediction from Gamma(0)(2). We present evidence that experiments giving results that deviate substantially from the symmetry predictions are not cold enough to be in the quantum critical domain. We show how the modular symmetry extended by a non-holomorphic particle hole duality leads to an extensive web of dualities related to those in plateau insulator transitions, and we derive a formula relating dual pairs (B, B(d)) of magnetic field strengths across any transition. The experimental data obtained for the transition studied so far is in excellent agreement with the duality relations following from this emergent symmetry, and rule out...
Tunneling Spectroscopy of Quantum Hall States in Bilayer Graphene
Wang, Ke; Harzheim, Achim; Watanabe, Kenji; Taniguchi, Takashi; Kim, Philip
In the quantum Hall (QH) regime, ballistic conducting paths along the physical edges of a sample appear, leading to quantized Hall conductance and vanishing longitudinal magnetoconductance. These QH edge states are often described as ballistic compressible strips separated by insulating incompressible strips, the spatial profiles of which can be crucial in understanding the stability and emergence of interaction driven QH states. In this work, we present tunneling transport between two QH edge states in bilayer graphene. Employing locally gated device structure, we guide and control the separation between the QH edge states in bilayer graphene. Using resonant Landau level tunneling as a spectroscopy tool, we measure the energy gap in bilayer graphene as a function of displacement field and probe the emergence and evolution of incompressible strips.
Admittance measurements in the quantum Hall effect regime
Energy Technology Data Exchange (ETDEWEB)
Hernández, C., E-mail: carlos.hernandezr@unimilitar.edu.co [Departamento de Física, Universidad Militar Nueva Granada, Carrera 11 # 101-80, Bogotá D.C. (Colombia); Laboratorio de Magnetismo, Departamento de Física, Universidad de los Andes, A.A. 4976, Bogotá D.C. (Colombia); Consejo, C.; Chaubet, C. [Laboratoire Charles Coulomb L2C, Université Montpellier II, Pl. E. Bataillon, 34095 Montpellier Cedex 5 (France)
2014-11-15
In this work we present an admittance study of a two-dimensional electron gas (2DEG) in the quantum Hall effect (QHE) regime. We have studied several Hall bars in different contacts configurations in the frequency range 100 Hz–1 MHz. Our interpretation is based on the Landauer–Büttiker theory and takes into account both the capacitance and the topology of the coaxial cables which are connected to the sample holder. We show that we always observe losses through the capacitive impedance of the coaxial cables, except in the two contacts configuration in which the cable capacitance does not influence the admittance measurement of the sample. In this case, we measure the electrochemical capacitance of the 2DEG and show its dependence with the filling factor ν.
Edge states and integer quantum Hall effect in topological insulator thin films.
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.
On-chip microwave circulators using quantum Hall plasmonics
Mahoney, Alice; Colless, James; Pauka, Sebastian; Hornibrook, John; Doherty, Andrew; Reilly, David; Peeters, Lucas; Fox, Eli; Goldhaber-Gordon, David; Kou, Xuefeng; Pan, Lei; Wang, Kang; Watson, John; Gardner, Geoffrey; Manfra, Michael
Circulators are directional circuit elements integral to technologies including radar systems, microwave communication transceivers and the readout of quantum information devices. Their non-reciprocity commonly arises from the interference of microwaves over the centimetre-scale of the signal wavelength in the presence of bulky magnetic media that breaks time-reversal symmetry. We present a completely passive on-chip microwave circulator with size 1/1000th the wavelength by exploiting the chiral, `slow-light' response of a GaAs/AlGaAs 2-dimensional electron gas in the quantum Hall regime. Further, by implementing this circulator design on a thin film of a magnetic topological insulator (Cr0.12(Bi0.26Sb0.62)2Te3), we show that similar non-reciprocity can be achieved at zero magnetic field. This additional mode of operation serves as a non-invasive probe of edge states in the quantum anomalous Hall effect, while also extending the possibility for integration with superconducting devices.
Extreme Soft Limit Observation of Quantum Hall Effect in a 3-d Semiconductor
Bleiweiss, Michael; Yin, Ming; Amirzadeh, Jafar; Preston, Harry; Datta, Timir
2004-03-01
We report on the evidence for quantum hall effect at 38K and in magnetic fields (B) as low as 1k-Orsted. Our specimens were semiconducting, carbon replica opal (CRO) structures. CRO are three dimensional bulk systems where the carbon is grown by CVD into the porous regions in artificial silica opals. The carbon forms layers on top of the silica spheres as eggshells. The shells are of uneven thickness and are perforated at the contacts points of the opal spheres and form a closed packed, three dimensional crystal structure. Plateaus in inverse R_xy that are conjugated with well-defined Subnikov-deHass modulations in R_xx were observed. The quantum steps that are particularly prominent were the states with fill factors v = p/q (p,q are integers) were the well know fractions, 1/3, 1/2, 3/5, 1 and 5/2. QHE steps indicate that the carriers are localized in two-dimensional regions, which may be due to the extremely large surface to volume ratio associated with replica opal structure. From the B-1 vs v straight line, the effective surface carrier density, ns = 2.2 x 10^14 m-2. To the best of our knowledge, the current work is the first to report fractional quantum hall plateaus in a bulk system.
Complex scattering dynamics and the integer quantum Hall effect
International Nuclear Information System (INIS)
Trugman, S.A.; Waugh, F.R.
1987-01-01
The effect of a magnetic field on potential scattering is investigated microscopically. A magnetic field renders the scattering of a classical charged particle far more complex than previously suspected. Consequences include possible 1/f noise and an explanation of the observed breakdown of the quantum Hall effect at large currents. A particular scatterer is described by a discontinuous one dimensional Hamiltonian map, a class of maps that has not previously been studied. A renormalization group analysis indicates that singular behavior arises from the interplay of electron orbits that are periodic and orbits that are quasiperiodic
Composite fermion theory for bosonic quantum Hall states on lattices.
Möller, G; Cooper, N R
2009-09-04
We study the ground states of the Bose-Hubbard model in a uniform magnetic field, motivated by the physics of cold atomic gases on lattices at high vortex density. Mapping the bosons to composite fermions (CF) leads to the prediction of quantum Hall fluids that have no counterpart in the continuum. We construct trial states for these phases and test numerically the predictions of the CF model. We establish the existence of strongly correlated phases beyond those in the continuum limit and provide evidence for a wider scope of the composite fermion approach beyond its application to the lowest Landau level.
Gaussian free fields at the integer quantum Hall plateau transition
Energy Technology Data Exchange (ETDEWEB)
Bondesan, R., E-mail: roberto.bondesan@phys.ox.ac.uk [Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford OX1 3NP (United Kingdom); Wieczorek, D.; Zirnbauer, M.R. [Institut für Theoretische Physik, Universität zu Köln, Zülpicher Straße 77, 50937 Köln (Germany)
2017-05-15
In this work we put forward an effective Gaussian free field description of critical wavefunctions at the transition between plateaus of the integer quantum Hall effect. To this end, we expound our earlier proposal that powers of critical wave intensities prepared via point contacts behave as pure scaling fields obeying an Abelian operator product expansion. Our arguments employ the framework of conformal field theory and, in particular, lead to a multifractality spectrum which is parabolic. We also derive a number of old and new identities that hold exactly at the lattice level and hinge on the correspondence between the Chalker–Coddington network model and a supersymmetric vertex model.
Current Percolation in Medium with Boundaries under Quantum Hall Effect Conditions
Directory of Open Access Journals (Sweden)
M. U. Malakeeva
2012-01-01
Full Text Available The current percolation has been considered in the medium with boundaries under quantum Hall effect conditions. It has been shown that in that case the effective Hall conductivity has a nonzero value due to percolation of the Hall current through the finite number of singular points (in our model these are corners at the phase joints.
Tunneling time in space fractional quantum mechanics
Hasan, Mohammad; Mandal, Bhabani Prasad
2018-02-01
We calculate the time taken by a wave packet to travel through a classically forbidden region of space in space fractional quantum mechanics. We obtain the close form expression of tunneling time from a rectangular barrier by stationary phase method. We show that tunneling time depends upon the width b of the barrier for b → ∞ and therefore Hartman effect doesn't exist in space fractional quantum mechanics. Interestingly we found that the tunneling time monotonically reduces with increasing b. The tunneling time is smaller in space fractional quantum mechanics as compared to the case of standard quantum mechanics. We recover the Hartman effect of standard quantum mechanics as a special case of space fractional quantum mechanics.
Quantum spin/valley Hall effect and topological insulator phase transitions in silicene
Tahir, M.
2013-04-26
We present a theoretical realization of quantum spin and quantum valley Hall effects in silicene. We show that combination of an electric field and intrinsic spin-orbit interaction leads to quantum phase transitions at the charge neutrality point. This phase transition from a two dimensional topological insulator to a trivial insulating state is accompanied by a quenching of the quantum spin Hall effect and the onset of a quantum valley Hall effect, providing a tool to experimentally tune the topological state of silicene. In contrast to graphene and other conventional topological insulators, the proposed effects in silicene are accessible to experiments.
Quantum spin/valley Hall effect and topological insulator phase transitions in silicene
Tahir, M.; Manchon, Aurelien; Sabeeh, K.; Schwingenschlö gl, Udo
2013-01-01
We present a theoretical realization of quantum spin and quantum valley Hall effects in silicene. We show that combination of an electric field and intrinsic spin-orbit interaction leads to quantum phase transitions at the charge neutrality point. This phase transition from a two dimensional topological insulator to a trivial insulating state is accompanied by a quenching of the quantum spin Hall effect and the onset of a quantum valley Hall effect, providing a tool to experimentally tune the topological state of silicene. In contrast to graphene and other conventional topological insulators, the proposed effects in silicene are accessible to experiments.
Quantum Hall effects recent theoretical and experimental developments
Ezawa, Zyun Francis
2013-01-01
Enthusiasm for research on the quantum Hall effect (QHE) is unbounded. The QHE is one of the most fascinating and beautiful phenomena in all branches of physics. Tremendous theoretical and experimental developments are still being made in this sphere. Composite bosons, composite fermions and anyons were among distinguishing ideas in the original edition. In the 2nd edition, fantastic phenomena associated with the interlayer phase coherence in the bilayer system were extensively described. The microscopic theory of the QHE was formulated based on the noncommutative geometry. Furthermore, the unconventional QHE in graphene was reviewed, where the electron dynamics can be treated as relativistic Dirac fermions and even the supersymmetric quantum mechanics plays a key role. In this 3rd edition, all chapters are carefully reexamined and updated. A highlight is the new chapter on topological insulators. Indeed, the concept of topological insulator stems from the QHE. Other new topics are recent prominent experime...
Edge physics of the quantum spin Hall insulator from a quantum dot excited by optical absorption.
Vasseur, Romain; Moore, Joel E
2014-04-11
The gapless edge modes of the quantum spin Hall insulator form a helical liquid in which the direction of motion along the edge is determined by the spin orientation of the electrons. In order to probe the Luttinger liquid physics of these edge states and their interaction with a magnetic (Kondo) impurity, we consider a setup where the helical liquid is tunnel coupled to a semiconductor quantum dot that is excited by optical absorption, thereby inducing an effective quantum quench of the tunneling. At low energy, the absorption spectrum is dominated by a power-law singularity. The corresponding exponent is directly related to the interaction strength (Luttinger parameter) and can be computed exactly using boundary conformal field theory thanks to the unique nature of the quantum spin Hall edge.
Integer Quantum Magnon Hall Plateau-Plateau Transition in a Spin Ice Model
Xu, Baolong; Ohtsuki, Tomi; Shindou, Ryuichi
2016-01-01
Low-energy magnon bands in a two-dimensional spin ice model become integer quantum magnon Hall bands. By calculating the localization length and the two-terminal conductance of magnon transport, we show that the magnon bands with disorders undergo a quantum phase transition from an integer quantum magnon Hall regime to a conventional magnon localized regime. Finite size scaling analysis as well as a critical conductance distribution shows that the quantum critical point belongs to the same un...
Quantum Hall bilayers and the chiral sine-Gordon equation
International Nuclear Information System (INIS)
Naud, J.D.; Pryadko, Leonid P.; Sondhi, S.L.
2000-01-01
The edge state theory of a class of symmetric double-layer quantum Hall systems with interlayer electron tunneling reduces to the sum of a free field theory and a field theory of a chiral Bose field with a self-interaction of the sine-Gordon form. We argue that the perturbative renormalization group flow of this chiral sine-Gordon theory is distinct from the standard (non-chiral) sine-Gordon theory, contrary to a previous assertion by Renn, and that the theory is manifestly sensible only at a discrete set of values of the inverse period of the cosine interaction (β-circumflex). We obtain exact solutions for the spectra and correlation functions of the chiral sine-Gordon theory at the two values of β-circumflex at which electron tunneling in bilayers is not irrelevant. Of these, the marginal case (β-circumflex 2 =4) is of greatest interest: the spectrum of the interacting theory is that of two Majorana fermions with different, dynamically generated, velocities. For the experimentally observed bilayer 331 state at filling factor 1/2, this implies the trifurcation of electrons added to the edge. We also present a method for fermionizing the theory at the discrete points (β-circumflex 2 is an element of Z + ) by the introduction of auxiliary degrees of freedom that could prove useful in other problems involving quantum Hall multi-layers
Pinning mode of integer quantum Hall Wigner crystal of skyrmions
Zhu, Han; Sambandamurthy, G.; Chen, Y. P.; Jiang, P.-H.; Engel, L. W.; Tsui, D. C.; Pfeiffer, L. N.; West, K. W.
2009-03-01
Just away from integer Landau level (LL) filling factors ν, the dilute quasi-particles/holes at the partially filled LL form an integer-quantum-Hall Wigner crystal, which exhibits microwave pinning mode resonances [1]. Due to electron-electron interaction, it was predicted that the elementary excitation around ν= 1 is not a single spin flip, but a larger-scale spin texture, known as a skyrmion [2]. We have compared the pinning mode resonances [1] of integer quantum Hall Wigner crystals formed in the partly filled LL just away from ν= 1 and ν= 2, in the presence of an in-plane magnetic field. As an in-plane field is applied, the peak frequencies of the resonances near ν= 1 increase, while the peak frequencies below ν= 2 show neligible dependence on in-plane field. We interpret this observation as due to a skyrmion crystal phase around ν= 1 and a single-hole Wigner crystal phase below ν= 2. The in-plane field increases the Zeeman gap and causes shrinking of the skyrmion size toward single spin flips. [1] Yong P. Chen et al., Phys. Rev. Lett. 91, 016801 (2003). [2] S. L. Sondhi et al., Phys. Rev. B 47, 16 419 (1993); L. Brey et al., Phys. Rev. Lett. 75, 2562 (1995).
The fractional dynamics of quantum systems
Lu, Longzhao; Yu, Xiangyang
2018-05-01
The fractional dynamic process of a quantum system is a novel and complicated problem. The establishment of a fractional dynamic model is a significant attempt that is expected to reveal the mechanism of fractional quantum system. In this paper, a generalized time fractional Schrödinger equation is proposed. To study the fractional dynamics of quantum systems, we take the two-level system as an example and derive the time fractional equations of motion. The basic properties of the system are investigated by solving this set of equations in the absence of light field analytically. Then, when the system is subject to the light field, the equations are solved numerically. It shows that the two-level system described by the time fractional Schrödinger equation we proposed is a confirmable system.
Anomalous Integer Quantum Hall Effect in the Ballistic Regime with Quantum Point Contacts
Wees, B.J. van; Willems, E.M.M.; Harmans, C.J.P.M.; Beenakker, C.W.J.; Houten, H. van; Williamson, J.G.; Foxon, C.T.; Harris, J.J.
1989-01-01
The Hall conductance of a wide two-dimensional electron gas has been measured in a geometry in which two quantum point contacts form controllable current and voltage probes, separated by less than the transport mean free path. Adjustable barriers in the point contacts allow selective population and
Optical probing of quantum Hall effect of composite fermions and of the liquid-insulator transition
International Nuclear Information System (INIS)
Rossella, F; Bellani, V; Dionigi, F; Amado, M; Diez, E; Kowalik, K; Biasiol, G; Sorba, L
2011-01-01
In the photoluminescence spectra of a two-dimensional electron gas in the fractional quantum Hall regime we observe the states at filling factors ν = 4/5, 5/7, 4/11 and 3/8 as clear minima in the intensity or area emission peak. The first three states are described as interacting composite fermions in fractional quantum Hall regime. The minimum in the intensity at ν 3/8, which is not explained within this picture, can be an evidence of a suppression of the screening of the Coulomb interaction among the effective quasi-particles involved in this intriguing state. The magnetic field energy dispersion at very low temperatures is also discussed. At low field the emission follows a Landau dispersion with a screened magneto-Coulomb contribution. At intermediate fields the hidden symmetry manifests. At high field above ν = 1/3 the electrons correlate into an insulating phase, and the optical emission behaviour at the liquid-insulator transition is coherent with a charge ordering driven by Coulomb correlations.
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.
Interplay of Chiral and Helical States in a Quantum Spin Hall Insulator Lateral Junction
Calvo, M. R.; de Juan, F.; Ilan, R.; Fox, E. J.; Bestwick, A. J.; Mühlbauer, M.; Wang, J.; Ames, C.; Leubner, P.; Brüne, C.; Zhang, S. C.; Buhmann, H.; Molenkamp, L. W.; Goldhaber-Gordon, D.
2017-12-01
We study the electronic transport across an electrostatically gated lateral junction in a HgTe quantum well, a canonical 2D topological insulator, with and without an applied magnetic field. We control the carrier density inside and outside a junction region independently and hence tune the number and nature of 1D edge modes propagating in each of those regions. Outside the bulk gap, the magnetic field drives the system to the quantum Hall regime, and chiral states propagate at the edge. In this regime, we observe fractional plateaus that reflect the equilibration between 1D chiral modes across the junction. As the carrier density approaches zero in the central region and at moderate fields, we observe oscillations in the resistance that we attribute to Fabry-Perot interference in the helical states, enabled by the broken time reversal symmetry. At higher fields, those oscillations disappear, in agreement with the expected absence of helical states when band inversion is lifted.
Sahasrabudhe, Harshad; Fallahi, Saeed; Nakamura, James; Povolotskyi, Michael; Novakovic, Bozidar; Rahman, Rajib; Manfra, Michael; Klimeck, Gerhard
Quantum Point Contacts (QPCs) are extensively used in semiconductor devices for charge sensing, tunneling and interference experiments. Fabry-Pérot interferometers containing 2 QPCs have applications in quantum computing, in which electrons/quasi-particles undergo interference due to back-scattering from the QPCs. Such experiments have turned out to be difficult because of the complex structure of edge states near the QPC boundary. We present realistic simulations of the edge states in QPCs based on GaAs/AlGaAs heterostructures, which can be used to predict conductance and edge state velocities. Conduction band profile is obtained by solving decoupled effective mass Schrödinger and Poisson equations self-consistently on a finite element mesh of a realistic geometry. In the integer quantum Hall regime, we obtain compressible and in-compressible regions near the edges. We then use the recursive Green`s function algorithm to solve Schrödinger equation with open boundary conditions for calculating transmission and local current density in the QPCs. Impurities are treated by inserting bumps in the potential with a Gaussian distribution. We compare observables with experiments for fitting some adjustable parameters. The authors would like to thank Purdue Research Foundation and Purdue Center for Topological Materials for their support.
Fractional statistics and quantum theory
Khare, Avinash
1997-01-01
This book explains the subtleties of quantum statistical mechanics in lower dimensions and their possible ramifications in quantum theory. The discussion is at a pedagogical level and is addressed to both graduate students and advanced research workers with a reasonable background in quantum and statistical mechanics. The main emphasis will be on explaining new concepts. Topics in the first part of the book includes the flux tube model of anyons, the braid group and quantum and statistical mechanics of noninteracting anyon gas. The second part of the book provides a detailed discussion about f
Topological superconductivity, topological confinement, and the vortex quantum Hall effect
International Nuclear Information System (INIS)
Diamantini, M. Cristina; Trugenberger, Carlo A.
2011-01-01
Topological matter is characterized by the presence of a topological BF term in its long-distance effective action. Topological defects due to the compactness of the U(1) gauge fields induce quantum phase transitions between topological insulators, topological superconductors, and topological confinement. In conventional superconductivity, because of spontaneous symmetry breaking, the photon acquires a mass due to the Anderson-Higgs mechanism. In this paper we derive the corresponding effective actions for the electromagnetic field in topological superconductors and topological confinement phases. In topological superconductors magnetic flux is confined and the photon acquires a topological mass through the BF mechanism: no symmetry breaking is involved, the ground state has topological order, and the transition is induced by quantum fluctuations. In topological confinement, instead, electric charge is linearly confined and the photon becomes a massive antisymmetric tensor via the Stueckelberg mechanism. Oblique confinement phases arise when the string condensate carries both magnetic and electric flux (dyonic strings). Such phases are characterized by a vortex quantum Hall effect potentially relevant for the dissipationless transport of information stored on vortices.
Imaging of Coulomb-Driven Quantum Hall Edge States
Lai, Keji
2011-10-01
The edges of a two-dimensional electron gas (2DEG) in the quantum Hall effect (QHE) regime are divided into alternating metallic and insulating strips, with their widths determined by the energy gaps of the QHE states and the electrostatic Coulomb interaction. Local probing of these submicrometer features, however, is challenging due to the buried 2DEG structures. Using a newly developed microwave impedance microscope, we demonstrate the real-space conductivity mapping of the edge and bulk states. The sizes, positions, and field dependence of the edge strips around the sample perimeter agree quantitatively with the self-consistent electrostatic picture. The evolution of microwave images as a function of magnetic fields provides rich microscopic information around the ν=2 QHE state. © 2011 American Physical Society.
Breakdown of Counterflow Superfluidity in a Disordered Quantum Hall Bilayer
International Nuclear Information System (INIS)
Lee, D.K.K.; Eastham, P.R.; Cooper, N.R.
2011-01-01
We present a theory for the regime of coherent interlayer tunneling in a disordered quantum Hall bilayer at total filling factor one, allowing for the effect of static vortices. We find that the system consists of domains of polarized superfluid phase. Injected currents introduce phase slips between the polarized domains which are pinned by disorder. We present a model of saturated tunneling domains that predicts a critical current for the breakdown of coherent tunneling that is extensive in the system size. This theory is supported by numerical results from a disordered phase model in two dimensions. We also discuss how our picture might be used to interpret experiments in the counterflow geometry and in two-terminal measurements
Breakdown of Counterflow Superfluidity in a Disordered Quantum Hall Bilayer
Directory of Open Access Journals (Sweden)
D. K. K. Lee
2011-01-01
Full Text Available We present a theory for the regime of coherent interlayer tunneling in a disordered quantum Hall bilayer at total filling factor one, allowing for the effect of static vortices. We find that the system consists of domains of polarized superfluid phase. Injected currents introduce phase slips between the polarized domains which are pinned by disorder. We present a model of saturated tunneling domains that predicts a critical current for the breakdown of coherent tunneling that is extensive in the system size. This theory is supported by numerical results from a disordered phase model in two dimensions. We also discuss how our picture might be used to interpret experiments in the counterflow geometry and in two-terminal measurements.
Theory of activated transport in bilayer quantum Hall systems.
Roostaei, B; Mullen, K J; Fertig, H A; Simon, S H
2008-07-25
We analyze the transport properties of bilayer quantum Hall systems at total filling factor nu=1 in drag geometries as a function of interlayer bias, in the limit where the disorder is sufficiently strong to unbind meron-antimeron pairs, the charged topological defects of the system. We compute the typical energy barrier for these objects to cross incompressible regions within the disordered system using a Hartree-Fock approach, and show how this leads to multiple activation energies when the system is biased. We then demonstrate using a bosonic Chern-Simons theory that in drag geometries current in a single layer directly leads to forces on only two of the four types of merons, inducing dissipation only in the drive layer. Dissipation in the drag layer results from interactions among the merons, resulting in very different temperature dependences for the drag and drive layers, in qualitative agreement with experiment.
Quantum Hall effect and hopping conductivity in n-InGaAs/InAlAs nanoheterostructures
Energy Technology Data Exchange (ETDEWEB)
Gudina, S. V., E-mail: svpopova@imp.uran.ru; Arapov, Yu. G.; Saveliev, A. P.; Neverov, V. N.; Podgornykh, S. M.; Shelushinina, N. G.; Yakunin, M. V. [Russian Academy of Sciences, Mikheev Institute of Metal Physics, Ural Branch (Russian Federation); Vasil’evskii, I. S.; Vinichenko, A. N. [National Research Nuclear University MEPhI (Russian Federation)
2016-12-15
The longitudinal and Hall magnetoresistances are measured in the quantum Hall effect regime in the n-InGaAs/InAlAs heterostructures at temperatures of T = (1.8–30) K in magnetic fields up to B = 9 T. Temperature-induced transport in the region of the longitudinal resistance minima, corresponding to the plateau regions at Hall resistance, is investigated within the framework of the concept of hopping conductivity in a strongly localized electron system. The analysis of variable-range hopping conductivity in the region of the second, third, and fourth plateau of the quantum Hall effect provides the possibility of determining the localization length exponent.
Jacak, Janusz; Łydżba, Patrycja; Jacak, Lucjan
2017-05-01
In this paper the topological approach to quantum Hall effects is carefully described. Commensurability conditions together with proposed generators of a system braid group are employed to establish the fractional quantum Hall effect hierarchies of conventional semiconductors, monolayer and bilayer graphene structures. Obtained filling factors are compared with experimental data and a very good agreement is achieved. Preliminary constructions of ground-state wave functions in the lowest Landau level are put forward. Furthermore, this work explains why pyramids of fillings from higher bands are not counterparts of the well-known composite-fermion hierarchy - it provides with the cause for an intriguing robustness of ν = 7/3 , 8/3 and 5/2 states (also in graphene). The argumentation why paired states can be developed in two-subband systems (wide quantum wells) only when the Fermi energy lies in the first Landau level is specified. Finally, the paper also clarifies how an additional surface in bilayer systems contributes to an observation of the fractional quantum Hall effect near half-filling, ν = 1/2 .
On the Conformable Fractional Quantum Mechanics
Mozaffari, F. S.; Hassanabadi, H.; Sobhani, H.; Chung, W. S.
2018-05-01
In this paper, a conformable fractional quantum mechanic has been introduced using three postulates. Then in such a formalism, Schr¨odinger equation, probability density, probability flux and continuity equation have been derived. As an application of considered formalism, a fractional-radial harmonic oscillator has been considered. After obtaining its wave function and energy spectrum, effects of the conformable fractional parameter on some quantities have been investigated and plotted for different excited states.
International Nuclear Information System (INIS)
Kramer, T.
2006-01-01
I review some aspects of an alternative model of the quantum Hall effect, which is not based on the presence of disorder potentials. Instead, a quantization of the electronic drift current in the presence of crossed electric and magnetic fields is employed to construct a non-linear transport theory. Another important ingredient of the alternative theory is the coupling of the two-dimensional electron gas to the leads and the applied voltages. By working in a picture where the external voltages fix the chemical potential in the 2D subsystem, the experimentally observed linear relation between the voltage and the location of the quantum Hall plateaus finds an natural explanation. Also, the classical Hall effect emerges as a natural limit of the quantum Hall effect. For low temperatures (or high currents), a non-integer substructure splits higher Landau levels into sublevels. The appearance of substructure and non-integer plateaus in the resistivity is not linked to electron-electron interactions, but caused by the presence of a (linear) electric field. Some of the resulting fractions correspond exactly to half-integer plateaus. (Author)
Carpentier, David
1998-01-01
Using the renormalisation group (RG) we study two dimensional electromagnetic coulomb gas and extended Sine-Gordon theories invariant under the modular group SL(2,Z). The flow diagram is established from the scaling equations, and we derive the critical behaviour at the various transition points of the diagram. Following proposal for a SL(2,Z) duality between different quantum Hall fluids, we discuss the analogy between this flow and the global quantum Hall phase diagram.
Prediction of a quantum anomalous Hall state in Co-decorated silicene
Kaloni, Thaneshwor P.
2014-01-09
Based on first-principles calculations, we demonstrate that Co-decorated silicene can host a quantum anomalous Hall state. The exchange field induced by the Co atoms combined with the strong spin-orbit coupling of the silicene opens a nontrivial band gap at the K point. As compared to other transition metals, Co-decorated silicene is unique in this respect, since usually hybridization and spin-polarization induced in the silicene suppress a quantum anomalous Hall state.
Prediction of a quantum anomalous Hall state in Co-decorated silicene
Kaloni, Thaneshwor P.; Schwingenschlö gl, Udo; Singh, Nirpendra
2014-01-01
Based on first-principles calculations, we demonstrate that Co-decorated silicene can host a quantum anomalous Hall state. The exchange field induced by the Co atoms combined with the strong spin-orbit coupling of the silicene opens a nontrivial band gap at the K point. As compared to other transition metals, Co-decorated silicene is unique in this respect, since usually hybridization and spin-polarization induced in the silicene suppress a quantum anomalous Hall state.
Characterization of the Quantized Hall Insulator Phase in the Quantum Critical Regime
Song, Juntao; Prodan, Emil
2013-01-01
The conductivity $\\sigma$ and resistivity $\\rho$ tensors of the disordered Hofstadter model are mapped as functions of Fermi energy $E_F$ and temperature $T$ in the quantum critical regime of the plateau-insulator transition (PIT). The finite-size errors are eliminated by using the non-commutative Kubo-formula. The results reproduce all the key experimental characteristics of this transition in Integer Quantum Hall (IQHE) systems. In particular, the Quantized Hall Insulator (QHI) phase is det...
Competing Quantum Hall Phases in the Second Landau Level in Low Density Limit
Energy Technology Data Exchange (ETDEWEB)
Pan, Wei [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Serafin, A. [Univ. of Florida, Gainesville, FL (United States). National High Magnetic Field Lab. (MagLab); Xia, J. S. [Univ. of Florida, Gainesville, FL (United States). National High Magnetic Field Lab. (MagLab); Liang, Y. [Univ. of Florida, Gainesville, FL (United States). National High Magnetic Field Lab. (MagLab); Sullivan, N. S. [Univ. of Florida, Gainesville, FL (United States). National High Magnetic Field Lab. (MagLab); Baldwin, K. W. [Princeton Univ., NJ (United States); West, K. W. [Princeton Univ., NJ (United States); Pfeiffer, L. N. [Princeton Univ., NJ (United States); Tsui, D. C. [Princeton Univ., NJ (United States)
2015-01-01
Up to date, studies of the fractional quantum Hall effect (FQHE) states in the second Landau level have mainly been carried out in the high electron density regime, where the electron mobility is the highest. Only recently, with the advance of high quality low density MBE growth, experiments have been pushed to the low density regime [1], where the electron-electron interactions are strong and the Landau level mixing parameter, defined by κ = e^{2}/εI_{B}/ℏω_{e}, is large. Here, l_{B} = (ℏe/B)^{1/2} is the magnetic length and ω_{c} = eB/m the cyclotron frequency. All other parameters have their normal meanings. It has been shown that a large Landau level mixing effect strongly affects the electron physics in the second Landau level [2].
International Nuclear Information System (INIS)
Braggio, A; Ferraro, D; Sassetti, M; Carrega, M; Magnoli, N
2012-01-01
We propose a general mechanism for the renormalization of the tunnelling exponents in edge states of the fractional quantum Hall effect. Mutual effects of the coupling with out-of-equilibrium 1/f noise and dissipation are considered for both the Laughlin sequence and the composite co- and counter-propagating edge states with Abelian or non-Abelian statistics. For states with counter-propagating modes, we demonstrate the robustness of the proposed mechanism in the so-called disorder-dominated phase. Prototypes of these states, such as ν = 2/3 and ν = 5/2, are discussed in detail, and the rich phenomenology induced by the presence of a noisy environment is presented. The proposed mechanism could help justify the strong renormalizations reported in many experimental observations carried out at low temperatures. We show how environmental effects could affect the relevance of the tunnelling excitations, leading to important implications, in particular for the ν = 5/2 case. (paper)
The Josephson and Quantum Hall effect in metrology
International Nuclear Information System (INIS)
Lifka, E.
1990-01-01
This first generation of DC voltage standards based upon the Josephson effect made use of one tunnel junction coupled with microwaves via an external resonator. The needed output voltage level of 1 V was derived either by means of room temperature resistive divider or the cryogenic current comparator from the quantized microwave-induced voltage drop on the Josephson tunnel junction. In order to increase the accuracy of th standard, series arrays of Josephson tunnel junctions, in which the quantized voltage drops are added together thus providing reference voltage of several hundreds mV, are commonly used in some national laboratories. As the radiating frequency used is 70 GHz or higher the actual sample containing tunnel junction array takes form of an millimeter wave integrated circuit feeded by the thin film fin-line. This improved DC voltage standard has relative uncertainty lower by an amount which equals to the contribution of the resistive divider and allied measuring circuitry. This paper traces the present and future of studies involving the use of the Josephson and Quantum Hall Effect in meteorology
Cabo-Montes de Oca, Alejandro
2002-01-01
It is shown how the electromagnetic response of 2DEG under Quantum Hall Effect regime, characterized by the Chern-Simons topological action, transforms the sample impurities and defects in charge-reservoirs that stabilize the Hall conductivity plateaus. The results determine the basic dynamical origin of the singular properties of localization under the occurrence of the Quantum Hall Effect obtained in the pioneering works of Laughlin and of Joynt and Prange, by means of a gauge invariance argument and a purely electronic analysis, respectively. The common intuitive picture of electrons moving along the equipotential lines gets an analytical realization through the Chern-Simons current and charge densities.
Multiparticle quantum mechanics obeying fractional statistics
International Nuclear Information System (INIS)
Wu, Y.
1984-01-01
We obtain the rule governing many-body wave functions for particles obeying fractional statistics in two (space) dimensions. It generalizes and continuously interpolates the usual symmetrization and antisymmetrization. Quantum mechanics of more than two particles is discussed and some new features are found
3D Quantum Hall Effect of Fermi Arc in Topological Semimetals
Wang, C. M.; Sun, Hai-Peng; Lu, Hai-Zhou; Xie, X. C.
2017-09-01
The quantum Hall effect is usually observed in 2D systems. We show that the Fermi arcs can give rise to a distinctive 3D quantum Hall effect in topological semimetals. Because of the topological constraint, the Fermi arc at a single surface has an open Fermi surface, which cannot host the quantum Hall effect. Via a "wormhole" tunneling assisted by the Weyl nodes, the Fermi arcs at opposite surfaces can form a complete Fermi loop and support the quantum Hall effect. The edge states of the Fermi arcs show a unique 3D distribution, giving an example of (d -2 )-dimensional boundary states. This is distinctly different from the surface-state quantum Hall effect from a single surface of topological insulator. As the Fermi energy sweeps through the Weyl nodes, the sheet Hall conductivity evolves from the 1 /B dependence to quantized plateaus at the Weyl nodes. This behavior can be realized by tuning gate voltages in a slab of topological semimetal, such as the TaAs family, Cd3 As2 , or Na3Bi . This work will be instructive not only for searching transport signatures of the Fermi arcs but also for exploring novel electron gases in other topological phases of matter.
Universal signatures of fractionalized quantum critical points.
Isakov, Sergei V; Melko, Roger G; Hastings, Matthew B
2012-01-13
Ground states of certain materials can support exotic excitations with a charge equal to a fraction of the fundamental electron charge. The condensation of these fractionalized particles has been predicted to drive unusual quantum phase transitions. Through numerical and theoretical analysis of a physical model of interacting lattice bosons, we establish the existence of such an exotic critical point, called XY*. We measure a highly nonclassical critical exponent η = 1.493 and construct a universal scaling function of winding number distributions that directly demonstrates the distinct topological sectors of an emergent Z(2) gauge field. The universal quantities used to establish this exotic transition can be used to detect other fractionalized quantum critical points in future model and material systems.
Exploring 4D quantum Hall physics with a 2D topological charge pump
Lohse, Michael; Schweizer, Christian; Price, Hannah M.; Zilberberg, Oded; Bloch, Immanuel
2018-01-01
The discovery of topological states of matter has greatly improved our understanding of phase transitions in physical systems. Instead of being described by local order parameters, topological phases are described by global topological invariants and are therefore robust against perturbations. A prominent example is the two-dimensional (2D) integer quantum Hall effect: it is characterized by the first Chern number, which manifests in the quantized Hall response that is induced by an external electric field. Generalizing the quantum Hall effect to four-dimensional (4D) systems leads to the appearance of an additional quantized Hall response, but one that is nonlinear and described by a 4D topological invariant—the second Chern number. Here we report the observation of a bulk response with intrinsic 4D topology and demonstrate its quantization by measuring the associated second Chern number. By implementing a 2D topological charge pump using ultracold bosonic atoms in an angled optical superlattice, we realize a dynamical version of the 4D integer quantum Hall effect. Using a small cloud of atoms as a local probe, we fully characterize the nonlinear response of the system via in situ imaging and site-resolved band mapping. Our findings pave the way to experimentally probing higher-dimensional quantum Hall systems, in which additional strongly correlated topological phases, exotic collective excitations and boundary phenomena such as isolated Weyl fermions are predicted.
Exploring 4D quantum Hall physics with a 2D topological charge pump.
Lohse, Michael; Schweizer, Christian; Price, Hannah M; Zilberberg, Oded; Bloch, Immanuel
2018-01-03
The discovery of topological states of matter has greatly improved our understanding of phase transitions in physical systems. Instead of being described by local order parameters, topological phases are described by global topological invariants and are therefore robust against perturbations. A prominent example is the two-dimensional (2D) integer quantum Hall effect: it is characterized by the first Chern number, which manifests in the quantized Hall response that is induced by an external electric field. Generalizing the quantum Hall effect to four-dimensional (4D) systems leads to the appearance of an additional quantized Hall response, but one that is nonlinear and described by a 4D topological invariant-the second Chern number. Here we report the observation of a bulk response with intrinsic 4D topology and demonstrate its quantization by measuring the associated second Chern number. By implementing a 2D topological charge pump using ultracold bosonic atoms in an angled optical superlattice, we realize a dynamical version of the 4D integer quantum Hall effect. Using a small cloud of atoms as a local probe, we fully characterize the nonlinear response of the system via in situ imaging and site-resolved band mapping. Our findings pave the way to experimentally probing higher-dimensional quantum Hall systems, in which additional strongly correlated topological phases, exotic collective excitations and boundary phenomena such as isolated Weyl fermions are predicted.
Quantum critical behaviour of the plateau-insulator transition in the quantum Hall regime
International Nuclear Information System (INIS)
Visser, A de; Ponomarenko, L A; Galistu, G; Lang, D T N de; Pruisken, A M M; Zeitler, U; Maude, D
2006-01-01
High-field magnetotransport experiments provide an excellent tool to investigate the plateau-insulator phase transition in the integral quantum Hall effect. Here we review recent low-temperature high-field magnetotransport studies carried out on several InGaAs/InP heterostructures and an InGaAs/GaAs quantum well. We find that the longitudinal resistivity ρ xx near the critical filling factor ν c ∼ 0.5 follows the universal scaling law ρ xx (ν, T) ∝ exp(-Δν/(T/T 0 ) κ ), where Δν = ν-ν c . The critical exponent κ equals 0.56 ± 0.02, which indicates that the plateau-insulator transition falls in a non-Fermi liquid universality class
AdS/QHE: towards a holographic description of quantum Hall experiments
International Nuclear Information System (INIS)
Bayntun, Allan; Burgess, C P; Lee, Sung-Sik; Dolan, Brian P
2011-01-01
Transitions among quantum Hall plateaux share a suite of remarkable experimental features, such as semicircle laws and duality relations, whose accuracy and robustness are difficult to explain directly in terms of the detailed dynamics of the microscopic electrons. They would naturally follow if the low-energy transport properties were governed by an emergent discrete duality group relating the different plateaux, but no explicit examples of interacting systems having such a group are known. Recent progress using the AdS/CFT correspondence has identified examples with similar duality groups, but without the dc ohmic conductivity characteristic of quantum Hall experiments. We use this to propose a simple holographic model for low-energy quantum Hall systems, with a nonzero dc conductivity that automatically exhibits all of the observed consequences of duality, including the existence of the plateaux and the semicircle transitions between them. The model can be regarded as a strongly coupled analogue of the old 'composite boson' picture of quantum Hall systems. Non-universal features of the model can be used to test whether it describes actual materials, and we comment on some of these in our proposed model. In particular, the model indicates the value 2/5 for low-temperature scaling exponents for transitions among quantum Hall plateaux, in agreement with the measured value 0.42±0.01.
W∞ gauge theory and the quantum Hall effect
International Nuclear Information System (INIS)
Shizuya, K.
1994-05-01
It is shown that a planar system of Hall electrons coupled to an applied electromagnetic field is written in the form of a W ∞ gauge theory. The associated W ∞ gauge field is expressed nonlinearly in terms of an infinite set of multipoles of the electromagnetic field. The W ∞ transformations generate mixing among the Landau levels. They provide a systematic way to classify the electromagnetic characteristics of the Hall system according to the resolution of external probes. In particular, an exact long-wavelength connection is derived between the carrier density and the Hall conductance in the presence of electron-electron interactions. Our approach is complementary to an earlier one and reveals a dual role the W ∞ gauge symmetry plays in the Hall dynamics. (author)
Greiter, Martin
2011-01-01
This monograph introduces an exact model for a critical spin chain with arbitrary spin S, which includes the Haldane--Shastry model as the special case S=1/2. While spinons in the Haldane-Shastry model obey abelian half-fermi statistics, the spinons in the general model introduced here obey non-abelian statistics. This manifests itself through topological choices for the fractional momentum spacings. The general model is derived by mapping exact models of quantized Hall states onto spin chains. The book begins with pedagogical review of all the relevant models including the non-abelian statistics in the Pfaffian Hall state, and is understandable to every student with a graduate course in quantum mechanics.
International Nuclear Information System (INIS)
Eaves, L.
2001-01-01
The breakdown of the integer quantum Hall effect at high currents sometimes occurs a series of regular steps in the dissipative voltage drop bars used to maintain the US Resistance Standard, but have also been reported in other devices. It is proposed that the origin of the steps can be understood in terms of instability in the dissipationless flow at high electron drift velocities. The instability is induced by impurity- or defect- related inter-Landau level scattering processes in local macroscopic regions of the Hall bar. Electron-hole pairs (magneto-excitons) are generated in the quantum Hall fluid in these regions and that the electronic motion can be envisaged as a quantum analogue of the Karman vortex street which forms when a classical fluid flows past an obstacle. (author)
Engineering the quantum anomalous Hall effect in graphene with uniaxial strains
Energy Technology Data Exchange (ETDEWEB)
Diniz, G. S., E-mail: ginetom@gmail.com; Guassi, M. R. [Institute of Physics, University of Brasília, 70919-970 Brasília-DF (Brazil); Qu, F. [Institute of Physics, University of Brasília, 70919-970 Brasília-DF (Brazil); Department of Physics, The University of Texas at Austin, Austin, Texas 78712 (United States)
2013-12-28
We theoretically investigate the manipulation of the quantum anomalous Hall effect (QAHE) in graphene by means of the uniaxial strain. The values of Chern number and Hall conductance demonstrate that the strained graphene in presence of Rashba spin-orbit coupling and exchange field, for vanishing intrinsic spin-orbit coupling, possesses non-trivial topological phase, which is robust against the direction and modulus of the strain. Besides, we also find that the interplay between Rashba and intrinsic spin-orbit couplings results in a topological phase transition in the strained graphene. Remarkably, as the strain strength is increased beyond approximately 7%, the critical parameters of the exchange field for triggering the quantum anomalous Hall phase transition show distinct behaviors—decrease (increase) for strains along zigzag (armchair) direction. Our findings open up a new platform for manipulation of the QAHE by an experimentally accessible strain deformation of the graphene structure, with promising application on novel quantum electronic devices with high efficiency.
Engineering the quantum anomalous Hall effect in graphene with uniaxial strains
International Nuclear Information System (INIS)
Diniz, G. S.; Guassi, M. R.; Qu, F.
2013-01-01
We theoretically investigate the manipulation of the quantum anomalous Hall effect (QAHE) in graphene by means of the uniaxial strain. The values of Chern number and Hall conductance demonstrate that the strained graphene in presence of Rashba spin-orbit coupling and exchange field, for vanishing intrinsic spin-orbit coupling, possesses non-trivial topological phase, which is robust against the direction and modulus of the strain. Besides, we also find that the interplay between Rashba and intrinsic spin-orbit couplings results in a topological phase transition in the strained graphene. Remarkably, as the strain strength is increased beyond approximately 7%, the critical parameters of the exchange field for triggering the quantum anomalous Hall phase transition show distinct behaviors—decrease (increase) for strains along zigzag (armchair) direction. Our findings open up a new platform for manipulation of the QAHE by an experimentally accessible strain deformation of the graphene structure, with promising application on novel quantum electronic devices with high efficiency
The effective action for edge states in higher-dimensional quantum Hall systems
International Nuclear Information System (INIS)
Karabali, Dimitra; Nair, V.P.
2004-01-01
We show that the effective action for the edge excitations of a quantum Hall droplet of fermions in higher dimensions is generically given by a chiral bosonic action. We explicitly analyze the quantum Hall effect on complex projective spaces CP k , with a U(1) background magnetic field. The edge excitations are described by Abelian bosonic fields on S 2k-1 with only one spatial direction along the boundary of the droplet relevant for the dynamics. Our analysis also leads to an action for edge excitations for the case of the Zhang-Hu four-dimensional quantum Hall effect defined on S 4 with an SU(2) background magnetic field, using the fact that CP 3 is an S 2 -bundle over S 4
Parity effect of bipolar quantum Hall edge transport around graphene antidots.
Matsuo, Sadashige; Nakaharai, Shu; Komatsu, Katsuyoshi; Tsukagoshi, Kazuhito; Moriyama, Takahiro; Ono, Teruo; Kobayashi, Kensuke
2015-06-30
Parity effect, which means that even-odd property of an integer physical parameter results in an essential difference, ubiquitously appears and enables us to grasp its physical essence as the microscopic mechanism is less significant in coarse graining. Here we report a new parity effect of quantum Hall edge transport in graphene antidot devices with pn junctions (PNJs). We found and experimentally verified that the bipolar quantum Hall edge transport is drastically affected by the parity of the number of PNJs. This parity effect is universal in bipolar quantum Hall edge transport of not only graphene but also massless Dirac electron systems. These results offer a promising way to design electron interferometers in graphene.
Analytical theory and possible detection of the ac quantum spin Hall effect.
Deng, W Y; Ren, Y J; Lin, Z X; Shen, R; Sheng, L; Sheng, D N; Xing, D Y
2017-07-11
We develop an analytical theory of the low-frequency ac quantum spin Hall (QSH) effect based upon the scattering matrix formalism. It is shown that the ac QSH effect can be interpreted as a bulk quantum pumping effect. When the electron spin is conserved, the integer-quantized ac spin Hall conductivity can be linked to the winding numbers of the reflection matrices in the electrodes, which also equal to the bulk spin Chern numbers of the QSH material. Furthermore, a possible experimental scheme by using ferromagnetic metals as electrodes is proposed to detect the topological ac spin current by electrical means.
Brueckner, Reinhold
2000-01-01
We propose an experiment using a three-gate quantum Hall device to probe the dependence of the integral quantum Hall effect (IQHE) on the shape of the lateral confining potential in edge regions. This shape can, in a certain configuration determine whether or not the IQHE occurs.
International Nuclear Information System (INIS)
Riess, J.; Duport, C.
1991-01-01
We report the first numerical results (with realistic parameter values) for the time evolution of a scattered Landau function in a model system. They give a striking illustration for the Hall velocity increase beyond the classical value of the conduction electrons in the quantum Hall regime. This phenomenon, which is crucial for the integer quantum Hall effect, is caused by a special kind of nonclassical particle dynamics induced by disorder and cannot be described by linear response theory
Reply to "Comment on 'Fractional quantum mechanics' and 'Fractional Schrödinger equation' ".
Laskin, Nick
2016-06-01
The fractional uncertainty relation is a mathematical formulation of Heisenberg's uncertainty principle in the framework of fractional quantum mechanics. Two mistaken statements presented in the Comment have been revealed. The origin of each mistaken statement has been clarified and corrected statements have been made. A map between standard quantum mechanics and fractional quantum mechanics has been presented to emphasize the features of fractional quantum mechanics and to avoid misinterpretations of the fractional uncertainty relation. It has been shown that the fractional probability current equation is correct in the area of its applicability. Further studies have to be done to find meaningful quantum physics problems with involvement of the fractional probability current density vector and the extra term emerging in the framework of fractional quantum mechanics.
Topological phase transitions and quantum Hall effect in the graphene family
Ledwith, P.; Kort-Kamp, W. J. M.; Dalvit, D. A. R.
2018-04-01
Monolayer staggered materials of the graphene family present intrinsic spin-orbit coupling and can be driven through several topological phase transitions using external circularly polarized lasers and static electric or magnetic fields. We show how topological features arising from photoinduced phase transitions and the magnetic-field-induced quantum Hall effect coexist in these materials and simultaneously impact their Hall conductivity through their corresponding charge Chern numbers. We also show that the spectral response of the longitudinal conductivity contains signatures of the various phase-transition boundaries, that the transverse conductivity encodes information about the topology of the band structure, and that both present resonant peaks which can be unequivocally associated with one of the four inequivalent Dirac cones present in these materials. This complex optoelectronic response can be probed with straightforward Faraday rotation experiments, allowing the study of the crossroads between quantum Hall physics, spintronics, and valleytronics.
Nonlinear response of the quantum Hall system to a strong electromagnetic radiation
International Nuclear Information System (INIS)
Avetissian, H.K.; Mkrtchian, G.F.
2016-01-01
We study nonlinear response of a quantum Hall system in semiconductor-hetero-structures via third harmonic generation process and nonlinear Faraday effect. We demonstrate that Faraday rotation angle and third harmonic radiation intensity have a characteristic Hall plateaus feature. These nonlinear effects remain robust against the significant broadening of Landau levels. We predict realization of an experiment through the observation of the third harmonic signal and Faraday rotation angle, which are within the experimental feasibility. - Highlights: • Nonlinear optical response of a quantum Hall system has specific plateaus feature. • This effect remains robust against the significant broadening of Landau levels. • It can be observed via the third harmonic signal and the nonlinear Faraday effect.
Gap Structure and Gapless Structure in Fractional Quantum Hall Effect
Directory of Open Access Journals (Sweden)
Shosuke Sasaki
2012-01-01
Full Text Available Higher-order composite fermion states are correlated with many quasiparticles. The energy calculations are very complicated. We develop the theory of Tao and Thouless to explain them. The total Hamiltonian is (+, where includes Landau energies and classical Coulomb energies. We find the most uniform electron configuration in Landau states which has the minimum energy of . At =(2−1/(2, all the nearest electron pairs are forbidden to transfer to any empty states because of momentum conservation. Therefore, perturbation energies of the nearest electron pairs are zero in all order of perturbation. At =/(2−1, /(2+1, all the nearest electron (or hole pairs can transfer to all hole (or electron states. At =4/11, 4/13, 5/13, 5/17, 6/17, only the specific nearest hole pairs can transfer to all electron states. For example, the nearest-hole-pair energy at =4/11 is lower than the limiting energies from both sides (the left side =(4+1/(11+3 and the right side =(4−1/(11−3 for infinitely large . Thus, the nearest-hole-pair energy at specific is different from the limiting values from both sides. The property yields energy gap for the specific . Also gapless structure appears at other filling factors (e.g., at =1/2.
On the ground state for fractional quantum hall effect
International Nuclear Information System (INIS)
Jellal, A.
1998-09-01
In the present letter, we investigate the ground state wave function for an explicit model of electrons in an external magnetic field with specific inter-particle interactions. The excitation states of this model are also given. (author)
A novel method of including Landau level mixing in numerical studies of the quantum Hall effect
International Nuclear Information System (INIS)
Wooten, Rachel; Quinn, John; Macek, Joseph
2013-01-01
Landau level mixing should influence the quantum Hall effect for all except the strongest applied magnetic fields. We propose a simple method for examining the effects of Landau level mixing by incorporating multiple Landau levels into the Haldane pseudopotentials through exact numerical diagonalization. Some of the resulting pseudopotentials for the lowest and first excited Landau levels will be presented
Can Hall drag be observed in Coulomb coupled quantum wells in a magnetic field?
DEFF Research Database (Denmark)
Hu, Ben Yu-Kuang
1997-01-01
We study the transresistivity rho(21) (or equivalently, the drag rate) of two Coulomb-coupled quantum wells in the presence of a perpendicular magnetic field, using semi-classical transport theory. Elementary arguments seem to preclude any possibility of observation of ''Hall drag'' (i.e., a non...
Bhakta, S.; Prajapati, R. P.
2018-02-01
The effects of Hall current and finite electrical resistivity are studied on the stability of uniformly rotating and self-gravitating anisotropic quantum plasma. The generalized Ohm's law modified by Hall current and electrical resistivity is used along with the quantum magnetohydrodynamic fluid equations. The general dispersion relation is derived using normal mode analysis and discussed in the parallel and perpendicular propagations. In the parallel propagation, the Jeans instability criterion, expression of critical Jeans wavenumber, and Jeans length are found to be independent of non-ideal effects and uniform rotation but in perpendicular propagation only rotation affects the Jeans instability criterion. The unstable gravitating mode modified by Bohm potential and the stable Alfven mode modified by non-ideal effects are obtained separately. The criterion of firehose instability remains unaffected due to the presence of non-ideal effects. In the perpendicular propagation, finite electrical resistivity and quantum pressure anisotropy modify the dispersion relation, whereas no effect of Hall current was observed in the dispersion characteristics. The Hall current, finite electrical resistivity, rotation, and quantum corrections stabilize the growth rate. The stability of the dynamical system is analyzed using the Routh-Hurwitz criterion.
Exact diagonalization study of domain structures in integer filling factor quantum Hall ferromagnets
Czech Academy of Sciences Publication Activity Database
Rezayi, E. H.; Jungwirth, Tomáš; MacDonald, A. H.; Haldane, F. D. M.
2003-01-01
Roč. 67, č. 20 (2003), s. 201305-1 - 201305-4 ISSN 0163-1829 R&D Projects: GA ČR GA202/01/0754 Institutional research plan: CEZ:AV0Z1010914 Keywords : domain structure * integer filling factor * quantum Hall ferromagnets Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 2.962, year: 2003
Charged spin textures over the Moore-Read quantum Hall state
Romers, J.C.; Huijse, L.; Schoutens, K.
2011-01-01
We study the composite Charged Spin Texture (CST) over the Moore-Read quantum Hall state that arises when a collection of elementary CSTs are moved to the same location. Following an algebraic approach based on the characteristic pair correlations of the Moore- Read state, we and that the resulting
Quantum Hall effect in InAs/AlSb double quantum well
International Nuclear Information System (INIS)
Yakunin, M.V.; Podgornykh, S.M.; Sadof'ev, Yu.G.
2009-01-01
Double quantum wells (DQWs) were first implemented in the InAs/AlSb heterosystem, which is characterized by a large Lande g factor |g|=15 of the InAs layers forming the well, much larger than the bulk g factor |g|=0.4 of the GaAs in conventional GaAs/AlGaAs DQWs. The quality of the samples is good enough to permit observation of a clear picture of the quantum Hall effect (QHE). Despite the small tunneling gap, which is due to the large barrier height (1.4 eV), features with odd filling factors ν=3,5,7, ... are present in the QHE, due to collectivized interlayer states of the DQW. When the field is rotated relative to the normal to the layers, the ν=3 state is suppressed, confirming the collectivized nature of that state and denying that it could owe its existence to a strong asymmetry of the DQW. Previously the destruction of the collectivized QHE states by a parallel field had been observed only for the ν=1 state. The observation of a similar effect for ν=3 in an InAs/AlSb DQW may be due to the large bulk g factor of InAs
General topological features and instanton vacuum in quantum Hall and spin liquids
International Nuclear Information System (INIS)
Pruisken, A.M.M.; Shankar, R.; Surendran, Naveen
2005-01-01
We introduce the concept of superuniversality in quantum Hall liquids and spin liquids. This concept has emerged from previous studies of the quantum Hall effect and states that all the fundamental features of the quantum Hall effect are generically displayed as general topological features of the θ parameter in nonlinear σ models in two dimensions. To establish superuniversality in spin liquids we revisit the mapping by Haldane who argued that the antiferromagnetic Heisenberg spin-s chain in 1+1 space-time dimensions is effectively described by the O(3) nonlinear σ model with a θ term. By combining the path integral representation for the dimerized spin s=1/2 chain with renormalization-group decimation techniques we generalize the Haldane approach to include a more complicated theory, the fermionic rotor chain, involving four different renormalization-group parameters. We show how the renormalization-group calculation technique can be used to build a bridge between the fermionic rotor chain and the O(3) nonlinear σ model with the θ term. As an integral and fundamental aspect of the mapping we establish the topological significance of the dangling spin at the edge of the chain. The edge spin in spin liquids is in all respects identical to the massless chiral edge excitations in quantum Hall liquids. We consider various different geometries of the spin chain such as open and closed chains, chains with an even and odd number of sides. We show that for each of the different geometries the θ term has a distinctly different physical meaning. We compare each case with a topologically equivalent quantum Hall liquid
Zhou, Jian; Sun, Qiang; Wang, Qian; Kawazoe, Yoshiyuki; Jena, Puru
2016-06-07
Exploring a two-dimensional intrinsic quantum spin Hall state with a large band gap as well as an anomalous Hall state in realizable materials is one of the most fundamental and important goals for future applications in spintronics, valleytronics, and quantum computing. Here, by combining first-principles calculations with a tight-binding model, we predict that Sb or Bi can epitaxially grow on a stable and ferromagnetic MnO2 thin film substrate, forming a flat honeycomb sheet. The flatness of Sb or Bi provides an opportunity for the existence of Dirac points in the Brillouin zone, with its position effectively tuned by surface hydrogenation. The Dirac points in spin up and spin down channels split due to the proximity effects induced by MnO2. In the presence of both intrinsic and Rashba spin-orbit coupling, we find two band gaps exhibiting a large band gap quantum spin Hall state and a nearly quantized anomalous Hall state which can be tuned by adjusting the Fermi level. Our findings provide an efficient way to realize both quantized intrinsic spin Hall conductivity and anomalous Hall conductivity in a single material.
Universal conductance and conductivity at critical points in integer quantum Hall systems.
Schweitzer, L; Markos, P
2005-12-16
The sample averaged longitudinal two-terminal conductance and the respective Kubo conductivity are calculated at quantum critical points in the integer quantum Hall regime. In the limit of large system size, both transport quantities are found to be the same within numerical uncertainty in the lowest Landau band, and , respectively. In the second-lowest Landau band, a critical conductance is obtained which indeed supports the notion of universality. However, these numbers are significantly at variance with the hitherto commonly believed value . We argue that this difference is due to the multifractal structure of critical wave functions, a property that should generically show up in the conductance at quantum critical points.
Circularly polarized near-field optical mapping of spin-resolved quantum Hall chiral edge states.
Mamyouda, Syuhei; Ito, Hironori; Shibata, Yusuke; Kashiwaya, Satoshi; Yamaguchi, Masumi; Akazaki, Tatsushi; Tamura, Hiroyuki; Ootuka, Youiti; Nomura, Shintaro
2015-04-08
We have successfully developed a circularly polarized near-field scanning optical microscope (NSOM) that enables us to irradiate circularly polarized light with spatial resolution below the diffraction limit. As a demonstration, we perform real-space mapping of the quantum Hall chiral edge states near the edge of a Hall-bar structure by injecting spin polarized electrons optically at low temperature. The obtained real-space mappings show that spin-polarized electrons are injected optically to the two-dimensional electron layer. Our general method to locally inject spins using a circularly polarized NSOM should be broadly applicable to characterize a variety of nanomaterials and nanostructures.
Levitation of current carrying states in the lattice model for the integer quantum Hall effect.
Koschny, T; Potempa, H; Schweitzer, L
2001-04-23
The disorder driven quantum Hall to insulator transition is investigated for a two-dimensional lattice model. The Hall conductivity and the localization length are calculated numerically near the transition. For uncorrelated and weakly correlated disorder potentials the current carrying states are annihilated by the negative Chern states originating from the band center. In the presence of correlated disorder potentials with correlation length larger than approximately half the lattice constant the floating up of the critical states in energy without merging is observed. This behavior is similar to the levitation scenario proposed for the continuum model.
Scaling of anomalous hall effect in amorphous CoFeB Films with accompanying quantum correction
Zhang, Yan
2015-05-08
Scaling of anomalous Hall effect in amorphous CoFeB films with thickness ranging from 2 to 160 nm have been investigated. We have found that the scaling relationship between longitudinal (ρxx) and anomalous Hall (ρAH) resistivity is distinctly different in the Bloch and localization regions. For ultrathin CoFeB films, the sheet resistance (Rxx) and anomalous Hall conductance (GAH) received quantum correction from electron localization showing two different scaling relationships at different temperature regions. In contrast, the thicker films show a metallic conductance, which have only one scaling relationship in the entire temperature range. Furthermore, in the dirty regime of localization regions, an unconventional scaling relationship View the MathML sourceσAH∝σxxα with α=1.99 is found, rather than α=1.60 predicted by the unified theory.
Magnon spin Hall magnetoresistance of a gapped quantum paramagnet
Ulloa, Camilo; Duine, R.A.
2018-01-01
Motivated by recent experimental work, we consider spin transport between a normal metal and a gapped quantum paramagnet. We model the latter as the magnonic Mott-insulating phase of an easy-plane ferromagnetic insulator. We evaluate the spin current mediated by the interface exchange coupling
Fractional decay of quantum dots in photonic crystals
DEFF Research Database (Denmark)
Kristensen, Philip Trøst; Koenderink, Femius; Lodahl, Peter
2008-01-01
We define a practical measure for the degree of fractional decay and establish conditions for the effect to be observable for quantum dots in photonic crystals exhibiting absorptive losses.......We define a practical measure for the degree of fractional decay and establish conditions for the effect to be observable for quantum dots in photonic crystals exhibiting absorptive losses....
Photonic topological boundary pumping as a probe of 4D quantum Hall physics.
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
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.
Prediction of a Large-Gap and Switchable Kane-Mele Quantum Spin Hall Insulator
Marrazzo, Antimo; Gibertini, Marco; Campi, Davide; Mounet, Nicolas; Marzari, Nicola
2018-03-01
Fundamental research and technological applications of topological insulators are hindered by the rarity of materials exhibiting a robust topologically nontrivial phase, especially in two dimensions. Here, by means of extensive first-principles calculations, we propose a novel quantum spin Hall insulator with a sizable band gap of ˜0.5 eV that is a monolayer of jacutingaite, a naturally occurring layered mineral first discovered in 2008 in Brazil and recently synthesized. This system realizes the paradigmatic Kane-Mele model for quantum spin Hall insulators in a potentially exfoliable two-dimensional monolayer, with helical edge states that are robust and that can be manipulated exploiting a unique strong interplay between spin-orbit coupling, crystal-symmetry breaking, and dielectric response.
Valley polarized quantum Hall effect and topological insulator phase transitions in silicene
Tahir, M.
2013-01-25
The electronic properties of silicene are distinct from both the conventional two dimensional electron gas and the famous graphene due to strong spin orbit interaction and the buckled structure. Silicene has the potential to overcome limitations encountered for graphene, in particular the zero band gap and weak spin orbit interaction. We demonstrate a valley polarized quantum Hall effect and topological insulator phase transitions. We use the Kubo formalism to discuss the Hall conductivity and address the longitudinal conductivity for elastic impurity scattering in the first Born approximation. We show that the combination of an electric field with intrinsic spin orbit interaction leads to quantum phase transitions at the charge neutrality point, providing a tool to experimentally tune the topological state. Silicene constitutes a model system for exploring the spin and valley physics not accessible in graphene due to the small spin orbit interaction.
Theory of the disordered ν =5/2 quantum thermal Hall state: Emergent symmetry and phase diagram
Lian, Biao; Wang, Juven
2018-04-01
Fractional quantum Hall (FQH) system at Landau level filling fraction ν =5 /2 has long been suggested to be non-Abelian, either Pfaffian (Pf) or antiPfaffian (APf) states by numerical studies, both with quantized Hall conductance σx y=5 e2/2 h . Thermal Hall conductances of the Pf and APf states are quantized at κx y=7 /2 and κx y=3 /2 , respectively, in a proper unit. However, a recent experiment shows the thermal Hall conductance of ν =5 /2 FQH state is κx y=5 /2 . It has been speculated that the system contains random Pf and APf domains driven by disorders, and the neutral chiral Majorana modes on the domain walls may undergo a percolation transition to a κx y=5 /2 phase. In this paper, we do perturbative and nonperturbative analyses on the domain walls between Pf and APf. We show the domain wall theory possesses an emergent SO(4) symmetry at energy scales below a threshold Λ1, which is lowered to an emergent U (1 )×U (1) symmetry at energy scales between Λ1 and a higher value Λ2, and is finally lowered to the composite fermion parity symmetry Z2F above Λ2. Based on the emergent symmetries, we propose a phase diagram of the disordered ν =5 /2 FQH system and show that a κx y=5 /2 phase arises at disorder energy scales Λ >Λ1 . Furthermore, we show the gapped double-semion sector of ND compact domain walls contributes nonlocal topological degeneracy 2ND-1, causing a low-temperature peak in the heat capacity. We implement a nonperturbative method to bootstrap generic topological 1 +1 D domain walls (two-surface defects) applicable to any 2 +1 D non-Abelian topological order. We also identify potentially relevant spin topological quantum field theories (TQFTs) for various ν =5 /2 FQH states in terms of fermionic version of U (1) ±8 Chern-Simons theory ×Z8 -class TQFTs.
Scaling behavior and variable hopping conductivity in the quantum Hall plateau transition
International Nuclear Information System (INIS)
Tu, Tao; Zhao, Yong-Jie; Guo, Guo-Ping; Hao, Xiao-Jie; Guo, Guang-Can
2007-01-01
We have measured the temperature dependence of the longitudinal resistivity ρ xx of a two-dimensional electron system in the regime of the quantum Hall plateau transition. We extracted the quantitative form of scaling function for ρ xx and compared it with the results of ordinary scaling theory and variable range hopping based theory. We find that the two alternative theoretically proposed scaling functions are valid in different regions
Realization of quantum anomalous Hall effect from a magnetic Weyl semimetal
Muechler, Lukas; Liu, Enke; Xu, Qiunan; Felser, Claudia; Sun, Yan
2017-01-01
The quantum anomalous Hall effect (QAHE) and magnetic Weyl semimetals (WSMs) are topological states induced by intrinsic magnetic moments and spin-orbital coupling. Their similarity suggests the possibility of achieving the QAHE by dimensional confinement of a magnetic WSM along one direction. In this study, we investigate the emergence of the QAHE in the two dimensional (2D) limit of magnetic WSMs due to finite size effects. We demonstrate the feasibility of this approach with effective mode...
Quantum spin Hall states in graphene interacting with WS2 or WSe2
Kaloni, T. P.
2014-12-08
In the framework of first-principles calculations, we investigate the structural and electronic properties of graphene in contact with as well as sandwiched between WS2 and WSe2 monolayers. We report the modification of the band characteristics due to the interaction at the interface and demonstrate that the presence of the dichalcogenide results in quantum spin Hall states in the absence of a magnetic field.
Wuertz, A.; Wildfeuer, R.; Lorke, A.; Deviatov, E. V.; Dolgopolov, V. T.
2001-01-01
Using an innovative combination of a quasi-Corbino sample geometry and the cross-gate technique, we have developed a method that enables us to separately contact single edge channels in the quantum Hall regime and investigate equilibration among them. Performing 4-point resistance measurements, we directly obtain information on the energetic and geometric structure of the edge region and the equilibration-length for current transport across the Landau- as well as the spin-gap. Based on an alm...
Resistance spikes and domain wall loops in Ising quantum Hall ferromagnets
Czech Academy of Sciences Publication Activity Database
Jungwirth, Tomáš; MacDonald, A. H.
2001-01-01
Roč. 87, č. 21 (2001), s. 236801-1 - 216501-4 ISSN 0031-9007 R&D Projects: GA MŠk OC P5.10; GA ČR GA202/01/0754 Institutional research plan: CEZ:AV0Z1010914 Keywords : quantum Hall ferromagnet * domains Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 6.668, year: 2001
Quantum spin Hall states in graphene interacting with WS2 or WSe2
Kaloni, T. P.; Kou, L.; Frauenheim, T.; Schwingenschlö gl, Udo
2014-01-01
In the framework of first-principles calculations, we investigate the structural and electronic properties of graphene in contact with as well as sandwiched between WS2 and WSe2 monolayers. We report the modification of the band characteristics due to the interaction at the interface and demonstrate that the presence of the dichalcogenide results in quantum spin Hall states in the absence of a magnetic field.
Assessment of bilayer silicene to probe as quantum spin and valley Hall effect
Rehman, Majeed Ur; Qiao, Zhenhua
2018-02-01
Silicene takes precedence over graphene due to its buckling type structure and strong spin orbit coupling. Motivated by these properties, we study the silicene bilayer in the presence of applied perpendicular electric field and intrinsic spin orbit coupling to probe as quantum spin/valley Hall effect. Using analytical approach, we calculate the spin Chern-number of bilayer silicene and then compare it with monolayer silicene. We reveal that bilayer silicene hosts double spin Chern-number as compared to single layer silicene and therefore accordingly has twice as many edge states in contrast to single layer silicene. In addition, we investigate the combined effect of intrinsic spin orbit coupling and the external electric field, we find that bilayer silicene, likewise single layer silicene, goes through a phase transitions from a quantum spin Hall state to a quantum valley Hall state when the strength of the applied electric field exceeds the intrinsic spin orbit coupling strength. We believe that the results and outcomes obtained for bilayer silicene are experimentally more accessible as compared to bilayer graphene, because of strong SO coupling in bilayer silicene.
SO(8) fermion dynamical symmetry and strongly correlated quantum Hall states in monolayer graphene
Wu, Lian-Ao; Murphy, Matthew; Guidry, Mike
2017-03-01
A formalism is presented for treating strongly correlated graphene quantum Hall states in terms of an SO(8) fermion dynamical symmetry that includes pairing as well as particle-hole generators. The graphene SO(8) algebra is isomorphic to an SO(8) algebra that has found broad application in nuclear physics, albeit with physically very different generators, and exhibits a strong formal similarity to SU(4) symmetries that have been proposed to describe high-temperature superconductors. The well-known SU(4) symmetry of quantum Hall ferromagnetism for single-layer graphene is recovered as one subgroup of SO(8), but the dynamical symmetry structure associated with the full set of SO(8) subgroup chains extends quantum Hall ferromagnetism and allows analytical many-body solutions for a rich set of collective states exhibiting spontaneously broken symmetry that may be important for the low-energy physics of graphene in strong magnetic fields. The SO(8) symmetry permits a natural definition of generalized coherent states that correspond to symmetry-constrained Hartree-Fock-Bogoliubov solutions, or equivalently a microscopically derived Ginzburg-Landau formalism, exhibiting the interplay between competing spontaneously broken symmetries in determining the ground state.
Interplay between snake and quantum edge states in a graphene Hall bar with a pn-junction
Energy Technology Data Exchange (ETDEWEB)
Milovanović, S. P., E-mail: slavisa.milovanovic@uantwerpen.be; Peeters, F. M., E-mail: francois.peeters@uantwerpen.be [Departement Fysica, Universiteit Antwerpen, Groenenborgerlaan 171, B-2020 Antwerpen (Belgium); Ramezani Masir, M., E-mail: mrmphys@gmail.com [Departement Fysica, Universiteit Antwerpen, Groenenborgerlaan 171, B-2020 Antwerpen (Belgium); Department of Physics, University of Texas at Austin, 2515 Speedway, C1600 Austin, Texas 78712-1192 (United States)
2014-09-22
The magneto- and Hall resistance of a locally gated cross shaped graphene Hall bar is calculated. The edge of the top gate is placed diagonally across the center of the Hall cross. Four-probe resistance is calculated using the Landauer-Büttiker formalism, while the transmission coefficients are obtained using the non-equilibrium Green's function approach. The interplay between transport due to edge channels and snake states is investigated. When two edge channels are occupied, we predict oscillations in the Hall and the bend resistance as function of the magnetic field, which are a consequence of quantum interference between the occupied snake states.
DC resistance comparison between a current comparator bridge and the quantum Hall system at Inmetro
International Nuclear Information System (INIS)
Da Silva, M C; Vasconcellos, R T B; Carvalho, H R
2016-01-01
This paper presents a comparison results between the Quantum Hall System (QHS) under development at the Quantum Electrical Metrology Laboratory (Lameq) and the current comparator calibration system, traceable to the Bureau International des Poids et Mesures (BIPM), at the Electrical Standardization Metrology Laboratory (Lampe), both part of the Electrical Metrology Division, at Inmetro. Comparisons were performed with 1 Ω, 10 Ω, 100 Ω, 1 kΩ and 10 kΩ resistors. The results obtained over two years of work are presented here, showing that the comparison contributed to improve the calibration systems of both Lampe and Lameq. (paper)
International Nuclear Information System (INIS)
Lal, Siddhartha
2007-09-01
Motivated by surprises in recent experimental findings, we study transport in a model of a quantum Hall edge system with a gate-voltage controlled constriction. A finite backscattered current at finite edge-bias is explained as arising from the splitting of edge current caused by the difference in the filling fractions of the bulk (ν 1 ) and constriction (ν 2 ) quantum Hall fluid regions. We develop a hydrodynamic theory for bosonic edge modes inspired by this model. The constriction region splits the incident long-wavelength chiral edge density-wave excitations among the transmitting and reflecting edge states encircling it. The competition between two interedge tunneling processes taking place inside the constriction, related by a quasiparticle-quasihole (qp-qh) symmetry, is accounted for by computing the boundary theories of the system. This competition is found to determine the strong coupling configuration of the system. A separatrix of qp-qh symmetric gapless critical states is found to lie between the relevant RG flows to a metallic and an insulating configuration of the constriction system. This constitutes an interesting generalisation of the Kane-Fisher quantum impurity model. The features of the RG phase diagram are also confirmed by computing various correlators and chiral linear conductances of the system. In this way, our results find excellent agreement with many recent puzzling experimental results for the cases of ν 1 = 1/3, 1. We also discuss and make predictions for the case of a constriction system with ν 2 = 5/2. (author)
Optimization of edge state velocity in the integer quantum Hall regime
Sahasrabudhe, H.; Novakovic, B.; Nakamura, J.; Fallahi, S.; Povolotskyi, M.; Klimeck, G.; Rahman, R.; Manfra, M. J.
2018-02-01
Observation of interference in the quantum Hall regime may be hampered by a small edge state velocity due to finite phase coherence time. Therefore designing two quantum point contact (QPCs) interferometers having a high edge state velocity is desirable. Here we present a new simulation method for designing heterostructures with high edge state velocity by realistically modeling edge states near QPCs in the integer quantum Hall effect (IQHE) regime. Using this simulation method, we also predict the filling factor at the center of QPCs and their conductance at different gate voltages. The 3D Schrödinger equation is split into 1D and 2D parts. Quasi-1D Schrödinger and Poisson equations are solved self-consistently in the IQHE regime to obtain the potential profile, and quantum transport is used to solve for the edge state wave functions. The velocity of edge states is found to be /B , where is the expectation value of the electric field for the edge state. Anisotropically etched trench gated heterostructures with double-sided delta doping have the highest edge state velocity among the structures considered.
Role of helical edge modes in the chiral quantum anomalous Hall state.
Mani, Arjun; Benjamin, Colin
2018-01-22
Although indications are that a single chiral quantum anomalous Hall(QAH) edge mode might have been experimentally detected. There have been very many recent experiments which conjecture that a chiral QAH edge mode always materializes along with a pair of quasi-helical quantum spin Hall (QSH) edge modes. In this work we deal with a substantial 'What If?' question- in case the QSH edge modes, from which these QAH edge modes evolve, are not topologically-protected then the QAH edge modes wont be topologically-protected too and thus unfit for use in any applications. Further, as a corollary one can also ask if the topological-protection of QSH edge modes does not carry over during the evolution process to QAH edge modes then again our 'What if?' scenario becomes apparent. The 'how' of the resolution of this 'What if?' conundrum is the main objective of our work. We show in similar set-ups affected by disorder and inelastic scattering, transport via trivial QAH edge mode leads to quantization of Hall resistance and not that via topological QAH edge modes. This perhaps begs a substantial reinterpretation of those experiments which purported to find signatures of chiral(topological) QAH edge modes albeit in conjunction with quasi helical QSH edge modes.
Field effect in the quantum Hall regime of a high mobility graphene wire
Energy Technology Data Exchange (ETDEWEB)
Barraud, C., E-mail: cbarraud@phys.ethz.ch, E-mail: clement.barraud@univ-paris-diderot.fr; Choi, T.; Ihn, T.; Ensslin, K. [Solid State Physics Laboratory, ETH Zürich, CH-8093 Zürich (Switzerland); Butti, P.; Shorubalko, I. [Swiss Federal Laboratories of Materials Science and Technologies, EMPA Elect. Metrol. Reliabil. Lab., CH-8600 Dübendorf (Switzerland); Taniguchi, T.; Watanabe, K. [National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044 (Japan)
2014-08-21
In graphene-based electronic devices like in transistors, the field effect applied thanks to a gate electrode allows tuning the charge density in the graphene layer and passing continuously from the electron to the hole doped regime across the Dirac point. Homogeneous doping is crucial to understand electrical measurements and for the operation of future graphene-based electronic devices. However, recently theoretical and experimental studies highlighted the role of the electrostatic edge due to fringing electrostatic field lines at the graphene edges [P. Silvestrov and K. Efetov, Phys. Rev. B 77, 155436 (2008); F. T. Vasko and I. V. Zozoulenko, Appl. Phys. Lett. 97, 092115 (2010)]. This effect originates from the particular geometric design of the samples. A direct consequence is a charge accumulation at the graphene edges giving a value for the density, which deviates from the simple picture of a plate capacitor and also varies along the width of the graphene sample. Entering the quantum Hall regime would, in principle, allow probing this accumulation thanks to the extreme sensitivity of this quantum effect to charge density and the charge distribution. Moreover, the presence of an additional and counter-propagating edge channel has been predicted [P. Silvestrov and K. Efetov, Phys. Rev. B 77, 155436 (2008)] giving a fundamental aspect to this technological issue. In this article, we investigate this effect by tuning a high mobility graphene wire into the quantum Hall regime in which charge carriers probe the electrostatic potential at high magnetic field close to the edges. We observe a slight deviation to the linear shift of the quantum Hall plateaus with magnetic field and we study its evolution for different filling factors, which correspond to different probed regions in real space. We discuss the possible origins of this effect including an increase of the charge density towards the edges.
Georgiev, Lachezar S.
2006-12-01
We extend the topological quantum computation scheme using the Pfaffian quantum Hall state, which has been recently proposed by Das Sarma , in a way that might potentially allow for the topologically protected construction of a universal set of quantum gates. We construct, for the first time, a topologically protected controlled-NOT gate, which is entirely based on quasihole braidings of Pfaffian qubits. All single-qubit gates, except for the π/8 gate, are also explicitly implemented by quasihole braidings. Instead of the π/8 gate we try to construct a topologically protected Toffoli gate, in terms of the controlled-phase gate and CNOT or by a braid-group-based controlled-controlled- Z precursor. We also give a topologically protected realization of the Bravyi-Kitaev two-qubit gate g3 .
Signatures of a Nonthermal Metastable State in Copropagating Quantum Hall Edge Channels
Itoh, Kosuke; Nakazawa, Ryo; Ota, Tomoaki; Hashisaka, Masayuki; Muraki, Koji; Fujisawa, Toshimasa
2018-05-01
A Tomonaga-Luttinger (TL) liquid is known as an integrable system, in which a nonequilibrium many-body state survives without relaxing to a thermalized state. This intriguing characteristic is tested experimentally in copropagating quantum Hall edge channels at bulk filling factor ν =2 . The unidirectional transport allows us to investigate the time evolution by measuring the spatial evolution of the electronic states. The initial state is prepared with a biased quantum point contact, and its spatial evolution is measured with a quantum-dot energy spectrometer. We find strong evidence for a nonthermal metastable state in agreement with the TL theory before the system relaxes to thermal equilibrium with coupling to the environment.
Circuit models and SPICE macro-models for quantum Hall effect devices
International Nuclear Information System (INIS)
Ortolano, Massimo; Callegaro, Luca
2015-01-01
Precise electrical measurement technology based on the quantum Hall effect is one of the pillars of modern quantum electrical metrology. Electrical networks including one or more QHE elements can be used as quantum resistance and impedance standards. The analysis of these networks allows metrologists to evaluate the effect of the inevitable parasitic parameters on their performance as standards. This paper presents a concise review of the various circuit models for QHE elements proposed in the literature, and the development of a new model. This last model is particularly suited to be employed with the analogue electronic circuit simulator SPICE. The SPICE macro-model and examples of SPICE simulations, validated by comparison with the corresponding analytical solution and/or experimental data, are provided. (paper)
Intrinsic quantum anomalous hall effect in a two-dimensional anilato-based lattice.
Ni, Xiaojuan; Jiang, Wei; Huang, Huaqing; Jin, Kyung-Hwan; Liu, Feng
2018-06-13
Using first-principles calculations, we predict an intrinsic quantum anomalous Hall (QAH) state in a monolayer anilato-based metal-organic framework M2(C6O4X2)3 (M = Mn and Tc, X = F, Cl, Br and I). The spin-orbit coupling of M d orbitals opens a nontrivial band gap up to 18 meV at the Dirac point. The electron counting rule is used to explain the intrinsic nature of the QAH state. The calculated nonzero Chern number, gapless edge states and quantized Hall conductance all confirm the nontrivial topological properties in the anilato-based lattice. Our findings provide an organic materials platform for the realization of the QAH effect without the need for magnetic and charge doping, which are highly desirable for the development of low-energy-consumption spintronic devices.
Photoinduced quantum spin and valley Hall effects, and orbital magnetization in monolayer MoS2
Tahir, M.
2014-09-22
We theoretically demonstrate that 100% valley-polarized transport in monolayers of MoS2 and other group-VI dichalcogenides can be obtained using off-resonant circularly polarized light. By tuning the intensity of the off-resonant light the intrinsic band gap in one valley is reduced, while it is enhanced in the other valley, enabling single valley quantum transport. As a consequence, we predict (i) enhancement of the longitudinal electrical conductivity, accompanied by an increase in the spin polarization of the flowing electrons, (ii) enhancement of the intrinsic spin Hall effect, together with a reduction of the intrinsic valley Hall effect, and (iii) enhancement of the orbital magnetic moment and orbital magnetization. These mechanisms provide appealing opportunities to the design of nanoelectronics based on dichalcogenides.
Photoinduced quantum spin and valley Hall effects, and orbital magnetization in monolayer MoS2
Tahir, M.; Manchon, Aurelien; Schwingenschlö gl, Udo
2014-01-01
We theoretically demonstrate that 100% valley-polarized transport in monolayers of MoS2 and other group-VI dichalcogenides can be obtained using off-resonant circularly polarized light. By tuning the intensity of the off-resonant light the intrinsic band gap in one valley is reduced, while it is enhanced in the other valley, enabling single valley quantum transport. As a consequence, we predict (i) enhancement of the longitudinal electrical conductivity, accompanied by an increase in the spin polarization of the flowing electrons, (ii) enhancement of the intrinsic spin Hall effect, together with a reduction of the intrinsic valley Hall effect, and (iii) enhancement of the orbital magnetic moment and orbital magnetization. These mechanisms provide appealing opportunities to the design of nanoelectronics based on dichalcogenides.
Transport in constricted quantum Hall systems: beyond the Kane-Fisher paradigm
International Nuclear Information System (INIS)
Lal, Siddhartha
2007-08-01
A simple model of edge transport in a constricted quantum Hall system with a lowered local fi lling factor is studied. The current backscattered from the constriction is explained from a matching of the properties of the edge-current excitations in the constriction (ν 2 ) and bulk (ν 1 ) regions. We develop a hydrodynamic theory for bosonic edge modes inspired by this model, stressing the importance of boundary conditions in elucidating the nature of current transport. By invoking a generalised quasiparticle-quasihole symmetry of the quantum Hall circuit system, we fi nd that a competition between two tunneling process determines the fate of the low-bias transmission conductance. A novel generalisation of the Kane-Fisher quantum impurity model is found, describing transitions from a weak-coupling theory at partial transmission to strong- coupling theories for perfect transmission and reflection as well as a new symmetry dictated fixed point. These results provide satisfactory explanations for recent experimental results at fi lling-factors of 1/3 and 1. (author)
Levitation of the quantum Hall extended states in the $B\\to$ 0 limit
Koschny, Th.; Schweitzer, L.
2004-01-01
We investigate the fate of the quantum Hall extended states within a continuum model with spatially correlated disorder potentials. The model can be projected onto a couple of the lowest Landau bands. Levitation of the $n=0$ critical states is observed if at least the two lowest Landau bands are considered. The dependence on the magnetic length $l_B=(\\hbar/(eB))^{1/2}$ and on the correlation length of the disorder potential $\\eta$ is combined into a single dimensionless parameter $\\hat\\eta=\\e...
Non-adiabatic effect on Laughlin's argument of the quantum Hall effect
International Nuclear Information System (INIS)
Maruyama, I; Hatsugai, Y
2009-01-01
We have numerically studied a non-adiabatic charge transport in the quantum Hall system pumped by a magnetic flux, as one of the simplest theoretical realizations of non-adiabatic Thouless pumping. In the adiabatic limit, a pumped charge is quantized, known as Laughlin's argument in a cylindrical lattice. In a uniform electric field, we obtained a formula connecting quantized pumping in the adiabatic limit and no-pumping in the sudden limit. The intermediate region between the two limits is determined by the Landau gap. A randomness or impurity effect is also discussed.
Current distribution and conductance quantization in the integer quantum Hall regime
International Nuclear Information System (INIS)
Cresti, Alessandro; Farchioni, Riccardo; Grosso, Giuseppe; Parravicini, Giuseppe Pastori
2003-01-01
Charge transport of a two-dimensional electron gas in the presence of a magnetic field is studied by means of the Keldysh-Green function formalism and the tight-binding method. We evaluate the spatial distributions of persistent (equilibrium) and transport (nonequilibrium) currents, and give a vivid picture of their profiles. In the quantum Hall regime, we find exact conductance quantization both for persistent currents and for transport currents, even in the presence of impurity scattering centres and moderate disorder. (letter to the editor)
Current distribution and conductance quantization in the integer quantum Hall regime
Energy Technology Data Exchange (ETDEWEB)
Cresti, Alessandro [NEST-INFM and Dipartimento di Fisica ' E Fermi' , Universita di Pisa, via F Buonarroti 2, I-56127 Pisa (Italy); Farchioni, Riccardo [NEST-INFM and Dipartimento di Fisica ' E Fermi' , Universita di Pisa, via F Buonarroti 2, I-56127 Pisa (Italy); Grosso, Giuseppe [NEST-INFM and Dipartimento di Fisica ' E Fermi' , Universita di Pisa, via F Buonarroti 2, I-56127 Pisa (Italy); Parravicini, Giuseppe Pastori [NEST-INFM and Dipartimento di Fisica ' A Volta' , Universita di Pavia, via A Bassi 6, I-27100 Pavia (Italy)
2003-06-25
Charge transport of a two-dimensional electron gas in the presence of a magnetic field is studied by means of the Keldysh-Green function formalism and the tight-binding method. We evaluate the spatial distributions of persistent (equilibrium) and transport (nonequilibrium) currents, and give a vivid picture of their profiles. In the quantum Hall regime, we find exact conductance quantization both for persistent currents and for transport currents, even in the presence of impurity scattering centres and moderate disorder. (letter to the editor)
Valley-filtered edge states and quantum valley Hall effect in gated bilayer graphene.
Zhang, Xu-Long; Xu, Lei; Zhang, Jun
2017-05-10
Electron edge states in gated bilayer graphene in the quantum valley Hall (QVH) effect regime can carry both charge and valley currents. We show that an interlayer potential splits the zero-energy level and opens a bulk gap, yielding counter-propagating edge modes with different valleys. A rich variety of valley current states can be obtained by tuning the applied boundary potential and lead to the QVH effect, as well as to the unbalanced QVH effect. A method to individually manipulate the edge states by the boundary potentials is proposed.
The self-consistent calculation of the edge states in bilayer quantum Hall bar
International Nuclear Information System (INIS)
Kavruk, A E; Orzturk, T; Orzturk, A; Atav, U; Yuksel, H
2011-01-01
In this study, we present the spatial distributions of the edge channels for each layer in bilayer quantum Hall bar geometry for a wide range of applied magnetic fields. For this purpose, we employ a self-consistent Thomas-Fermi-Poisson approach to obtain the electron density distributions and related screened potential distributions. In order to have a more realistic description of the system we solve three dimensional Poisson equation numerically in each iteration step to obtain self consistency in the Thomas-Fermi-Poisson approach instead of employing a 'frozen gate' approximation.
Fractional quantum integral operator with general kernels and applications
Babakhani, Azizollah; Neamaty, Abdolali; Yadollahzadeh, Milad; Agahi, Hamzeh
In this paper, we first introduce the concept of fractional quantum integral with general kernels, which generalizes several types of fractional integrals known from the literature. Then we give more general versions of some integral inequalities for this operator, thus generalizing some previous results obtained by many researchers.2,8,25,29,30,36
Implementation of quantum and classical discrete fractional Fourier transforms
Weimann, Steffen; Perez-Leija, Armando; Lebugle, Maxime; Keil, Robert; Tichy, Malte; Gräfe, Markus; Heilmann, René; Nolte, Stefan; Moya-Cessa, Hector; Weihs, Gregor; Christodoulides, Demetrios N.; Szameit, Alexander
2016-01-01
Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools. PMID:27006089
Implementation of quantum and classical discrete fractional Fourier transforms.
Weimann, Steffen; Perez-Leija, Armando; Lebugle, Maxime; Keil, Robert; Tichy, Malte; Gräfe, Markus; Heilmann, René; Nolte, Stefan; Moya-Cessa, Hector; Weihs, Gregor; Christodoulides, Demetrios N; Szameit, Alexander
2016-03-23
Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools.
Outline of a theory of the two-dimensional hall effect in the quantum limit
Energy Technology Data Exchange (ETDEWEB)
Tosatti, E. (Scuola Internazionale Superiore di Studi Avanzati, Trieste (Italy); International Centre for Theoretical Physics, Trieste (Italy); Consiglio Nazionale delle Ricerche, Trieste (Italy). Gruppo Nazionale di Struttura della Materia); Parrinello, M. (International Centre for Theoretical Physics, Trieste (Italy); Scuola Internazionale Superiore di Studi Avanzati, Trieste (Italy); Consiglio Nazionale delle Ricerche, Trieste (Italy). Gruppo Nazionale di Struttura della Materia)
1983-03-05
The ground state of two-dimensional electrons of density N/L/sup 2/ in a strong transverse magnetic field B is discussed in terms of localized magnetic functions. For all ''commensurate'' fractional fillings of the n=0 Landau level, occurring at Bsub(st)=(s/sup 2/+t/sup 2/+st)2..pi..(h/2..pi..)cN/eL/sup 2/, with s, t integers, it is found that the ground state is a triangular lattice. This lattice has unusual properties, because it is tied to the magnetic functions. In particular, it has a finite Hall conductivity sigmasub(xy)=e/sup 2//2..pi..(h/2..pi..)(s/sup 2/+t/sup 2/+st) and it also exhibits perfect diamagnetism relative to Bsub(st). It does, however, display no proper Meissner effect, because the London depth is macroscopically large. The excess field B-Bsub(st) gives rise instead to defects in the lattice, where the extra electrons (holes) become ''interstitials'' (''vacancies''). If the defects are free to move, the Hall conductivity will not stay quantized. On the other hand, if all defects are pinned by inhomogeneities, Hall plateaux are expected around each Bsub(st). This picture, while providing a natural explanation for the quantized Hall effect at both integer and fractional filling, leads to a simple understanding of the plateau width vs. temperature and simple quality, and can also explain, at finite temperatures, the behaviour of the longitudinal conductivity sigmasub(yy) and its observed asymmetry for integer filling.
Fractional Quantum Field Theory: From Lattice to Continuum
Directory of Open Access Journals (Sweden)
Vasily E. Tarasov
2014-01-01
Full Text Available An approach to formulate fractional field theories on unbounded lattice space-time is suggested. A fractional-order analog of the lattice quantum field theories is considered. Lattice analogs of the fractional-order 4-dimensional differential operators are proposed. We prove that continuum limit of the suggested lattice field theory gives a fractional field theory for the continuum 4-dimensional space-time. The fractional field equations, which are derived from equations for lattice space-time with long-range properties of power-law type, contain the Riesz type derivatives on noninteger orders with respect to space-time coordinates.
Realization of the Axion Insulator State in Quantum Anomalous Hall Sandwich Heterostructures
Xiao, Di; Jiang, Jue; Shin, Jae-Ho; Wang, Wenbo; Wang, Fei; Zhao, Yi-Fan; Liu, Chaoxing; Wu, Weida; Chan, Moses H. W.; Samarth, Nitin; Chang, Cui-Zu
2018-02-01
The "magnetoelectric effect" arises from the coupling between magnetic and electric properties in materials. The Z2 invariant of topological insulators (TIs) leads to a quantized version of this phenomenon, known as the topological magnetoelectric (TME) effect. This effect can be realized in a new topological phase called an "axion insulator" whose surface states are all gapped but the interior still obeys time reversal symmetry. We demonstrate such a phase using electrical transport measurements in a quantum anomalous Hall (QAH) sandwich heterostructure, in which two compositionally different magnetic TI layers are separated by an undoped TI layer. Magnetic force microscopy images of the same sample reveal sequential magnetization reversals of the top and bottom layers at different coercive fields, a consequence of the weak interlayer exchange coupling due to the spacer. When the magnetization is antiparallel, both the Hall resistance and Hall conductance show zero plateaus, accompanied by a large longitudinal resistance and vanishing longitudinal conductance, indicating the realization of an axion insulator state. Our findings thus show evidence for a phase of matter distinct from the established QAH state and provide a promising platform for the realization of the TME effect.
Quantum phase transitions and anomalous Hall effect in a pyrochlore Kondo lattice
Grefe, Sarah; Ding, Wenxin; Si, Qimiao
The metallic variant of the pyrochlore iridates Pr2Ir2O7 has shown characteristics of a possible chiral spin liquid state [PRL 96 087204 (2006), PRL 98, 057203 (2007), Nature 463, 210 (2010)] and quantum criticality [Nat. Mater. 13, 356 (2014)]. An important question surrounding the significant anomalous Hall response observed in Pr2Ir2O7 is the nature of the f-electron local moments, including their Kondo coupling with the conduction d-electrons. The heavy effective mass and related thermodynamic characteristics indicate the involvement of the Kondo effect in this system's electronic properties. In this work, we study the effects of Kondo coupling on candidate time-reversal-symmetry-breaking spin liquid states on the pyrochlore lattice. Representing the f-moments as slave fermions Kondo-coupled to conduction electrons, we study the competition between Kondo-singlet formation and chiral spin correlations and determine the zero-temperature phase diagram. We derive an effective chiral interaction between the local moments and the conduction electrons and calculate the anomalous Hall response across the quantum phase transition from the Kondo destroyed phase to the Kondo screened phase. We discuss our results' implications for Pr2Ir2O7 and related frustrated Kondo-lattice systems.
Quantum phase transitions and anomalous Hall effect in frustrated Kondo lattices
Paschen, Silke; Grefe, Sarah Elaine; Ding, Wenxin; Si, Qimiao
Among the pyrochlore iridates, the metallic compound Pr2 Ir2O7 (Pr-227) has shown characteristics of a possible chiral spin liquid state and quantum criticality. An important question surrounding the significant anomalous Hall response observed in Pr-227 is the nature of the f-electron local moments, including their Kondo coupling with the conduction d-electrons. The heavy effective mass and related thermodynamic characteristics indicate the involvement of the Kondo effect in this system's electronic properties. In this work, we study the effects of Kondo coupling on candidate time-reversal-symmetry-breaking spin liquid states on frustrated lattices. Representing the f-moments as slave fermions Kondo-coupled to conduction electrons, we study the competition between Kondo-singlet formation and chiral spin correlations. We derive an effective chiral interaction between the local moments and the conduction electrons and calculate the anomalous Hall response across the quantum phase transition from the Kondo destroyed phase to the Kondo screened phase. We discuss our results' implications for Pr-227 and related frustrated Kondo-lattice systems.
Quantum Hall resistance standard in graphene devices under relaxed experimental conditions
Schopfer, F.; Ribeiro-Palau, R.; Lafont, F.; Brun-Picard, J.; Kazazis, D.; Michon, A.; Cheynis, F.; Couturaud, O.; Consejo, C.; Jouault, B.; Poirier, W.
Large-area and high-quality graphene devices synthesized by CVD on SiC are used to develop reliable electrical resistance standards, based on the quantum Hall effect (QHE), with state-of-the-art accuracy of 1x10-9 and under an extended range of experimental conditions of magnetic field (down to 3.5 T), temperature (up to 10 K) or current (up to 0.5 mA). These conditions are much relaxed as compared to what is required by GaAs/AlGaAs standards and will enable to broaden the use of the primary quantum electrical standards to the benefit of Science and Industry for electrical measurements. Furthermore, by comparison of these graphene devices with GaAs/AlGaAs standards, we demonstrate the universality of the QHE within an ultimate uncertainty of 8.2x10-11. This suggests the exact relation of the quantized Hall resistance with the Planck constant and the electron charge, which is crucial for the new SI to be based on fixing such fundamental constants. These results show that graphene realizes its promises and demonstrates its superiority over other materials for a demanding application. Nature Nanotech. 10, 965-971, 2015, Nature Commun. 6, 6806, 2015
Non-commutative algebra of functions of 4-dimensional quantum Hall droplet
International Nuclear Information System (INIS)
Chen Yixin; Hou Boyu; Hou Boyuan
2002-01-01
We develop the description of non-commutative geometry of the 4-dimensional quantum Hall fluid's theory proposed recently by Zhang and Hu. The non-commutative structure of fuzzy S 4 , which is the base of the bundle S 7 obtained by the second Hopf fibration, i.e., S 7 /S 3 =S 4 , appears naturally in this theory. The fuzzy monopole harmonics, which are the essential elements in the non-commutative algebra of functions on S 4 , are explicitly constructed and their obeying the matrix algebra is obtained. This matrix algebra is associative. We also propose a fusion scheme of the fuzzy monopole harmonics of the coupling system from those of the subsystems, and determine the fusion rule in such fusion scheme. By products, we provide some essential ingredients of the theory of SO(5) angular momentum. In particular, the explicit expression of the coupling coefficients, in the theory of SO(5) angular momentum, are given. We also discuss some possible applications of our results to the 4-dimensional quantum Hall system and the matrix brane construction in M-theory
Quantum mechanics and field theory with fractional spin and statistics
International Nuclear Information System (INIS)
Forte, S.
1992-01-01
Planar systems admit quantum states that are neither bosons nor fermions, i.e., whose angular momentum is neither integer nor half-integer. After a discussion of some examples of familiar models in which fractional spin may arise, the relevant (nonrelativistic) quantum mechanics is developed from first principles. The appropriate generalization of statistics is also discussed. Some physical effects of fractional spin and statistics are worked out explicitly. The group theory underlying relativistic models with fractional spin and statistics is then introduced and applied to relativistic particle mechanics and field theory. Field-theoretical models in 2+1 dimensions are presented which admit solitons that carry fractional statistics, and are discussed in a semiclassical approach, in the functional integral approach, and in the canonical approach. Finally, fundamental field theories whose Fock states carry fractional spin and statistics are discussed
Physcicists rewarded for 'fractional electrons'
Ball, P
1998-01-01
The 1998 Nobel prize for physics has been awarded to Horst Stormer, Daniel Tsui and Robert Laughlin.Stormer and Tsui were the first to observe the fractional quantum Hall effect and Laughlin provided the theory shortly afterwards (1 page).
Analogous behavior in the quantum hall effect, anyon superconductivity, and the standard model
International Nuclear Information System (INIS)
Laughlin, R.B.
1991-07-01
Similarities between physical behavior known to occur, or suspected of occurring, in simple condensed matter systems and behavior postulated by the standard model are identified and discussed. Particular emphasis is given to quantum number fractionalization, spontaneous occurrence of gauge forces, spontaneous violation of P and T, and anomaly cancellation. 46 refs
International Nuclear Information System (INIS)
Chandelier, F.
2003-12-01
The quantum Hall effect appears in low temperature electron systems submitted to intense magnetic fields. Electrons are trapped in a thin layer (∼ 100.10 -8 cm thick) at the interface between 2 semiconductors or between a semiconductor and an insulating material. This thesis presents 3 personal contributions to the physics of plane systems and particularly to quantum Hall effect systems. The first contribution is a topological approach, it involves the study of Landau's problem in a geometry nearing that of Hall effect experiments. A mathematical formalism has been defined and by using the Kubo's formula, the quantification of the Hall conductivity can be linked to the Chern class of threaded holes. The second contribution represents a phenomenological approach based on dual symmetries and particularly on modular symmetries. This contribution uses visibility diagrams that have already produced right predictions concerning resistivity curves or band structures. The introduction of a physical equivalence has allowed us to build a phase diagram for the quantum Hall effect at zero temperature. This phase diagram agrees with the experimental facts concerning : -) the existence of 2 insulating phases, -) direct transitions between an insulating phase and any Hall phase through integer or fractionary values of the filling factor (ν), -) selection rules, and -) classification of the Hall states and their distribution around a metal state. The third contribution concerns another phenomenological approach based on duality symmetries. We have considered a class of (2+1)-dimensional effective models with a Maxwell-Chern-Simons part that includes a non-locality. This non-locality implies the existence of a hidden duality symmetry with a Z 2 component: z → 1/z. This symmetry has allowed us to meet the results of the Fisher's law concerning the components of the resistivity tensor. (A.C.)
Fractional quantum mechanics on networks: Long-range dynamics and quantum transport.
Riascos, A P; Mateos, José L
2015-11-01
In this paper we study the quantum transport on networks with a temporal evolution governed by the fractional Schrödinger equation. We generalize the dynamics based on continuous-time quantum walks, with transitions to nearest neighbors on the network, to the fractional case that allows long-range displacements. By using the fractional Laplacian matrix of a network, we establish a formalism that combines a long-range dynamics with the quantum superposition of states; this general approach applies to any type of connected undirected networks, including regular, random, and complex networks, and can be implemented from the spectral properties of the Laplacian matrix. We study the fractional dynamics and its capacity to explore the network by means of the transition probability, the average probability of return, and global quantities that characterize the efficiency of this quantum process. As a particular case, we explore analytically these quantities for circulant networks such as rings, interacting cycles, and complete graphs.
Electronic transport in the quantum spin Hall state due to the presence of adatoms in graphene
Lima, Leandro; Lewenkopf, Caio
Heavy adatoms, even at low concentrations, are predicted to turn a graphene sheet into a topological insulator with substantial gap. The adatoms mediate the spin-orbit coupling that is fundamental to the quantum spin Hall effect. The adatoms act as local spin-orbit scatterer inducing hopping processes between distant carbon atoms giving origin to transverse spin currents. Although there are effective models that describe spectral properties of such systems with great detail, quantitative theoretical work for the transport counterpart is still lacking. We developed a multiprobe recursive Green's function technique with spin resolution to analyze the transport properties for large geometries. We use an effective tight-binding Hamiltonian to describe the problem of adatoms randomly placed at the center of the honeycomb hexagons, which is the case for most transition metals. Our choice of current and voltage probes is favorable to experiments since it filters the contribution of only one spin orientation, leading to a quantized spin Hall conductance of e2 / h . We also discuss the electronic propagation in the system by imaging the local density of states and the electronic current densities. The authors acknowledge the Brazilian agencies CNPq, CAPES, FAPERJ and INCT de Nanoestruturas de Carbono for financial support.
Investigation of Supercurrent in the Quantum Hall Regime in Graphene Josephson Junctions
Draelos, Anne W.; Wei, Ming Tso; Seredinski, Andrew; Ke, Chung Ting; Mehta, Yash; Chamberlain, Russell; Watanabe, Kenji; Taniguchi, Takashi; Yamamoto, Michihisa; Tarucha, Seigo; Borzenets, Ivan V.; Amet, François; Finkelstein, Gleb
2018-06-01
In this study, we examine multiple encapsulated graphene Josephson junctions to determine which mechanisms may be responsible for the supercurrent observed in the quantum Hall (QH) regime. Rectangular junctions with various widths and lengths were studied to identify which parameters affect the occurrence of QH supercurrent. We also studied additional samples where the graphene region is extended beyond the contacts on one side, making that edge of the mesa significantly longer than the opposite edge. This is done in order to distinguish two potential mechanisms: (a) supercurrents independently flowing along both non-contacted edges of graphene mesa, and (b) opposite sides of the mesa being coupled by hybrid electron-hole modes flowing along the superconductor/graphene boundary. The supercurrent appears suppressed in extended junctions, suggesting the latter mechanism.
Anderson Localization from the Berry-Curvature Interchange in Quantum Anomalous Hall Systems
Han, Yulei; Qiao, Zhenhua
In this talk, we theoretically investigate the localization mechanism of the quantum anomalous Hall effect (QAHE) in the presence of spin-flip disorders. We show that the QAHE stays quantized at weak disorders, then enters a Berry-curvature mediated metallic phase at moderate disorders, and finally goes into the Anderson insulating phase at strong disorders. From the phase diagram, we find that at the charge neutrality point although the QAHE is most robust against disorders, the corresponding metallic phase is much easier to be localized into the Anderson insulating phase due to the interchange of Berry curvatures carried, respectively, by the conduction and valence bands. In the end, we provide a phenomenological picture related to the topological charges to better understand the underlying physical origin of the QAHE Anderson localization.
Quantum anomalous Hall phase in a one-dimensional optical lattice
Liu, Sheng; Shao, L. B.; Hou, Qi-Zhe; Xue, Zheng-Yuan
2018-03-01
We propose to simulate and detect quantum anomalous Hall phase with ultracold atoms in a one-dimensional optical lattice, with the other synthetic dimension being realized by modulating spin-orbit coupling. We show that the system manifests a topologically nontrivial phase with two chiral edge states which can be readily detected in this synthetic two-dimensional system. Moreover, it is interesting that at the phase transition point there is a flat energy band and this system can also be in a topologically nontrivial phase with two Fermi zero modes existing at the boundaries by considering the synthetic dimension as a modulated parameter. We also show how to measure these topological phases experimentally in ultracold atoms. Another model with a random Rashba and Dresselhaus spin-orbit coupling strength is also found to exhibit topological nontrivial phase, and the impact of the disorder to the system is revealed.
Interactions, Disorder and Dephasing in Superconducting Films and Quantum Hall Systems
International Nuclear Information System (INIS)
Auerbach, A.
1999-01-01
It is shown that a large class of two dimensional Superconductor to Insulator (SC-I), and (Quantum Hall to Insulator (QH-I) transitions can be understood by assuming that the thermodynamic transition in the clean system is first order. The finite correlation lengths at that transition yield a natural separation of the disorder into short and long wavelengths which are then straightforward to incorporate perturbatively and semi classically respectively. This approach reduces problems of disorder+interactions to puddle network models, whose studies have already yielded insight into experiments of QH-I and SC-I. For the CQH-I, the difference between Landauer-Buttiker and Boltzman theories highlights effects of dephasing
Quantum Hall Effect and Semimetallic Behavior of Dual-Gated ABA-Stacked Trilayer Graphene
Directory of Open Access Journals (Sweden)
E. A. Henriksen
2012-01-01
Full Text Available The electronic structure of multilayer graphenes depends strongly on the number of layers as well as the stacking order. Here we explore the electronic transport of purely ABA-stacked trilayer graphenes in a dual-gated field-effect device configuration. We find both that the zero-magnetic-field transport and the quantum Hall effect at high magnetic fields are distinctly different from the monolayer and bilayer graphenes, and that they show electron-hole asymmetries that are strongly suggestive of a semimetallic band overlap. When the ABA trilayers are subjected to an electric field perpendicular to the sheet, Landau-level splittings due to a lifting of the valley degeneracy are clearly observed.
Xu, Yong; Uddin, Salah; Wang, Jun; Wu, Jiansheng; Liu, Jun-Feng
2017-08-08
We have studied numerically the penetration depth of quantum spin hall edge states in chiral honeycomb nanoribbons based on the Green's function method. The changing of edge orientation from armchair to zigzag direction decreases the penetration depth drastically. The penetration depth is used to estimate the gap opened for the finite-size effect. Beside this, we also proposed a nonlocal transistor based on the zigzag-like chiral ribbons in which the current is carried at one edge and the manipulation is by the edge magnetization at the other edge. The difficulty that the edge magnetization is unstable in the presence of a ballistic current can be removed by this nonlocal manipulation.
Mandal, Sudhansu S.; Mukherjee, Sutirtha; Ray, Koushik
2018-03-01
A method for determining the ground state of a planar interacting many-electron system in a magnetic field perpendicular to the plane is described. The ground state wave-function is expressed as a linear combination of a set of basis functions. Given only the flux and the number of electrons describing an incompressible state, we use the combinatorics of partitioning the flux among the electrons to derive the basis wave-functions as linear combinations of Schur polynomials. The procedure ensures that the basis wave-functions form representations of the angular momentum algebra. We exemplify the method by deriving the basis functions for the 5/2 quantum Hall state with a few particles. We find that one of the basis functions is precisely the Moore-Read Pfaffian wave function.
Wave Function and Emergent SU(2) Symmetry in the ν_{T}=1 Quantum Hall Bilayer.
Lian, Biao; Zhang, Shou-Cheng
2018-02-16
We propose a trial wave function for the quantum Hall bilayer system of total filling factor ν_{T}=1 at a layer distance d to magnetic length ℓ ratio d/ℓ=κ_{c1}≈1.1, where the lowest charged excitation is known to have a level crossing. The wave function has two-particle correlations, which fit well with those in previous numerical studies, and can be viewed as a Bose-Einstein condensate of free excitons formed by composite bosons and anticomposite bosons in different layers. We show the free nature of these excitons indicating an emergent SU(2) symmetry for the composite bosons at d/ℓ=κ_{c1}, which leads to the level crossing in low-lying charged excitations. We further show the overlap between the trial wave function, and the ground state of a small size exact diagonalization is peaked near d/ℓ=κ_{c1}, which supports our theory.
Terahertz spectroscopy on Faraday and Kerr rotations in a quantum anomalous Hall state.
Okada, Ken N; Takahashi, Youtarou; Mogi, Masataka; Yoshimi, Ryutaro; Tsukazaki, Atsushi; Takahashi, Kei S; Ogawa, Naoki; Kawasaki, Masashi; Tokura, Yoshinori
2016-07-20
Electrodynamic responses from three-dimensional topological insulators are characterized by the universal magnetoelectric term constituent of the Lagrangian formalism. The quantized magnetoelectric coupling, which is generally referred to as topological magnetoelectric effect, has been predicted to induce exotic phenomena including the universal low-energy magneto-optical effects. Here we report the experimental indication of the topological magnetoelectric effect, which is exemplified by magneto-optical Faraday and Kerr rotations in the quantum anomalous Hall states of magnetic topological insulator surfaces by terahertz magneto-optics. The universal relation composed of the observed Faraday and Kerr rotation angles but not of any material parameters (for example, dielectric constant and magnetic susceptibility) well exhibits the trajectory towards the fine structure constant in the quantized limit.
Fractional decay of quantum dots in real photonic crystals
DEFF Research Database (Denmark)
Kristensen, Philip Trøst; Koenderink, A. Femius; Lodahl, Peter
2008-01-01
We show that fractional decay may be observable in experiments using quantum dots and photonic crystals with parameters that are currently achievable. We focus on the case of inverse opal photonic crystals and locate the position in the crystal where the effect is most pronounced. Furthermore, we...
Quantum mechanics in fractional and other anomalous spacetimes
Calcagni, Gianluca; Nardelli, Giuseppe; Scalisi, Marco
2012-01-01
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the wave-functions minimizing the uncertainty are found. In spite of the
International Nuclear Information System (INIS)
Kjoensberg, H.; Leinaas, J.M.
1999-01-01
We present Monte Carlo studies of charge expectation values and charge fluctuations for quasi-particles in the quantum Hall system. We have studied the Laughlin wave functions for quasi-hole and quasi-electron, and also Jain's definition of the quasi-electron wave function. The considered systems consist of from 50 to 200 electrons, and the filling fraction is 1/3. For all quasi-particles our calculations reproduce well the expected values of charge; ((-1)/(3)) times the electron charge for the quasi-hole, and 1/3 for the quasi-electron. Regarding fluctuations in the charge, our results for the quasi-hole and Jain quasi-electron are consistent with the expected value zero in the bulk of the system, but for the Laughlin quasi-electron we find small, but significant, deviations from zero throughout the whole electron droplet. We also present Berry phase calculations of charge and statistics parameter for the Jain quasi-electron, calculations which supplement earlier studies for the Laughlin quasi-particles. We find that the statistics parameter, calculated as a function of distance, is more well behaved for the Jain quasi-electron than it is for the Laughlin quasi-electron. However, the sign of the parameter is opposite of what is expected from qualitative arguments
Thermal and quantum depinning of a fractional Josephson vortex
Energy Technology Data Exchange (ETDEWEB)
Goldobin, Edward; Gaber, Tobias; Buckenmaier, Kai; Kienzle, Uta; Sickinger, Hanna; Koelle, Dieter; Kleiner, Reinhold [Physikalische Institut, University of Tuebingen, Auf der Morgenstelle 14, 72076 Tuebingen (Germany); Meckbach, Max; Kaiser, Christoph; Il' in, Konstantin; Siegel, Michael [Institut fuer Mikro- und Nanoelektronische Systeme, University of Karlsruhe, Hertzstrasse 16, 76187, Karlsruhe (Germany)
2011-07-01
We investigate the bias current induced depinning of a fractional Josephson vortex in a 0-{kappa} Josephson junction, where the {kappa}-discontinuity of the phase is induced by current injectors. At high temperatures T>or similar 100 mK the depinning is governed by thermal fluctuations. By measuring a depinning current histogram and extracting the effective barrier height vs. {kappa}, one can see the signatures of fractional vortex escape. At low T
Energy Technology Data Exchange (ETDEWEB)
Pokhabov, D. A., E-mail: pokhabov@isp.nsc.ru; Pogosov, A. G.; Budantsev, M. V.; Zhdanov, E. Yu.; Bakarov, A. K. [Russian Academy of Sciences, Rzhanov Institute of Semiconductor Physics, Siberian Branch (Russian Federation)
2016-08-15
The nonequilibrium state of a two-dimensional electron gas in the quantum-Hall-effect regime is studied in Hall bars equipped with additional inner contacts situated within the bar. The magnetic-field dependence of the voltage drop between different contact pairs are studied at various temperatures. It was found that the voltage between the inner and outer contacts exhibits peaks of significant amplitude in narrow magnetic-field intervals near integer filling factors. Furthermore, the magnetic-field dependence of the voltage in these intervals exhibits a hysteresis, whereas the voltage between the outer contacts remains zero in the entire magnetic-field range. The appearance of the observed voltage peaks and their hysteretic behavior can be explained by an imbalance between the chemical potentials of edge and bulk states, resulting from nonequilibrium charge redistribution between the edge and bulk states when the magnetic field sweeps under conditions of the quantum Hall effect. The results of the study significantly complement the conventional picture of the quantum Hall effect, explicitly indicating the existence of a significant imbalance at the edge of the two-dimensional electron gas: the experimentally observed difference between the electrochemical potentials of the edge and bulk exceeds the distance between Landau levels by tens of times.
Quantum Hall effect and anomalous transport in (TMTSF)2PF6
International Nuclear Information System (INIS)
Eom, J.; Cho, H.; Kang, W.; Chicago Univ., IL
1999-01-01
Under low temperatures and high magnetic fields, quasi-one dimensional organic conductor (TMTSFP) 2 PF 6 exhibits a series of transitions to field-induced spin density wave (FISDW). Slightly above the onset of superconductivity in (TMTSF) 2 PF 6 , we observe a series of intervening phases that interrupt the sequence of FISDW that gives rise to the quantum Hall effect. These phases can be identified either as negative quantum numbered FISDW states or a puzzling arboresecent phase. Detailed study of the QHE in (TMTSF) 2 PF 6 reveals that the transport in the FISDW phases is dominated by anomalous longitudinal resistivities ρ xx and ρ yy that remain finite at low temperatures. While the quantization of σ xy is not adversely affected at high magnetic fields, the transport in the intermediate magnetic field remains complicated. In addition, the conductivity along applied magnetic field, σ zz , cannot be easily understood in terms of three-dimensional QHE and is suggestive of the importance of inter-layer coupling. (orig.)
Quantum Hall effect with small numbers of vortices in Bose-Einstein condensates
Byrnes, Tim; Dowling, Jonathan P.
2015-08-01
When vortices are displaced in Bose-Einstein condensates (BECs), the Magnus force gives the system a momentum transverse in the direction to the displacement. We show that BECs in long channels with vortices exhibit a quantization of the current response with respect to the spatial vortex distribution. The quantization originates from the well-known topological property of the phase around a vortex; it is an integer multiple of 2 π . In a way similar to that of the integer quantum Hall effect, the current along the channel is related to this topological phase and can be extracted from two experimentally measurable quantities: the total momentum of the BEC and the spatial distribution. The quantization is in units of m /2 h , where m is the mass of the atoms and h is Planck's constant. We derive an exact vortex momentum-displacement relation for BECs in long channels under general circumstances. Our results present the possibility that the configuration described here can be used as a novel way of measuring the mass of the atoms in the BEC using a topological invariant of the system. If an accurate determination of the plateaus are experimentally possible, this gives the possibility of a topological quantum mass standard and precise determination of the fine structure constant.
Spin valley and giant quantum spin Hall gap of hydrofluorinated bismuth nanosheet.
Gao, Heng; Wu, Wei; Hu, Tao; Stroppa, Alessandro; Wang, Xinran; Wang, Baigeng; Miao, Feng; Ren, Wei
2018-05-09
Spin-valley and electronic band topological properties have been extensively explored in quantum material science, yet their coexistence has rarely been realized in stoichiometric two-dimensional (2D) materials. We theoretically predict the quantum spin Hall effect (QSHE) in the hydrofluorinated bismuth (Bi 2 HF) nanosheet where the hydrogen (H) and fluorine (F) atoms are functionalized on opposite sides of bismuth (Bi) atomic monolayer. Such Bi 2 HF nanosheet is found to be a 2D topological insulator with a giant band gap of 0.97 eV which might host room temperature QSHE. The atomistic structure of Bi 2 HF nanosheet is noncentrosymmetric and the spontaneous polarization arises from the hydrofluorinated morphology. The phonon spectrum and ab initio molecular dynamic (AIMD) calculations reveal that the proposed Bi 2 HF nanosheet is dynamically and thermally stable. The inversion symmetry breaking together with spin-orbit coupling (SOC) leads to the coupling between spin and valley in Bi 2 HF nanosheet. The emerging valley-dependent properties and the interplay between intrinsic dipole and SOC are investigated using first-principles calculations combined with an effective Hamiltonian model. The topological invariant of the Bi 2 HF nanosheet is confirmed by using Wilson loop method and the calculated helical metallic edge states are shown to host QSHE. The Bi 2 HF nanosheet is therefore a promising platform to realize room temperature QSHE and valley spintronics.
International Nuclear Information System (INIS)
Morimoto, Takahiro; Aoki, Hideo; Avishai, Yshai
2011-01-01
Dynamical scaling of the optical Hall conductivity σ xy (ε F , ω) at the n = 0 Landau level in graphene is analyzed for the 2D effective Dirac fermion and honeycomb lattice models with various types of disorder. In the Dirac fermion model with potential disorder, σ xy (ε F , ω) obeys a well-defined dynamical scaling, characterized by the localization exponent ν and the dynamical critical exponent z. In sharp distinction, scaling behavior of σ xy (ε F , ω) in the honeycomb lattice model with bond disorder (preserving chiral symmetry), becomes anomalous.
Fractional scaling of quantum walks on percolation lattices
International Nuclear Information System (INIS)
Kendon, Viv; Knott, Paul; Leung, Godfrey; Bailey, Joe
2011-01-01
Quantum walks can be used to model processes such as transport in spin chains and bio-molecules. The enhanced spreading and mixing properties of quantum walks compared with their classical counterparts have been well-studied on regular structures and also shown to be sensitive to defects and imperfections. Using numerical simulation, we study the spreading properties of quantum walks on percolation lattices for both bond and site percolation. The randomly missing edges or sites provide a controlled amount of disorder in the regular Cartesian lattice. In one dimension (the line) we introduce a simple model of quantum tunneling to allow the walk to proceed past the missing edges or sites. This allows the quantum walk to spread faster than a classical random walk for short times, but at longer times the disorder localises the quantum walk. In two dimensions, we observe fractional scaling of the spreading with the number of steps of the walk. For percolation above the 85% level, we obtain faster spreading than classical random walks on the full lattice.
International Nuclear Information System (INIS)
El-Nabulsi, Ahmad Rami
2009-01-01
Multidimensional fractional actionlike variational problem with time-dependent dynamical fractional exponents is constructed. Fractional Euler-Lagrange equations are derived and discussed in some details. The results obtained are used to explore some novel aspects of fractional quantum field theory where many interesting consequences are revealed, in particular the complexification of quantum field theory, in particular Dirac operators and the novel notion of 'mass without mass'.
Energy Technology Data Exchange (ETDEWEB)
Manger, Matthias
2008-07-01
This thesis is dedicated to the long wavelength collective excitations of quasi two-dimensional electron systems (Q2DEG) in GaAs under the influence of high magnetic fields. These excitations, which are classified into cyclotron resonances and magneto intersubband resonances, were experimentally investigated by means of far infrared Fourier spectroscopy. Cyclotron resonances were studied in a magnetic field range 0Fractional Quantum Hall Effects (FQHE) as well as to the regime of prominent polaron coupling at high temperatures. For the analysis and the interpretation of the experimental data, various theoretical models were presented and applied to the data. The theory took into account the multi-component character of cyclotron resonance in the presence of polaron coupling, bands nonparabolicity, and disorder under the combined influence of electronic screening and electron-electron coupling. The magneto intersubband resonances were investigated in the regime of the Integral Quantum Hall Effect. The grating coupler technique was used in order to couple the electromagnetic field to these collective excitations. Self consistent calculations of the subband structure and the collective modes were performed in the framework of the Hartree-Fock approximation scheme. These calculations were used for an interpretation of the experimental observations. (orig.)
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)
International Nuclear Information System (INIS)
Gvozdikov, V M; Taut, M
2009-01-01
We report on analytical and numerical studies of the magnetic quantum oscillations of the diagonal conductivity σ xx in a two-dimensional conductor with a weak square superlattice modulation under conditions of the integer quantum Hall (IQHE) effect. The quantum Hall effect in such a system differs from the conventional IQHE, in which the finite width of the Landau bands is due to disorder only. The superlattice modulation potential yields a fractal splitting of the Landau levels into Hofstadter minibands. For rational flux through a unit cell, the minibands have a finite width and intrinsic dispersion relations. We consider a regime, now accessible experimentally, in which disorder does not wash out the fractal internal gap structure of the Landau bands completely. We found the following distinctions from the conventional IQHE produced by the superlattice: (i) the peaks in diagonal conductivity are split due to the Hofstadter miniband structure of Landau bands; (ii) the number of split peaks in the bunch, their positions and heights depend irregularly on the magnetic field and the Fermi energy; (iii) the gaps between the split Landau bands (and related quantum Hall plateaus) become narrower with the superlattice modulation than without it.
Frequencies of the Edge-Magnetoplasmon Excitations in Gated Quantum Hall Edges
Endo, Akira; Koike, Keita; Katsumoto, Shingo; Iye, Yasuhiro
2018-06-01
We have investigated microwave transmission through the edge of quantum Hall systems by employing a coplanar waveguide (CPW) fabricated on the surface of a GaAs/AlGaAs two-dimensional electron gas (2DEG) wafer. An edge is introduced to the slot region of the CPW by applying a negative bias Vg to the central electrode (CE) and depleting the 2DEG below the CE. We observe peaks attributable to the excitation of edge magnetoplasmons (EMP) at a fundamental frequency f0 and at its harmonics if0 (i = 2,3, \\ldots ). The frequency f0 increases with decreasing Vg, indicating that EMP propagates with higher velocity for more negative Vg. The dependence of f0 on Vg is interpreted in terms of the variation in the distance between the edge state and the CE, which alters the velocity by varying the capacitive coupling between them. The peaks are observed to continue, albeit with less clarity, up to the regions of Vg where 2DEG still remains below the CE.
Chowdhury, Debanjan; Skinner, Brian; Lee, Patrick A.
2018-05-01
Electron tunneling into a system with strong interactions is known to exhibit an anomaly, in which the tunneling conductance vanishes continuously at low energy due to many-body interactions. Recent measurements have probed this anomaly in a quantum Hall bilayer of the half-filled Landau level, and shown that the anomaly apparently gets stronger as the half-filled Landau level is increasingly spin polarized. Motivated by this result, we construct a semiclassical hydrodynamic theory of the tunneling anomaly in terms of the charge-spreading action associated with tunneling between two copies of the Halperin-Lee-Read state with partial spin polarization. This theory is complementary to our recent work (D. Chowdhury, B. Skinner, and P. A. Lee, arXiv:1709.06091) where the electron spectral function was computed directly using an instanton-based approach. Our results show that the experimental observation cannot be understood within conventional theories of the tunneling anomaly, in which the spreading of the injected charge is driven by the mean-field Coulomb energy. However, we identify a qualitatively new regime, in which the mean-field Coulomb energy is effectively quenched and the tunneling anomaly is dominated by the finite compressibility of the composite Fermion liquid.
Tuning the effects of Landau level mixing on anisotropic transport in quantum Hall systems
International Nuclear Information System (INIS)
Smith, Peter M; Kennett, Malcolm P
2012-01-01
Electron-electron interactions in half-filled high Landau levels in two-dimensional electron gases in a strong perpendicular magnetic field can lead to states with anisotropic longitudinal resistance. This longitudinal resistance is generally believed to arise from broken rotational invariance, which is indicated by charge density wave order in Hartree-Fock calculations. We use the Hartree-Fock approximation to study the influence of externally tuned Landau level mixing on the formation of interaction-induced states that break rotational invariance in two-dimensional electron and hole systems. We focus on the situation when there are two non-interacting states in the vicinity of the Fermi level and construct a Landau theory to study coupled charge density wave order that can occur as interactions are tuned and the filling or mixing are varied. We consider numerically a specific example where mixing is tuned externally through Rashba spin-orbit coupling. We calculate the phase diagram and find the possibility of ordering involving coupled striped or triangular charge density waves in the two levels. Our results may be relevant to recent transport experiments on quantum Hall nematics in which Landau level mixing plays an important role. (paper)
Propagation of superconducting coherence via chiral quantum-Hall edge channels.
Park, Geon-Hyoung; Kim, Minsoo; Watanabe, Kenji; Taniguchi, Takashi; Lee, Hu-Jong
2017-09-08
Recently, there has been significant interest in superconducting coherence via chiral quantum-Hall (QH) edge channels at an interface between a two-dimensional normal conductor and a superconductor (N-S) in a strong transverse magnetic field. In the field range where the superconductivity and the QH state coexist, the coherent confinement of electron- and hole-like quasiparticles by the interplay of Andreev reflection and the QH effect leads to the formation of Andreev edge states (AES) along the N-S interface. Here, we report the electrical conductance characteristics via the AES formed in graphene-superconductor hybrid systems in a three-terminal configuration. This measurement configuration, involving the QH edge states outside a graphene-S interface, allows the detection of the longitudinal and QH conductance separately, excluding the bulk contribution. Convincing evidence for the superconducting coherence and its propagation via the chiral QH edge channels is provided by the conductance enhancement on both the upstream and the downstream sides of the superconducting electrode as well as in bias spectroscopy results below the superconducting critical temperature. Propagation of superconducting coherence via QH edge states was more evident as more edge channels participate in the Andreev process for high filling factors with reduced valley-mixing scattering.
Stacked bilayer phosphorene: strain-induced quantum spin Hall state and optical measurement
Zhang, Tian; Lin, Jia-He; Yu, Yan-Mei; Chen, Xiang-Rong; Liu, Wu-Ming
2015-01-01
Bilayer phosphorene attracted considerable interest, giving a potential application in nanoelectronics owing to its natural bandgap and high carrier mobility. However, very little is known regarding the possible usefulness in spintronics as a quantum spin Hall (QSH) state of material characterized by a bulk energy gap and gapless spin-filtered edge states. Here, we report a strain-induced topological phase transition from normal to QSH state in bilayer phosphorene, accompanied by band-inversion that changes number from 0 to 1, which is highly dependent on interlayer stacking. When the bottom layer is shifted by 1/2 unit-cell along zigzag/armchair direction with respect to the top layer, the maximum topological bandgap 92.5 meV is sufficiently large to realize QSH effect even at room-temperature. An optical measurement of QSH effect is therefore suggested in view of the wide optical absorption spectrum extending to far infra-red, making bilayer phosphorene a promising candidate for opto-spintronic devices. PMID:26370771
Quantum spin Hall effect in IV-VI topological crystalline insulators
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.
Spin Singlet Quantum Hall Effect and nonabelian Landau-Ginzburg theory
International Nuclear Information System (INIS)
Balatsky, A.
1991-01-01
In this paper we present a theory of Singlet Quantum Hall Effect (SQHE). We show that the Halperin-Haldane SQHE wave function can be written in the form of a product of a wave function for charged semions in a magnetic field and a wave function for the Chiral Spin Liquid of neutral spin-1/2 semions. We introduce field-theoretic model in which the electron operators are factorized in terms of charged spinless semions (holons) and neutral spin-1/2 semions (spinons). Broken time reversal symmetry and short ranged spin correlations lead to Su(2) κ=1 Chern-Simons term in Landau-Ginzburg action for SQHE phase. We construct appropriate coherent states for SQHE phase and show the existence of SU(2) valued gauge potential. This potential appears as a result of ''spin rigidity'' of the ground state against any displacements of nodes of wave function from positions of the particles and reflects the nontrivial monodromy in the presence of these displacenmants. We argue that topological structure of Su(2) κ=1 Chern-Simons theory unambiguously dictates semion statistics of spinons. 19 refs
Fundamental relation between longitudinal and transverse conductivities in the quantum Hall system
International Nuclear Information System (INIS)
Endo, Akira; Hatano, Naomichi; Nakamura, Hiroaki; Shirasaki, Ryoen
2009-07-01
We investigate the relation between the diagonal (σ xx ) and off-diagonal (σ xy ) components of the conductivity tensor in the quantum Hall system. We calculate the conductivity components for a short-range impurity potential using the linear response theory, employing an approximation that simply replaces the self-energy by a constant value -iℎ/(2τ) with τ the scattering time. The approximation is equivalent to assuming that the broadening of a Landau level due to disorder is represented by a Lorentzian with the width Γ = ℎ/(2τ). Analytic formulas are obtained for both σ xx and σ xy within the framework of this simple approximation at low temperatures. By examining the leading terms in σ xx and σ xy , we find a proportional relation between dσ xy =dB and Bσ 2 xx . The relation, after slight modification to account for the long-range nature of the impurity potential, is shown to be in quantitative agreement with experimental results obtained in the GaAs/AlGaAs two-dimensional electron system at the low magnetic-field regime where spin splitting is negligibly small. (author)
Thermal and quantum escape of fractional Josephson vortices
Energy Technology Data Exchange (ETDEWEB)
Poehler, Hanna; Kienzle, Uta; Buckenmaier, Kai; Gaber, Tobias; Koelle, Dieter; Kleiner, Reinhold; Goldobin, Edward [Physikalisches Institut, Center for Collective Quantum Phenomena, Universitaet Tuebingen (Germany); Siegel, Michael [Institut fuer Mikro- und Nanoelektronische Systeme, Universitaet Karlsruhe (Germany)
2009-07-01
By using a pair of tiny current injectors one can create an arbitrary {kappa} discontinuity of the phase in a long Josephson junction (LJJ) and a fractional Josephson vortex (FJV), carrying a fraction {phi}/{phi}{sub 0}={kappa}/2{pi}{<=}1 of the magnetic flux quantum {phi}{sub 0}{approx}2.07 .10{sup -15} Wb, which is pinned at the discontinuity. If a bias current I, exceeds the critical value I{sub c}({kappa}), an integer fluxon is torn off the discontinuity and the LJJ switches to the voltage state. Due to thermal or quantum fluctuations this escape event may occur at I
International Nuclear Information System (INIS)
Greiter, M.
1992-01-01
This dissertation contains a collection of individual articles on various topics. Their significance in the corresponding field as well as connections between them are emphasized in a general and comprehensive introduction. In the first article, the author explores the consequences for macroscopic effective Lagrangians of assuming that the momentum density is proportional to the flow of conserved current. The universal corrections obtained for the macroscopic Lagrangian of a superconductor describe the London Hall effect, and provide a fully consistent derivation of it. In the second article, a heuristic principle is proposed for quantized Hall states: the existence and incompressibility of fractionally quantized Hall states is explained by an argument based on an adiabatic localization of magnetic flux, the process of trading uniform flux for an equal amount of fictitious flux attached to the particles. This principle is exactly implemented in the third article. For a certain class of model Hamiltonians, the author obtains Laughlin's Jastrow type wave functions explicitly from a filled Landau level, by smooth extrapolation in quantum statistics. The generalization of this analysis to the torus geometry shows that theorems restricting the possibilities of quantum statistics on closed surfaces are circumvented in the presence of a magnetic field. In the last article, the existence is proposed of a novel incompressible quantum liquid, a paired Hall state, at a half filled Landau level. This state arises adiabatically from free fermions in zero magnetic field, and reduces to a state previously proposed by Halperin in the limit of tightly bound pairs. It supports unusual excitations, including neutral fermions and charge e/4 anyons with statistical parameter θ = π/8
Scaling of anomalous hall effect in amorphous CoFeB Films with accompanying quantum correction
Zhang, Yan; Mi, Wenbo; Wang, Xiaocha; Guo, Zaibing
2015-01-01
Scaling of anomalous Hall effect in amorphous CoFeB films with thickness ranging from 2 to 160 nm have been investigated. We have found that the scaling relationship between longitudinal (ρxx) and anomalous Hall (ρAH) resistivity is distinctly
Strong Bulk-Edge Coupling in the Compressible Half-Filled Quantum Hall State
International Nuclear Information System (INIS)
Milovanovic, M.V.; Shimshoni, E.
1999-01-01
We studied analytically static correlators in the compressible half-filled quantum Hall state, which characterize the nature of charged excitations in the bulk and on the edge of the system. We employ a modified version of the plasma analogy - namely, a mapping to a classical two-dimensional system of interacting particles - similarly to what has been done in studies of the incompressible (Laughlin) states. However, the 'fake plasma' corresponding to the half-filled state is found to have anomalously weak screening properties. As a consequence, the correlations along the edge do not decay algebraically as in the incompressible case, thus indicating the breakdown of Wen's edge theory. On the other hand, the bulk correlator (which parallels the Girvin-MacDonald algebraic off-diagonal long range order) decays algebraically in a similar way as in the incompressible states, signifying the presence of some kind of bosonic order even in the compressible state. The above results suggest that due to the strong coupling between charged modes on the edge and the neutral Fermions (dipoles) in the bulk, the (attractive) correlation hole is not well defined on the edge. Hence, the system there can be modeled as a free Fermi gas of electrons (with an appropriate boundary condition). A possible experimental indication of a strong bulk-edge coupling at half-filling has been indeed observed in non-local resistance measurements [1]. We also suggest, that while our results contradict the validity of an effective one-dimensional description of the edge excitations on the static level, the dynamics may decouple the edge and bulk so as to recover the Laughlin-like behavior apparent in the experiment of Grayson et al
Comment on "Fractional quantum mechanics" and "Fractional Schrödinger equation".
Wei, Yuchuan
2016-06-01
In this Comment we point out some shortcomings in two papers [N. Laskin, Phys. Rev. E 62, 3135 (2000)10.1103/PhysRevE.62.3135; N. Laskin, Phys. Rev. E 66, 056108 (2002)10.1103/PhysRevE.66.056108]. We prove that the fractional uncertainty relation does not hold generally. The probability continuity equation in fractional quantum mechanics has a missing source term, which leads to particle teleportation, i.e., a particle can teleport from a place to another. Since the relativistic kinetic energy can be viewed as an approximate realization of the fractional kinetic energy, the particle teleportation should be an observable relativistic effect in quantum mechanics. With the help of this concept, superconductivity could be viewed as the teleportation of electrons from one side of a superconductor to another and superfluidity could be viewed as the teleportation of helium atoms from one end of a capillary tube to the other. We also point out how to teleport a particle to an arbitrary destination.
Directory of Open Access Journals (Sweden)
Manik Goyal
2018-02-01
Full Text Available Low-temperature magnetotransport studies are reported for (112Cd3As2 films grown on (111CdTe by molecular beam epitaxy as a function of the Cd3As2 film thickness. All films show Shubnikov-de Haas oscillations. An even-integer quantum Hall effect is observed for films thinner than 70 nm. For the thinnest films, the bulk is gapped and transport at low temperatures occurs only via the gapless, two-dimensional states. The lowest Landau level is reached at ∼10 T, and the longitudinal resistance nearly vanishes at the plateaus in the Hall resistance. The results are discussed in the context of the current theoretical understanding of topological surface states in three-dimensional Dirac semimetals.
International Nuclear Information System (INIS)
Wang Bo; Ma Zhongshui; Zhang, C
2012-01-01
We demonstrate that the trigonal warping observed in bilayer graphene is doubled in the presence of Rashba spin-orbit (RSO) coupling, i.e. the Dirac points along the three-fold symmetry axis are doubled. There are now seven Dirac points. Furthermore, the RSO interaction breaks the electron-hole symmetry of the magnetic band structure. The most intriguing feature is that the step of the quantum Hall plateau at zero energy is four times that at finite energy. The number of Dirac points and the zero energy Hall step are only determined by the existence of RSO coupling, but are independent of the strength of the coupling. The robustness of these phenomena suggests equivalence between the RSO coupling and the topological effect in bilayer coupling.
International Nuclear Information System (INIS)
Li Juan; Wang Yifei; Gong Changde
2011-01-01
We consider the tight-binding models of electrons on a two-dimensional triangular lattice and kagome lattice under staggered modulated magnetic fields. Such fields have two components: a uniform-flux part with strength φ, and a staggered-flux part with strength Δφ. Various properties of the Hall conductances and Hofstadter butterflies are studied. When φ is fixed, variation of Δφ leads to the quantum Hall transitions and Chern numbers of Landau subbands being redistributed between neighboring pairs. The energy spectra with nonzero Δφs have similar fractal structures but quite different energy gaps compared with the original Hofstadter butterflies of Δφ = 0. Moreover, the fan-like structure of Landau levels in the low magnetic field region is also modified appreciably by Δφ.
Energy Technology Data Exchange (ETDEWEB)
Li Juan; Wang Yifei; Gong Changde, E-mail: yfwang_nju@hotmail.com [Center for Statistical and Theoretical Condensed Matter Physics, and Department of Physics, Zhejiang Normal University, Jinhua 321004 (China)
2011-04-20
We consider the tight-binding models of electrons on a two-dimensional triangular lattice and kagome lattice under staggered modulated magnetic fields. Such fields have two components: a uniform-flux part with strength {phi}, and a staggered-flux part with strength {Delta}{phi}. Various properties of the Hall conductances and Hofstadter butterflies are studied. When {phi} is fixed, variation of {Delta}{phi} leads to the quantum Hall transitions and Chern numbers of Landau subbands being redistributed between neighboring pairs. The energy spectra with nonzero {Delta}{phi}s have similar fractal structures but quite different energy gaps compared with the original Hofstadter butterflies of {Delta}{phi} = 0. Moreover, the fan-like structure of Landau levels in the low magnetic field region is also modified appreciably by {Delta}{phi}.
International Nuclear Information System (INIS)
Saminadayar, L.
2001-01-01
20 years ago fractional charges were imagined to explain values of conductivity in some materials. Recent experiments have proved the existence of charges whose value is the third of the electron charge. This article presents the experimental facts that have led theorists to predict the existence of fractional charges from the motion of quasi-particles in a linear chain of poly-acetylene to the quantum Hall effect. According to the latest theories, fractional charges are neither bosons nor fermions but anyons, they are submitted to an exclusive principle that is less stringent than that for fermions. (A.C.)
Boundary maps for C*-crossed products with R with an application to the quantum Hall effect
Kellendonk, J
2003-01-01
The boundary map in K-theory arising from the Wiener-Hopf extension of a crossed product algebra with $\\RR$ is the Connes-Thom isomorphism. In this article, the Wiener Hopf extension is combined with the Heisenberg group algebra to provide an elementary construction of a corresponding map in cyclic cohomology. It then follows directly from a non-commutative Stokes theorem that this map is dual w.r.t. Connes' pairing of cyclic cohomology with K-theory. As an application, we prove equality of quantized bulk and edge conductivities for the integer quantum Hall effect described by continuous magnetic Schrödinger operators.
Real-space mapping of a disordered two-dimensional electron system in the quantum Hall regime
International Nuclear Information System (INIS)
Hashimoto, K; Hirayama, Y; Wiebe, J; Wiesendanger, R; Inaoka, T; Morgenstern, M
2011-01-01
By using scanning tunnelling spectroscopy, we study the influence of potential disorder on an adsorbate-induced two-dimensional electron system in the integer quantum Hall regime. The real-space imaged local density of states exhibits transition from localized drift states encircling the potential minima to another type of localized drift states encircling the potential maxima. While the former states show regular round shapes, the latter have irregular-shaped patterns. This difference is induced by different sources for the potential minima and maxima, i.e., substrate donors and an inhomogeneous distribution of the adsorbates, respectively.
The Two-Dimensional MnO2/Graphene Interface: Half-metallicity and Quantum Anomalous Hall State
Gan, Liyong
2015-10-07
We explore the electronic properties of the MnO2/graphene interface by first-principles calculations, showing that MnO2 becomes half-metallic. MnO2 in the MnO2/graphene/MnO2 system provides time-reversal and inversion symmetry breaking. Spin splitting by proximity occurs at the Dirac points and a topologically nontrivial band gap is opened, enabling a quantum anomalous Hall state. The half-metallicity, spin splitting, and size of the band gap depend on the interfacial interaction, which can be tuned by strain engineering.
The Two-Dimensional MnO2/Graphene Interface: Half-metallicity and Quantum Anomalous Hall State
Gan, Liyong; Zhang, Qingyun; Guo, Chun-Sheng; Schwingenschlö gl, Udo; Zhao, Yong
2015-01-01
We explore the electronic properties of the MnO2/graphene interface by first-principles calculations, showing that MnO2 becomes half-metallic. MnO2 in the MnO2/graphene/MnO2 system provides time-reversal and inversion symmetry breaking. Spin splitting by proximity occurs at the Dirac points and a topologically nontrivial band gap is opened, enabling a quantum anomalous Hall state. The half-metallicity, spin splitting, and size of the band gap depend on the interfacial interaction, which can be tuned by strain engineering.
International Nuclear Information System (INIS)
Dong, Jianping
2011-01-01
The many-body space fractional quantum system is studied using the density matrix method. We give the new results of the Thomas-Fermi model, obtain the quantum pressure of the free electron gas. We also show the validity of the Hohenberg-Kohn theorems in the space fractional quantum mechanics and generalize the density functional theory to the fractional quantum mechanics. -- Highlights: → Thomas-Fermi model under the framework of fractional quantum mechanics is studied. → We show the validity of the HK theorems in the space fractional quantum mechanics. → The density functional theory is generalized to the fractional quantum mechanics.
Exotic quantum order in low-dimensional systems
Girvin, S. M.
1998-08-01
Strongly correlated quantum systems in low dimensions often exhibit novel quantum ordering. This ordering is sometimes hidden and can be revealed only by examining new "dual" types of correlations. Such ordering leads to novel collection modes and fractional quantum numbers. Examples will be presented from quantum spin chains and the quantum Hall effect.
Surface and 3D Quantum Hall Effects from Engineering of Exceptional Points in Nodal-Line Semimetals
Molina, Rafael A.; González, José
2018-04-01
We show that, under a strong magnetic field, a 3D nodal-line semimetal is driven into a topological insulating phase in which the electronic transport takes place at the surface of the material. When the magnetic field is perpendicular to the nodal ring, the surface states of the semimetal are transmuted into Landau states which correspond to exceptional points, i.e., branch points in the spectrum of a non-Hermitian Hamiltonian which arise upon the extension to complex values of the momentum. The complex structure of the spectrum then allows us to express the number of zero-energy flat bands in terms of a new topological invariant counting the number of exceptional points. When the magnetic field is parallel to the nodal ring, we find that the bulk states are built from the pairing of surfacelike evanescent waves, giving rise to a 3D quantum Hall effect with a flat level of Landau states residing in parallel 2D slices of the 3D material. The Hall conductance is quantized in either case in units of e2/h , leading in the 3D Hall effect to a number of channels growing linearly with the section of the surface and opening the possibility to observe a macroscopic chiral current at the surface of the material.
Quantum Hall effect on top and bottom surface states of topological insulator (Bi1-xSbx)2Te3 films.
Yoshimi, R; Tsukazaki, A; Kozuka, Y; Falson, J; Takahashi, K S; Checkelsky, J G; Nagaosa, N; Kawasaki, M; Tokura, Y
2015-04-14
The three-dimensional topological insulator is a novel state of matter characterized by two-dimensional metallic Dirac states on its surface. To verify the topological nature of the surface states, Bi-based chalcogenides such as Bi2Se3, Bi2Te3, Sb2Te3 and their combined/mixed compounds have been intensively studied. Here, we report the realization of the quantum Hall effect on the surface Dirac states in (Bi1-xSbx)2Te3 films. With electrostatic gate-tuning of the Fermi level in the bulk band gap under magnetic fields, the quantum Hall states with filling factor ±1 are resolved. Furthermore, the appearance of a quantum Hall plateau at filling factor zero reflects a pseudo-spin Hall insulator state when the Fermi level is tuned in between the energy levels of the non-degenerate top and bottom surface Dirac points. The observation of the quantum Hall effect in three-dimensional topological insulator films may pave a way toward topological insulator-based electronics.
Anomalous Hall effect in semiconductor quantum wells in proximity to chiral p -wave superconductors
Yang, F.; Yu, T.; Wu, M. W.
2018-05-01
By using the gauge-invariant optical Bloch equation, we perform a microscopic kinetic investigation on the anomalous Hall effect in chiral p -wave superconducting states. Specifically, the intrinsic anomalous Hall conductivity in the absence of the magnetic field is zero as a consequence of Galilean invariance in our description. As for the extrinsic channel, a finite anomalous Hall current is obtained from the impurity scattering with the optically excited normal quasiparticle current even at zero temperature. From our kinetic description, it can be clearly seen that the excited normal quasiparticle current is due to an induced center-of-mass momentum of Cooper pairs through the acceleration driven by ac electric field. For the induced anomalous Hall current, we show that the conventional skew-scattering channel in the linear response makes the dominant contribution in the strong impurity interaction. In this case, our kinetic description as a supplementary viewpoint mostly confirms the results of Kubo formalism in the literature. Nevertheless, in the weak impurity interaction, this skew-scattering channel becomes marginal and we reveal that an induction channel from the Born contribution dominates the anomalous Hall current. This channel, which has long been overlooked in the literature, is due to the particle-hole asymmetry by nonlinear optical excitation. Finally, we study the case in the chiral p -wave superconducting state with a transverse conical magnetization, which breaks the Galilean invariance. In this situation, the intrinsic anomalous Hall conductivity is no longer zero. Comparison of this intrinsic channel with the extrinsic one from impurity scattering is addressed.
Directory of Open Access Journals (Sweden)
Yu Huang
Full Text Available Parameter estimation for fractional-order chaotic systems is an important issue in fractional-order chaotic control and synchronization and could be essentially formulated as a multidimensional optimization problem. A novel algorithm called quantum parallel particle swarm optimization (QPPSO is proposed to solve the parameter estimation for fractional-order chaotic systems. The parallel characteristic of quantum computing is used in QPPSO. This characteristic increases the calculation of each generation exponentially. The behavior of particles in quantum space is restrained by the quantum evolution equation, which consists of the current rotation angle, individual optimal quantum rotation angle, and global optimal quantum rotation angle. Numerical simulation based on several typical fractional-order systems and comparisons with some typical existing algorithms show the effectiveness and efficiency of the proposed algorithm.
International Nuclear Information System (INIS)
Zhang, Xiao; Wei, Chaozhen; Liu, Yingming; Luo, Maokang
2014-01-01
In this paper we use Dirac function to construct a fractional operator called fractional corresponding operator, which is the general form of momentum corresponding operator. Then we give a judging theorem for this operator and with this judging theorem we prove that R–L, G–L, Caputo, Riesz fractional derivative operator and fractional derivative operator based on generalized functions, which are the most popular ones, coincide with the fractional corresponding operator. As a typical application, we use the fractional corresponding operator to construct a new fractional quantization scheme and then derive a uniform fractional Schrödinger equation in form. Additionally, we find that the five forms of fractional Schrödinger equation belong to the particular cases. As another main result of this paper, we use fractional corresponding operator to generalize fractional quantization scheme by using Lévy path integral and use it to derive the corresponding general form of fractional Schrödinger equation, which consequently proves that these two quantization schemes are equivalent. Meanwhile, relations between the theory in fractional quantum mechanics and that in classic quantum mechanics are also discussed. As a physical example, we consider a particle in an infinite potential well. We give its wave functions and energy spectrums in two ways and find that both results are the same
Li, C.; De Ronde, B.; Nikitin, A.; Huang, Y.; Golden, M.S.; De Visser, A.; Brinkman, A.
2017-01-01
The quantum Hall effect is studied in the topological insulator BiSbTeSe2. By employing top- and back-gate electric fields at high magnetic field, the Landau levels of the Dirac cones in the top and bottom topological surface states can be tuned independently. When one surface is tuned to the
Interlayer Hall effect in double quantum wells subject to in-plane magnetic fields
Czech Academy of Sciences Publication Activity Database
Kolorenč, Jindřich; Smrčka, Ludvík; Středa, Pavel
2002-01-01
Roč. 66, č. 8 (2002), s. 085301-1 - 085301-7 ISSN 0163-1829 R&D Projects: GA ČR GA202/01/0754; GA ČR GA202/01/0764 Institutional research plan: CEZ:AV0Z1010914 Keywords : double - layer two-dimensional electron system * magnetotransport * Hall effect Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 3.327, year: 2002
Prediction of giant intrinsic spin-Hall effect in strained p-GaAs quantum wells
Energy Technology Data Exchange (ETDEWEB)
Schindler, Christoph; Kubis, Tillmann; Vogl, Peter [Walter Schottky Institut, Technische Universitaet Muenchen, Garching (Germany)
2009-07-01
We present a systematic study of the intrinsic spin-Hall effect and its inverse effect in various two dimensional nanostructures using the non-equilibrium Green's function technique. We include elastic impurity scattering as well as inelastic acoustical phonon scattering. The parameters for the Dresselhaus and Rashba spin-orbit coupling are obtained from an atomistic tight binding calculation. We predict exceptionally large spin polarization effects in specially band engineered and geometrically designed nanostructures. In strained p-GasAs, we find a k-linear spin splitting that is enhanced by a factor of 50 compared to the unstrained case. We propose a T shaped three-terminal device that acts as a spin polarizer without external magnetic field. Optimizing the geometry with respect to the spin-precession length results in a spin accumulation at the drain contacts of up to 25%. We also study the inverse intrinsic spin-Hall effect. In a four-terminal ''H'' shaped structure it can be used to measure the direct spin-Hall effect by simply applying a gate voltage. For such a measurement, we predict a threshold value for the spin-orbit coupling strength that cannot be met by simple n-GaAs systems.
Morimoto, Takahiro; Furusaki, Akira; Nagaosa, Naoto
2015-04-10
Three-dimensional topological insulators of finite thickness can show the quantum Hall effect (QHE) at the filling factor ν=0 under an external magnetic field if there is a finite potential difference between the top and bottom surfaces. We calculate energy spectra of surface Weyl fermions in the ν=0 QHE and find that gapped edge states with helical spin structure are formed from Weyl fermions on the side surfaces under certain conditions. These edge channels account for the nonlocal charge transport in the ν=0 QHE which is observed in a recent experiment on (Bi_{1-x}Sb_{x})_{2}Te_{3} films. The edge channels also support spin transport due to the spin-momentum locking. We propose an experimental setup to observe various spintronics functions such as spin transport and spin conversion.
Zhang, Kai-Cheng; Li, Yong-Feng; Liu, Yong; Zhu, Yan
2018-04-01
Recently topological materials have attracted much attention due to their quantization transports as well as edge states. It will be excellent to realize the robust quantum anomalous Hall transports in graphene-based devices. Using density-functional theory and tight-binding method, we investigated the structural, magnetic and topological properties for the boron-doped graphene with Re-adsorption. A large band-gap of 32.5 meV is opened by the Rashba spin-orbital coupling, and the band-gap is robust against the shape deformation of ± 4% along the zigzag direction. Giant magnetic anisotropy emerges in this adsorption system together with the Fermi level lying in the band gap. Both the magnetic anisotropy and the band gap can be tuned by a moderate electric field. Calculations reveal that the system exhibits the quantization transports with the Chern number C=2 .
International Nuclear Information System (INIS)
Longhi, Stefano
2014-01-01
Quantum recurrence and dynamic localization are investigated in a class of ac-driven tight-binding Hamiltonians, the Krawtchouk quantum chain, which in the undriven case provides a paradigmatic Hamiltonian model that realizes perfect quantum state transfer and mirror inversion. The equivalence between the ac-driven single-particle Krawtchouk Hamiltonian H -hat (t) and the non-interacting ac-driven bosonic junction Hamiltonian enables to determine in a closed form the quasi energy spectrum of H -hat (t) and the conditions for exact wave packet reconstruction (dynamic localization). In particular, we show that quantum recurrence, which is predicted by the general quantum recurrence theorem, is exact for the Krawtchouk quantum chain in a dense range of the driving amplitude. Exact quantum recurrence provides perfect wave packet reconstruction at a frequency which is fractional than the driving frequency, a phenomenon that can be referred to as fractional dynamic localization
Light-Induced Type-II Band Inversion and Quantum Anomalous Hall State in Monolayer FeSe
Wang, Z. F.; Liu, Zhao; Yang, Jinlong; Liu, Feng
2018-04-01
Coupling a quantum anomalous Hall (QAH) state with a superconducting state offers an attractive approach to detect the signature alluding to a topological superconducting state [Q. L. He et al., Science 357, 294 (2017), 10.1126/science.aag2792], but its explanation could be clouded by disorder effects in magnetic doped QAH materials. On the other hand, an antiferromagnetic (AFM) quantum spin Hall (QSH) state is identified in the well-known high-temperature 2D superconductor of monolayer FeSe [Z. F. Wang et al., Nat. Mater. 15, 968 (2016), 10.1038/nmat4686]. Here, we report a light-induced type-II band inversion (BI) and a QSH-to-QAH phase transition in the monolayer FeSe. Depending on the handedness of light, a spin-tunable QAH state with a high Chern number of ±2 is realized. In contrast to the conventional type-I BI resulting from intrinsic spin-orbital coupling (SOC), which inverts the band an odd number of times and respects time reversal symmetry, the type-II BI results from a light-induced handedness-dependent effective SOC, which inverts the band an even number of times and does not respect time reversal symmetry. The interplay between these two SOC terms makes the spin-up and -down bands of an AFM QSH state respond oppositely to a circularly polarized light, leading to the type-II BI and an exotic topological phase transition. Our finding affords an exciting opportunity to detect Majorana fermions in one single material without magnetic doping.
Hall effect in noncommutative coordinates
International Nuclear Information System (INIS)
Dayi, Oemer F.; Jellal, Ahmed
2002-01-01
We consider electrons in uniform external magnetic and electric fields which move on a plane whose coordinates are noncommuting. Spectrum and eigenfunctions of the related Hamiltonian are obtained. We derive the electric current whose expectation value gives the Hall effect in terms of an effective magnetic field. We present a receipt to find the action which can be utilized in path integrals for noncommuting coordinates. In terms of this action we calculate the related Aharonov-Bohm phase and show that it also yields the same effective magnetic field. When magnetic field is strong enough this phase becomes independent of magnetic field. Measurement of it may give some hints on spatial noncommutativity. The noncommutativity parameter θ can be tuned such that electrons moving in noncommutative coordinates are interpreted as either leading to the fractional quantum Hall effect or composite fermions in the usual coordinates
Kim, Bom Soo
2018-05-01
We discuss the contribution of magnetic Skyrmions to the Hall viscosity and propose a simple way to identify it in experiments. The topological Skyrmion charge density has a distinct signature in the electric Hall conductivity that is identified in existing experimental data. In an electrically neutral system, the Skyrmion charge density is directly related to the thermal Hall conductivity. These results are direct consequences of the field theory Ward identities, which relate various physical quantities based on symmetries and have been previously applied to quantum Hall systems.
Coimbatore Balram, Ajit; Wójs, Arkadiusz; Jain, Jainendra
2014-03-01
Exact diagonalization studies have revealed that the energy spectrum of interacting electrons in the lowest Landau level splits, non-perturbatively, into bands. The theory of nearly free composite fermions (CFs) has been shown to be valid for the lowest band, and thus to capture the low temperature physics, but it over-predicts the number of states for the excited bands. We explain the state counting of higher bands in terms of composite fermions with an infinitely strong short range interaction between a CF particle and a CF hole. This interaction, the form of which we derive from the microscopic CF theory, eliminates configurations containing certain tightly bound CF excitons. With this modification, the CF theory reproduces, for all well-defined excited bands, an exact counting for ν > 1 / 3 , and an almost exact counting for ν The resulting insight clarifies that the corrections to the nearly free CF theory are not thermodynamically significant at sufficiently low temperatures, thus providing a microscopic explanation for why it has proved successful for the analysis of the various properties of the CF Fermi sea. NSF grants DMR-1005536 and DMR-0820404, Polish NCN grant 2011/01/B/ST3/04504 and EU Marie Curie Grant PCIG09-GA-2011-294186, Research Computing and Cyberinfrastructure, PSU and Wroclaw Centre for Networking and Supercomputing
Photoluminescence Detected Doublet Structure in the Integer and Fractional Quantum Hall Regime
International Nuclear Information System (INIS)
Kim, Yongmin; Munteanu, F.M.; Perry, C.H.; Reno, J.L.; Rickel, D.G.; Simmons, J.A.
1999-01-01
We present here the results of polarized magneto-photoluminescence measurements on a high mobility single-heterojunction. The presence of a doublet structure over a large magnetic field range (2>v>l/6) is interpreted as possible evidence for the existence of a magneto-roton minima of the charged density waves. This is understood as an indication of strong electronic correlation even in the case of the IQHE limit
Supersymmetric Hamiltonian approach to edge excitations in ν=5/2 fractional quantum Hall effect
International Nuclear Information System (INIS)
Yu Ming; Zhang Xin
2008-01-01
A supersymmetric Hamiltonian is constructed for the edge excitations of the Moore-Read (Pfaffian) like state, which is a realization of the N=2 supersymmetric CS model. Fermionic generators and their conjugates are introduced to deal with the fermion pairing, whose condensation form a BCS like state. After Bogoliubov transformation, an N=2 supersymmetric and nonrelativistic Hamiltonian is found to take a known form, which is integrable. The main difference between the Moore-Read state and our BCS like state is that the number of fermion pairs in our formalism is not fixed. However, we have also found that the excited states in our model looks similar but not exactly the same as Moore and Read's
Charge density wave crossover at low fillings in the fractional quantum Hall regime
International Nuclear Information System (INIS)
Cabo, A.; Claro, F.; Perez, A.; Maze, J.
2006-08-01
We show that besides the Wigner Crystal, the lowest Landau level supports a state with the same crystalline symmetry but qualitatively different charge density distribution at low densities. Instead of periodic peaks the new state forms percolating ridges that may favor an energy decrease through correlated ring exchange contributions. For the case of half electron per cell a crossover is found close to filling 1/7 between this new state and the Wigner-like solid, showing that transitions may occur from one to the other as the electron density is varied. This result is consistent with recent experimental findings. (author)
Ciftja, Orion
2018-05-01
It has now become evident that interplay between internal anisotropy parameters (such as electron mass anisotropy and/or anisotropic coupling of electrons to the substrate) and electron-electron correlation effects can create a rich variety of possibilities especially in quantum Hall systems. The electron mass anisotropy or material substrate effects (for example, the piezoelectric effect in GaAs) can lead to an effective anisotropic interaction potential between electrons. For lack of knowledge of realistic ab-initio potentials that may describe such effects, we adopt a phenomenological approach and assume that an anisotropic Coulomb interaction potential mimics the internal anisotropy of the system. In this work we investigate the emergence of liquid crystalline order at filling factor ν = 1/6 of the lowest Landau level, a state very close to the point where a transition from the liquid to the Wigner solid happens. We consider small finite systems of electrons interacting with an anisotropic Coulomb interaction potential and study the energy stability of an anisotropic liquid crystalline state relative to its isotropic Fermi-liquid counterpart. Quantum Monte Carlo simulation results in disk geometry show stabilization of liquid crystalline order driven by an anisotropic Coulomb interaction potential at all values of the interaction anisotropy parameter studied.
Direct observation of magnon fractionalization in the quantum spin ladder
Thielemann, B.; Rüegg, C.; Rønnow, H.M.; Läuchli, A.M.; Caux, J.S.; Normand, B.; Biner, D.; Krämer, K.W.; Güdel, H.U.; Stahn, J.; Habicht, K.; Kiefer, K.; Boehm, M.; McMorrow, D.F.; Mesot, J.
2009-01-01
We measure by inelastic neutron scattering the spin excitation spectra as a function of applied magnetic field in the quantum spin-ladder material (C5H12N)2CuBr4. Discrete magnon modes at low fields in the quantum disordered phase and at high fields in the saturated phase contrast sharply with a
Magnetotransport of Monolayer Graphene with Inert Gas Adsorption in the Quantum Hall Regime
Fukuda, A.; Terasawa, D.; Fujimoto, A.; Kanai, Y.; Matsumoto, K.
2018-03-01
The surface of graphene is easily accessible from outside, and thus it is a suitable material to study the effects of molecular adsorption on the electric transport properties. We investigate the magnetotransport of inert-gas-adsorbed monolayer graphene at a temperature of 4.4 K under a magnetic field ranging from 0 to 7 T. We introduce 4He or Ar gas at low temperature to graphene kept inside a sample cell. The magnetoresistance change ΔRxx and Hall resistance change ΔRxy from the pristine graphene are measured as a function of gate voltage and magnetic field for one layer of adsorbates. ΔRxx and ΔRxy show oscillating patterns related to the constant filling factor lines in a Landau-fan diagram. Magnitudes of these quantities are relatively higher around a charge neutral point and may be mass-sensitive. These conditions could be optimized for development of a highly sensitive gas sensor.
Beyond the hall effect: pratical engineering from relativistic quantum field theory
International Nuclear Information System (INIS)
Srivastava, Y.
1986-01-01
The author discusses the successful microscopic relativistic quantum field theory viz., quantum electrodynamic (QED) as applied to condensed matter systems. A circuit version of the Heisenberg argument is presented to show that the electric and magnetic flux cannot be measured simultaneously if the usual position/momentum uncertainty of a charged particle confined in a circuit is to be preserved. The author suggests that the electronic transport of a microchip itself obeys some of the same field equations for QED in particular. A comparative list is presented
International Nuclear Information System (INIS)
Dong Jianping; Xu Mingyu
2008-01-01
The space fractional Schroedinger equation with a finite square potential, periodic potential, and delta-function potential is studied in this paper. We find that the continuity or discontinuity condition of a fractional derivative of the wave functions should be considered to solve the fractional Schroedinger equation in fractional quantum mechanics. More parity states than those given by standard quantum mechanics for the finite square potential well are obtained. The corresponding energy equations are derived and then solved by graphical methods. We show the validity of Bloch's theorem and reveal the energy band structure for the periodic potential. The jump (discontinuity) condition for the fractional derivative of the wave function of the delta-function potential is given. With the help of the jump condition, we study some delta-function potential fields. For the delta-function potential well, an alternate expression of the wave function (the H function form of it was given by Dong and Xu [J. Math. Phys. 48, 072105 (2007)]) is obtained. The problems of a particle penetrating through a delta-function potential barrier and the fractional probability current density of the particle are also discussed. We study the Dirac comb and show the energy band structure at the end of the paper
Effective field theory of an anomalous Hall metal from interband quantum fluctuations
Chua, Victor; Assawasunthonnet, Wathid; Fradkin, Eduardo
2017-07-01
We construct an effective field theory, a two-dimensional two-component metallic system described by a model with two Fermi surfaces ("pockets"). This model describes a translationally invariant metallic system with two types of fermions, each with its own Fermi surface, with forward scattering interactions. This model, in addition to the O (2 ) rotational invariance, has a U (1 )×U (1 ) symmetry of separate charge conservation for each Fermi surface. For sufficiently attractive interactions in the d -wave (quadrupolar) channel, this model has an interesting phase diagram that includes a spontaneously generated anomalous Hall metal phase. We derive the Landau-Ginzburg effective action of quadrupolar order parameter fields which enjoys an O (2 )×U (1 ) global symmetry associated to spatial isotropy and the internal U (1 ) relative phase symmetries, respectively. We show that the order parameter theory is dynamically local with a dynamical scaling of z =2 and perform a one-loop renormalization group analysis of the Landau-Ginzburg theory. The electronic liquid crystal phases that result from spontaneous symmetry breaking are studied and we show the presence of Landau damped Nambu-Goldstone modes at low momenta that is a signature of non-Fermi-liquid behavior. Electromagnetic linear response is also analyzed in both the normal and symmetry broken phases from the point of view of the order parameter theory. The nature of the coupling of electromagnetism to the order parameter fields in the normal phase is non-minimal and decidedly contains a precursor to the anomalous Hall response in the form of a order-parameter-dependent Chern-Simons term in the effective action.
Quantum spin Hall effect and topological phase transition in InN x Bi y Sb1-x-y /InSb quantum wells
Song, Zhigang; Bose, Sumanta; Fan, Weijun; Zhang, Dao Hua; Zhang, Yan Yang; Shen Li, Shu
2017-07-01
Quantum spin Hall (QSH) effect, a fundamentally new quantum state of matter and topological phase transitions are characteristics of a kind of electronic material, popularly referred to as topological insulators (TIs). TIs are similar to ordinary insulator in terms of their bulk bandgap, but have gapless conducting edge-states that are topologically protected. These edge-states are facilitated by the time-reversal symmetry and they are robust against nonmagnetic impurity scattering. Recently, the quest for new materials exhibiting non-trivial topological state of matter has been of great research interest, as TIs find applications in new electronics and spintronics and quantum-computing devices. Here, we propose and demonstrate as a proof-of-concept that QSH effect and topological phase transitions can be realized in {{InN}}x{{Bi}}y{{Sb}}1-x-y/InSb semiconductor quantum wells (QWs). The simultaneous incorporation of nitrogen and bismuth in InSb is instrumental in lowering the bandgap, while inducing opposite kinds of strain to attain a near-lattice-matching conducive for lattice growth. Phase diagram for bandgap shows that as we increase the QW thickness, at a critical thickness, the electronic bandstructure switches from a normal to an inverted type. We confirm that such transition are topological phase transitions between a traditional insulator and a TI exhibiting QSH effect—by demonstrating the topologically protected edge-states using the bandstructure, edge-localized distribution of the wavefunctions and edge-state spin-momentum locking phenomenon, presence of non-zero conductance in spite of the Fermi energy lying in the bandgap window, crossover points of Landau levels in the zero-mode indicating topological band inversion in the absence of any magnetic field and presence of large Rashba spin-splitting, which is essential for spin-manipulation in TIs.
Breakdown of the quantum Hall effect in InAs/AlSb quantum wells due to counterflowing edge channels
Wees, B.J. van; Meijer, G.I.; Kuipers, J.J.; Klapwijk, T.M.; Graaf, W. van de; Borghs, G.
1995-01-01
We investigated magnetotransport in the two-dimensional electron gas (2DEG) present in InAs/AlSb quantum wells. The filling factor Ng underneath a gate electrode was reduced relative to the bulk filling factor Nb. For Ng
International Nuclear Information System (INIS)
Fan Hongyi; Hao Ren; Lu Hailiang
2008-01-01
Based on our previous paper (Commun. Theor. Phys. 39 (2003) 417) we derive the convolution theorem of fractional Fourier transformation in the context of quantum mechanics, which seems a convenient and neat way. Generalization of this method to the complex fractional Fourier transformation case is also possible
Fractional excitations in the square-lattice quantum antiferromagnet
DEFF Research Database (Denmark)
Piazza, B. Dalla; Mourigal, M.; Christensen, Niels Bech
2015-01-01
-projected trial wavefunctions. The excitation continuum is accounted for by the existence of spatially extended pairs of fractional S=1/2 quasiparticles, 2D analogues of 1D spinons. Away from the anomalous wavevector, these fractional excitations are bound and form conventional magnons. Our results establish...... the existence of fractional quasiparticles in the high-energy spectrum of a quasi-two-dimensional antiferromagnet, even in the absence of frustration....
Temperature dependent transport of two dimensional electrons in the integral quantum Hall regime
International Nuclear Information System (INIS)
Wi, H.P.
1986-01-01
This thesis is concerned with the temperature dependent electronic transport properties of a two dimensional electron gas subject to background potential fluctuations and a perpendicular magnetic field. The author carried out an extensive temperature dependent study of the transport coefficients, in the region of an integral quantum plateau, in an In/sub x/Ga/sub 1-x/As/InP heterostructure for 4.2K 10 cm -2 meV -1 ) even at the middle between two Landau levels, which is unexpected from model calculations based on short ranged randomness. In addition, the different T dependent behavior of rho/sub xx/ between the states in the tails and those near the center of a Landau level, indicates the existence of different electron states in a Landau level. Additionally, the author reports T-dependent transport measurements in the transition region between two quantum plateaus in several different materials
International Nuclear Information System (INIS)
Tyapkin, A.A.
1976-01-01
The problem is raised on the interpretation of quarks having fractional quantum numbers as structural quasi-particles. A new composite model is proposed on the basis of the fundamental triplet representation of fermions having integral quantum numbers
Engineering a Robust Quantum Spin Hall State in Graphene via Adatom Deposition
Directory of Open Access Journals (Sweden)
Conan Weeks
2011-10-01
Full Text Available The 2007 discovery of quantized conductance in HgTe quantum wells delivered the field of topological insulators (TIs its first experimental confirmation. While many three-dimensional TIs have since been identified, HgTe remains the only known two-dimensional system in this class. Difficulty fabricating HgTe quantum wells has, moreover, hampered their widespread use. With the goal of breaking this logjam, we provide a blueprint for stabilizing a robust TI state in a more readily available two-dimensional material—graphene. Using symmetry arguments, density functional theory, and tight-binding simulations, we predict that graphene endowed with certain heavy adatoms realizes a TI with substantial band gap. For indium and thallium, our most promising adatom candidates, a modest 6% coverage produces an estimated gap near 80 K and 240 K, respectively, which should be detectable in transport or spectroscopic measurements. Engineering such a robust topological phase in graphene could pave the way for a new generation of devices for spintronics, ultra-low-dissipation electronics, and quantum information processing.
Spin hall effect associated with SU(2) gauge field
Tao, Y.
2010-01-01
In this paper, we focus on the connection between spin Hall effect and spin force. Here we investigate that the spin force due to spin-orbit coupling, which, in two-dimensional system, is equivalent to forces of Hirsch and Chudnovsky besides constant factors 3 and frac{3}{2} respectively, is a part of classic Anandan force, and that the spin Hall effect is an anomalous Hall effect. Furthermore, we develop the method of AC phase to derive the expression for the spin force, and note that the most basic spin Hall effect indeed originate from the AC phase and is therefore an intrinsic quantum mechanical property of spin. This method differs from approach of Berry phase in the study of anomalous Hall effect , which is the intrinsic property of the perfect crystal. On the other hand, we use an elegant skill to show that the Chudnovsky-Drude model is reasonable. Here we have improved the theoretical values of spin Hall conductivity of Chudnovsky. Compared to the theoretical values of spin Hall conductivity in the Chudnovsky-Drude model, ours are in better agreement with experimentation. Finally, we discuss the relation between spin Hall effect and fractional statistics.
Kamhawi, Hani; Huang, Wensheng; Haag, Thomas
2014-01-01
The National Aeronautics and Space Administration (NASA) Science Mission Directorate In- Space Propulsion Technology office is sponsoring NASA Glenn Research Center (GRC) to develop a 4 kW-class Hall thruster propulsion system for implementation in NASA science missions. Tests were performed within NASA GRC Vacuum Facility 5 at background pressure levels that were six times lower than what has previously been attained in other vacuum facilities. A study was conducted to assess the impact of varying the cathode-to-anode flow fraction and cathode position on the performance and operational characteristics of the High Voltage Hall Accelerator (HiVHAc) thruster. In addition, the impact of injecting additional xenon propellant in the vicinity of the cathode was also assessed. Cathode-to-anode flow fraction sensitivity tests were performed for power levels between 1.0 and 3.9 kW. It was found that varying the cathode flow fraction from 5 to approximately 10% of the anode flow resulted in the cathode-to-ground voltage becoming more positive. For an operating condition of 3.8 kW and 500 V, varying the cathode position from a distance of closest approach to 600 mm away did not result in any substantial variation in thrust but resulted in the cathode-to-ground changing from -17 to -4 V. The change in the cathode-to-ground voltage along with visual observations indicated a change in how the cathode plume was coupling to the thruster discharge. Finally, the injection of secondary xenon flow in the vicinity of the cathode had an impact similar to increasing the cathode-to-anode flow fraction, where the cathode-to-ground voltage became more positive and discharge current and thrust increased slightly. Future tests of the HiVHAc thruster are planned with a centrally mounted cathode in order to further assess the impact of cathode position on thruster performance.
International Nuclear Information System (INIS)
Cheng Shuguang
2010-01-01
Recent experiments have confirmed that the electron-hole inhomogeneity in graphene is a new type of charge disorder. Motivated by such confirmation, we theoretically study the transport properties of a monolayer graphene (MLG) based p-n junction and a bilayer graphene (BLG) p-n junction in the quantum Hall regime where electron-hole puddles are considered. By using the non-equilibrium Green function method, both the current and conductance are obtained. We find that, in the presence of the electron-hole inhomogeneity, the lowest quantized conductance plateau at e 2 /h emerges in the MLG p-n junction under very small charge puddle disorder strength. For a BLG p-n junction, however, the conductance in the p-n region is enhanced with charge puddles, and the lowest quantized conductance plateau emerges at 2e 2 /h. Besides, when an ideal quantized conductance plateau is formed for a MLG p-n junction, the universal conductance fluctuation is found to be 2e 2 /3h. Furthermore, we also investigate the influence of Anderson disorder on such p-n junctions and the comparison and discussion are given accordingly. To compare the two models with different types of disorder, we investigate the conductance distribution specially. Finally the influence of disorder strength on the conductance of a MLG p-n junction is investigated.
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.
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.
Intrinsic Dirac half-metal and quantum anomalous Hall phase in a hexagonal metal-oxide lattice
Zhang, Shou-juan; Zhang, Chang-wen; Zhang, Shu-feng; Ji, Wei-xiao; Li, Ping; Wang, Pei-ji; Li, Sheng-shi; Yan, Shi-shen
2017-11-01
The quantum anomalous Hall (QAH) effect has attracted extensive attention due to time-reversal symmetry broken by a staggered magnetic flux emerging from ferromagnetic ordering and spin-orbit coupling. However, the experimental observations of the QAH effect are still challenging due to its small nontrivial bulk gap. Here, based on density functional theory and Berry curvature calculations, we propose the realization of intrinsic QAH effect in two-dimensional hexagonal metal-oxide lattice, N b2O3 , which is characterized by the nonzero Chern number (C =1 ) and chiral edge states. Spin-polarized calculations indicate that it exhibits a Dirac half-metal feature with temperature as large as TC=392 K using spin-wave theory. When the spin-orbit coupling is switched on, N b2O3 becomes a QAH insulator. Notably, the nontrivial topology is robust against biaxial strain with its band gap reaching up to Eg=75 meV , which is far beyond room temperature. A tight-binding model is further constructed to understand the origin of nontrivially electronic properties. Our findings on the Dirac half-metal and room-temperature QAH effect in the N b2O3 lattice can serve as an ideal platform for developing future topotronics devices.
Fractional revivals of coherence in quantum mechanical oscillators
Ross, J.C.; Capel, H.W.
2000-01-01
A case study is made of the delocalisation and revival dynamics of a continuously driven quantum pendulum in integrable and near integrable regimes, utilising the Husimi phase-space distribution function, and an entropy function which measures the degree of localisation. The numerical results can be
International Nuclear Information System (INIS)
Facer, G.R.; Kane, B.E.
1996-01-01
Full text: Two-dimensional electron gas (2DEG) GaAs/AIGaAs heterostructures have been grown by molecular beam epitaxy (MBE) in which gate-induced accumulation of carriers replaces the more usual modulation doping. These novel devices have the advantages of reduced disorder and a high degree of tunability in the carrier density. Because modulation doping is not used, disorder effects in the 2DEG due to nearby dopants are eliminated. Mean free paths for electrons exceed 30 μm at low temperatures. Electron densities are accurately tunable over nearly two orders of magnitude, from 9 x 10 9 cm -2 to 4 x 10 11 cm -2 . Very high electron mobilities, exceeding 3 x10 6 cm 2 /Vs at 4.2 K, are obtained. With such a combination of density tunability and low disorder, these layers provide unique opportunities for studying low dimensional systems following further lithography. Nanolithography with feature sizes under 50 nm will be possible at UNSW in early 1996. In preparation for 1-dimensional and 0-dimensional structure fabrication, the 2DEG samples have been characterised in steady fields at temperatures ∼ 50 mK. Recent theory has explained the fractional quantum Hall effect at electron filling factor ν=1/2 in terms of composite fermions (made up of interacting electrons) behaving as if they are a non-interacting system at B=0. The question of the mobility μ c of composite fermions in the new devices, and how it varies as the electron density varies, has been studied. Preliminary measurements at ν=1/2 yield μ c ∼ 10 4 cm 2 /Vs. The composite fermion mobility is nearly independent of electron density beyond an apparent threshold N = 0.5 x 10 11 cm -2 , and independent of temperature in the range 50 to 200 mK. The electron N threshold coincides with the crossover of the carrier Fermi wavelength and the mean free path
Self-organised fractional quantisation in a hole quantum wire
Gul, Y.; Holmes, S. N.; Myronov, M.; Kumar, S.; Pepper, M.
2018-03-01
We have investigated hole transport in quantum wires formed by electrostatic confinement in strained germanium two-dimensional layers. The ballistic conductance characteristics show the regular staircase of quantum levels with plateaux at n2e 2/h, where n is an integer, e is the fundamental unit of charge and h is Planck’s constant. However as the carrier concentration is reduced, the quantised levels show a behaviour that is indicative of the formation of a zig-zag structure and new quantised plateaux appear at low temperatures. In units of 2e 2/h the new quantised levels correspond to values of n = 1/4 reducing to 1/8 in the presence of a strong parallel magnetic field which lifts the spin degeneracy but does not quantise the wavefunction. A further plateau is observed corresponding to n = 1/32 which does not change in the presence of a parallel magnetic field. These values indicate that the system is behaving as if charge was fractionalised with values e/2 and e/4, possible mechanisms are discussed.
Li, Sheng-Shi; Ji, Wei-Xiao; Li, Ping; Hu, Shu-Jun; Cai, Li; Zhang, Chang-Wen; Yan, Shi-Shen
2017-06-28
The quantum spin Hall (QSH) effect is promising for achieving dissipationless transport devices due to their robust gapless edge states inside insulating bulk gap. However, the currently discussed QSH insulators usually suffer from ultrahigh vacuum or low temperature due to the small bulk gap, which limits their practical applications. Searching for large-gap QSH insulators is highly desirable. Here, the tunable QSH state of a Bi(110) films with a black phosphorus (BP) structure, which is robust against structural deformation and electric field, is explored by first-principles calculations. It is found that the two-monolayer BP-Bi(110) film obtains a tunable large bulk gap by strain engineering and its QSH effect shows a favorable robustness within a wide range of combinations of in-plane and out-of-plane strains, although a single in-plane compression or out-of-plane extension may restrict the topological phase due to the self-doping effect. More interestingly, in view of biaxial strain, two competing physics on band topology induced by bonding-antibonding and p x,y -p z band inversions are obtained. Meanwhile, the QSH effect can be persevered under an electric field of up to 0.9 V/Å. Moreover, with appropriate in-plane strain engineering, a nontrivial topological phase in a four-monolayer BP-Bi(110) film is identified. Our findings suggest that these two-dimensional BP-Bi(110) films are ideal platforms of the QSH effect for low-power dissipation devices.
Islam, M. F.; Canali, C. M.; Pertsova, A.; Balatsky, A.; Mahatha, S. K.; Carbone, C.; Barla, A.; Kokh, K. A.; Tereshchenko, O. E.; Jiménez, E.; Brookes, N. B.; Gargiani, P.; Valvidares, M.; Schatz, S.; Peixoto, T. R. F.; Bentmann, H.; Reinert, F.; Jung, J.; Bathon, T.; Fauth, K.; Bode, M.; Sessi, P.
2018-04-01
The quantum anomalous Hall effect (QAHE) has recently been reported to emerge in magnetically doped topological insulators. Although its general phenomenology is well established, the microscopic origin is far from being properly understood and controlled. Here, we report on a detailed and systematic investigation of transition metal (TM) doped Sb2Te3 . By combining density functional theory calculations with complementary experimental techniques, i.e., scanning tunneling microscopy, resonant photoemission, and x-ray magnetic circular dichroism, we provide a complete spectroscopic characterization of both electronic and magnetic properties. Our results reveal that the TM dopants not only affect the magnetic state of the host material, but also significantly alter the electronic structure by generating impurity-derived energy bands. Our findings demonstrate the existence of a delicate interplay between electronic and magnetic properties in TM doped topological insulators. In particular, we find that the fate of the topological surface states critically depends on the specific character of the TM impurity: while V- and Fe-doped Sb2Te3 display resonant impurity states in the vicinity of the Dirac point, Cr and Mn impurities leave the energy gap unaffected. The single-ion magnetic anisotropy energy and easy axis, which control the magnetic gap opening and its stability, are also found to be strongly TM impurity dependent and can vary from in plane to out of plane depending on the impurity and its distance from the surface. Overall, our results provide general guidelines for the realization of a robust QAHE in TM doped Sb2Te3 in the ferromagnetic state.
Quantum mechanics of the fractional-statistics gas: Random-phase approximation
International Nuclear Information System (INIS)
Dai, Q.; Levy, J.L.; Fetter, A.L.; Hanna, C.B.; Laughlin, R.B.
1992-01-01
A description of the fractional-statistics gas based on the complete summation of Hartree, Fock, ladder and bubble diagrams is presented. The superfluid properties identified previously in the random-phase-approximation (RPA) calculation of Fetter, Hanna, and Laughlin [Phys. Rev. B 39, 9679 (1989)] are substantially confirmed. The discrepancy between the RPA sound speed and the Hartree-Fock bulk modulus is found to be eliminated. The unusual Hall-effect behavior is found to vanish for the Bose gas test case but not for the fractional-statistics gas, implying that it is physically correct. Excellent agreement is obtained with the collective-mode dispersion obtained numerically by Xie, He, and Das Sarma [Phys. Rev. Lett. 65, 649 (1990)
DEFF Research Database (Denmark)
Olsen, Thomas
2016-01-01
opportunity to change the local topology by adsorption of atoms or molecules and thus comprise an ideal platform for designing topological heterostructures. Here we apply first-principles calculations to show that the quantum spin Hall insulator 1T'-MoS2 exhibits a phase transition to a trivial insulator upon....... This is in sharp contrast to topological edge states, which typically exhibit strong dispersion that are sensitive to a particular edge termination. The heterostructure is also suggestive of a simple design of one-dimensional metallic networks in sheets of 1T'-MoS2....
Relativistic quantum Hall conductivity for 3D and 2D electron plasma in an external magnetic field
International Nuclear Information System (INIS)
Gonzalez Felipe, R.; Perez Martinez, A.; Perez-Rojas, H.
1990-05-01
The complete antisymmetric form of the conductivity tensor in the static limit, as well as the expression for the Hall conductivity, is obtained for the relativistic 3D and 2D electron gas in a magnetic field. The non-relativistic 2D limit is also discussed. The typical step form of the 2D Hall conductivity at zero temperature is obtained under the simple hypothesis of constancy of the chemical potential. (author). 6 refs, 1 fig
International Nuclear Information System (INIS)
Kraak, W.; Nachtwei, G.; Herrmann, R.; Glinski, M.
1988-01-01
The magnetotransport properties of the two-dimensional electron gas (2DEG) confined at the interface of the grain boundary in p-type InSb bicrystals are investigated. Under high hydrostatic pressures and in high magnetic fields (B > 5 T) the integral quantum Hall regime is reached, where the Hall resistance ρ xy is quantized to h/e 2 j (j is the number of filled Landau levels of the 2DEG). In this high field regime detailed measurements are given of the resistivity ρ xx and the Hall resistance ρ xy as function of temperature T and current density j x . An unexpected high accuracy of the Hall resistance ρ xy at magnetic field values close to a fully occupied Landau level is found, despite the high value of the diagonal resistivity ρ xx . At high current densities j x in the quantum Hall regime (j = 1) a sudden breakdown of the quantized resistance value associated with a jump-like switching to the next lower quantized value h/2e 2 is observed. A simple macroscopic picture is proposed to account for these novel transport properties associated with the quantum Hall effect. (author)
Effet Hall quantique, liquides de Luttinger et charges fractionnaires
Roche, Patrice; Rodriguez, V.; Glattli, D. Christian
We review some basic properties of the Fractional Quantum Hall Effect and particularly address the physics of the edge states. The chiral Luttinger liquid properties of the edges are discussed and probed experimentally using transport measurements. Shot noise measurements, which allow determination of the quasiparticle charge are also discussed. To cite this article: P. Roche et al., C. R. Physique 3 (2002) 717-732.
Oscillating dipole with fractional quantum source in Aharonov-Bohm electrodynamics
Directory of Open Access Journals (Sweden)
Giovanni Modanese
Full Text Available We show, in the case of a special dipolar source, that electromagnetic fields in fractional quantum mechanics have an unexpected space dependence: propagating fields may have non-transverse components, and the distinction between near-field zone and wave zone is blurred. We employ an extension of Maxwell theory, Aharonov-Bohm electrodynamics, which is compatible with currents jν conserved globally but not locally; we have derived in another work the field equation ∂μFμν=jν+iν, where iν is a non-local function of jν, called “secondary current”. Y. Wei has recently proved that the probability current in fractional quantum mechanics is in general not locally conserved. We compute this current for a Gaussian wave packet with fractional parameter a=3/2 and find that in a suitable limit it can be approximated by our simplified dipolar source. Currents which are not locally conserved may be present also in other quantum systems whose wave functions satisfy non-local equations. The combined electromagnetic effects of such sources and their secondary currents are very interesting both theoretically and for potential applications. Keywords: Generalized Maxwell theory, Fractional Schrödinger equation, Local current conservation
Energy Technology Data Exchange (ETDEWEB)
Chandelier, F
2003-12-01
The quantum Hall effect appears in low temperature electron systems submitted to intense magnetic fields. Electrons are trapped in a thin layer ({approx} 100.10{sup -8} cm thick) at the interface between 2 semiconductors or between a semiconductor and an insulating material. This thesis presents 3 personal contributions to the physics of plane systems and particularly to quantum Hall effect systems. The first contribution is a topological approach, it involves the study of Landau's problem in a geometry nearing that of Hall effect experiments. A mathematical formalism has been defined and by using the Kubo's formula, the quantification of the Hall conductivity can be linked to the Chern class of threaded holes. The second contribution represents a phenomenological approach based on dual symmetries and particularly on modular symmetries. This contribution uses visibility diagrams that have already produced right predictions concerning resistivity curves or band structures. The introduction of a physical equivalence has allowed us to build a phase diagram for the quantum Hall effect at zero temperature. This phase diagram agrees with the experimental facts concerning : -) the existence of 2 insulating phases, -) direct transitions between an insulating phase and any Hall phase through integer or fractionary values of the filling factor ({nu}), -) selection rules, and -) classification of the Hall states and their distribution around a metal state. The third contribution concerns another phenomenological approach based on duality symmetries. We have considered a class of (2+1)-dimensional effective models with a Maxwell-Chern-Simons part that includes a non-locality. This non-locality implies the existence of a hidden duality symmetry with a Z{sub 2} component: z {yields} 1/z. This symmetry has allowed us to meet the results of the Fisher's law concerning the components of the resistivity tensor. (A.C.)
International Nuclear Information System (INIS)
Klitzing von, K.
1989-01-01
The quantized Hall effect is theoretically explained in detail as are its basic properties. The explanation is completed with the pertinent mathematical relations and illustrative figures. Experimental data are critically assessed obtained by quantum transport measurement in a magnetic field on two-dimensional systems. The results are reported for a MOSFET silicon transistor and for GaAs-Al x Ga 1-x As heterostructures. The application is discussed of the quantized Hall effect in determining the fine structure constant or in implementing the resistance standard. (M.D.). 27 figs., 57 refs
Czech Academy of Sciences Publication Activity Database
Semenchinsky, S. G.; Chrobok, P.; Svoboda, Pavel
2008-01-01
Roč. 51, č. 12 (2008), s. 1351-1356 ISSN 0543-1972 Institutional research plan: CEZ:AV0Z10100521 Keywords : resistance unit * quantum Hall effect * comparison * standards Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 0.151, year: 2008
Bound values for Hall conductivity of heterogeneous medium under ...
Indian Academy of Sciences (India)
- ditions in inhomogeneous medium has been studied. It is shown that bound values for. Hall conductivity differ from bound values for metallic conductivity. This is due to the unusual character of current percolation under quantum Hall effect ...
International Nuclear Information System (INIS)
Jackiw, R.; Massachusetts Inst. of Tech., Cambridge; Massachusetts Inst. of Tech., Cambridge
1984-01-01
The theory of fermion fractionization due to topologically generated fermion ground states is presented. Applications to one-dimensional conductors, to the MIT bag, and to the Hall effect are reviewed. (author)
International Nuclear Information System (INIS)
Huang, C F; Chang, Y H; Cheng, H H; Yang, Z P; Yeh, H D; Hsu, C H; Liang, C-T; Hang, D R; Lin, H H
2007-01-01
Magnetic-field-induced phase transitions were studied with a two-dimensional electron AlGaAs/GaAs system. The temperature-driven flow diagram shows features of the Γ(2) modular symmetry, which includes distorted flowlines and a shifted critical point. The deviation of the critical conductivities is attributed to a small but resolved spin splitting, which reduces the symmetry in Landau quantization (Dolan 2000 Phys. Rev. B 62 10278). Universal scaling is found under the reduction of the modular symmetry. It is also shown that the Hall conductivity can still be governed by the scaling law when the semicircle law and the scaling on the longitudinal conductivity are invalid
Federal Laboratory Consortium — The instrumentation in Hall A at the Thomas Jefferson National Accelerator Facility was designed to study electroand photo-induced reactions at very high luminosity...
Federal Laboratory Consortium — Hall C's initial complement of equipment (shown in the figure), includes two general-purpose magnetic spectrometers. The High Momentum Spectrometer (HMS) has a large...
Fractional statistics and quantum scaling properties of the integrable Penson-Kolb-Hubbard chain
Vitoriano, Carlindo; Coutinho-Filho, M. D.
2010-09-01
We investigate the ground-state and low-temperature properties of the integrable version of the Penson-Kolb-Hubbard chain. The model obeys fractional statistical properties, which give rise to fractional elementary excitations and manifest differently in the four regions of the phase diagram U/t versus n , where U is the Coulomb coupling, t is the correlated hopping amplitude, and n is the particle density. In fact, we can find local pair formation, fractionalization of the average occupation number per orbital k , or U - and n -dependent average electric charge per orbital k . We also study the scaling behavior near the U -driven quantum phase transitions and characterize their universality classes. Finally, it is shown that in the regime of parameters where local pair formation is energetically more favorable, the ground state exhibits power-law superconductivity; we also stress that above half filling the pair-hopping term stabilizes local Cooper pairs in the repulsive- U regime for U
Czech Academy of Sciences Publication Activity Database
Bartkiewicz, K.; Lemr, K.; Černoch, Antonín; Miranowicz, A.
2017-01-01
Roč. 95, č. 3 (2017), s. 1-7, č. článku 030102. ISSN 2469-9926 R&D Projects: GA ČR GAP205/12/0382 Institutional support: RVO:68378271 Keywords : Bell nonlocality * fully entangled fraction * entanglement-swapping device * quantum state tomography Subject RIV: BH - Optics, Masers, Lasers OBOR OECD: Optics (including laser optics and quantum optics) Impact factor: 2.925, year: 2016
Coxon, Bruce
2011-01-01
An account is given of the life, scientific contributions, and passing of Laurance David Hall (1938-2009), including his early history and education at the University of Bristol, UK, and the synthesis and NMR spectroscopy of carbohydrates and other natural products during ∼20 years of research and teaching at the University of British Columbia in Vancouver, Canada. Lists of graduate students, post-doctoral fellows, and sabbatical visitors are provided for this period. Following a generous endowment by Dr. Herchel Smith, Professor Hall built a new Department of Medicinal Chemistry at Cambridge University, UK, and greatly expanded his researches into the technology and applications of magnetic resonance imaging (MRI) and zero quantum NMR. MRI technology was applied both to medical problems such as the characterization of cartilage degeneration in knee joints, the measurement of ventricular function, lipid localization in animal models of atherosclerosis, paramagnetic metal complexes of polysaccharides as contrast agents, and studies of many other anatomical features, but also to several aspects of materials analysis, including food analyses, process control, and the elucidation of such physical phenomena as the flow of liquids through porous media, defects in concrete, and the visualization of fungal damage to wood. Professor Hall's many publications, patents, lectures, and honors and awards are described, and also his successful effort to keep the Asilomar facility in Pacific Grove, California as the alternating venue for the annual Experimental NMR Conference. Two memorial services for Professor Hall are remembered. Copyright © 2011 Elsevier Inc. All rights reserved.
Yoshitake, Junki; Nasu, Joji; Motome, Yukitoshi
2016-10-07
Experimental identification of quantum spin liquids remains a challenge, as the pristine nature is to be seen in asymptotically low temperatures. We here theoretically show that the precursor of quantum spin liquids appears in the spin dynamics in the paramagnetic state over a wide temperature range. Using the cluster dynamical mean-field theory and the continuous-time quantum Monte Carlo method, which are newly developed in the Majorana fermion representation, we calculate the dynamical spin structure factor, relaxation rate in nuclear magnetic resonance, and magnetic susceptibility for the honeycomb Kitaev model whose ground state is a canonical example of the quantum spin liquid. We find that dynamical spin correlations show peculiar temperature and frequency dependence even below the temperature where static correlations saturate. The results provide the experimentally accessible symptoms of the fluctuating fractionalized spins evincing the quantum spin liquids.
Thermodynamics of ideal quantum gas with fractional statistics in D dimensions.
Potter, Geoffrey G; Müller, Gerhard; Karbach, Michael
2007-06-01
We present exact and explicit results for the thermodynamic properties (isochores, isotherms, isobars, response functions, velocity of sound) of a quantum gas in dimensions D > or = 1 and with fractional exclusion statistics 0 < or = g < or =1 connecting bosons (g=0) and fermions (g=1) . In D=1 the results are equivalent to those of the Calogero-Sutherland model. Emphasis is given to the crossover between bosonlike and fermionlike features, caused by aspects of the statistical interaction that mimic long-range attraction and short-range repulsion. A phase transition along the isobar occurs at a nonzero temperature in all dimensions. The T dependence of the velocity of sound is in simple relation to isochores and isobars. The effects of soft container walls are accounted for rigorously for the case of a pure power-law potential.
Hall Effect Gyrators and Circulators
Viola, Giovanni; DiVincenzo, David P.
2014-04-01
The electronic circulator and its close relative the gyrator are invaluable tools for noise management and signal routing in the current generation of low-temperature microwave systems for the implementation of new quantum technologies. The current implementation of these devices using the Faraday effect is satisfactory but requires a bulky structure whose physical dimension is close to the microwave wavelength employed. The Hall effect is an alternative nonreciprocal effect that can also be used to produce desired device functionality. We review earlier efforts to use an Ohmically contacted four-terminal Hall bar, explaining why this approach leads to unacceptably high device loss. We find that capacitive coupling to such a Hall conductor has much greater promise for achieving good circulator and gyrator functionality. We formulate a classical Ohm-Hall analysis for calculating the properties of such a device, and show how this classical theory simplifies remarkably in the limiting case of the Hall angle approaching 90°. In this limit, we find that either a four-terminal or a three-terminal capacitive device can give excellent circulator behavior, with device dimensions far smaller than the ac wavelength. An experiment is proposed to achieve GHz-band gyration in millimeter (and smaller) scale structures employing either semiconductor heterostructure or graphene Hall conductors. An inductively coupled scheme for realizing a Hall gyrator is also analyzed.
Orbital-exchange and fractional quantum number excitations in an f-electron metal, Yb2Pt2Pb
Wu, L.S.; Gannon, W.J.; Zaliznyak, I.A.; Tsvelik, A.M.; Brockmann, M.; Caux, J.-S.; Kim, M.S.; Qiu, Y.; Copley, J.R.D.; Ehlers, G.; Podlesnyak, A.; Aronson, M.C.
2016-01-01
Exotic quantum states and fractionalized magnetic excitations, such as spinons in one-dimensional chains, are generally expected to occur in 3d transition metal systems with spin 1/2. Our neutron-scattering experiments on the 4f-electron metal Yb2Pt 2 Pb overturn this conventional wisdom. We observe
Universal intrinsic spin Hall effect
Czech Academy of Sciences Publication Activity Database
Sinova, J.; Culcer, D.; Sinitsyn, N. A.; Niu, Q.; Jungwirth, Tomáš; MacDonald, A. H.
2004-01-01
Roč. 92, č. 12 (2004), 126603/1-126603/4 ISSN 0031-9007 R&D Projects: GA ČR GA202/02/0912 Institutional research plan: CEZ:AV0Z1010914 Keywords : semiconductor quantum wells * spin-orbit interaction * spin Hall effect Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 7.218, year: 2004
Quantum spin Hall insulator BiXH (XH = OH, SH) monolayers with a large bulk band gap.
Hu, Xing-Kai; Lyu, Ji-Kai; Zhang, Chang-Wen; Wang, Pei-Ji; Ji, Wei-Xiao; Li, Ping
2018-05-16
A large bulk band gap is critical for the application of two-dimensional topological insulators (TIs) in spintronic devices operating at room temperature. On the basis of first-principles calculations, we predict BiXH (X = OH, SH) monolayers as TIs with an extraordinarily large bulk gap of 820 meV for BiOH and 850 meV for BiSH, and propose a tight-binding model considering spin-orbit coupling to describe the electronic properties of BiXH. These large gaps are entirely due to the strong spin-orbit interaction related to the pxy orbitals of the Bi atoms of the honeycomb lattice. The orbital filtering mechanism can be used to understand the topological properties of BiXH. The XH groups simply remove one branch of orbitals (pz of Bi) and reduce the trivial 6-band lattice into a 4-band, which is topologically non-trivial. The topological characteristics of BiXH monolayers are confirmed by nonzero topological invariant Z2 and a single pair of gapless helical edge states in the bulk gap. Owing to these features, the BiXH monolayers of the large-gap TIs are an ideal platform to realize many exotic phenomena and fabricate new quantum devices working at room temperature.
Unusual Thermal Hall Effect in a Kitaev Spin Liquid Candidate α -RuCl3
Kasahara, Y.; Sugii, K.; Ohnishi, T.; Shimozawa, M.; Yamashita, M.; Kurita, N.; Tanaka, H.; Nasu, J.; Motome, Y.; Shibauchi, T.; Matsuda, Y.
2018-05-01
The Kitaev quantum spin liquid displays the fractionalization of quantum spins into Majorana fermions. The emergent Majorana edge current is predicted to manifest itself in the form of a finite thermal Hall effect, a feature commonly discussed in topological superconductors. Here we report on thermal Hall conductivity κx y measurements in α -RuCl3 , a candidate Kitaev magnet with the two-dimensional honeycomb lattice. In a spin-liquid (Kitaev paramagnetic) state below the temperature characterized by the Kitaev interaction JK/kB˜80 K , positive κx y develops gradually upon cooling, demonstrating the presence of highly unusual itinerant excitations. Although the zero-temperature property is masked by the magnetic ordering at TN=7 K , the sign, magnitude, and T dependence of κx y/T at intermediate temperatures follows the predicted trend of the itinerant Majorana excitations.
Quantized Hall conductance as a topological invariant
International Nuclear Information System (INIS)
Niu, Q.; Thouless, Ds.J.; Wu, Y.S.
1984-10-01
Whenever the Fermi level lies in a gap (or mobility gap) the bulk Hall conductance can be expressed in a topologically invariant form showing the quantization explicitly. The new formulation generalizes the earlier result by TKNN to the situation where many body interaction and substrate disorder are also present. When applying to the fractional quantized Hall effect we draw the conclusion that there must be a symmetry breaking in the many body ground state. The possibility of writing the fractionally quantized Hall conductance as a topological invariant is also carefully discussed. 19 references
Chen, S. W.; Song, L.
2016-08-01
The fractional acoustoelectric (AE) current plateau in surface-acoustic-waves (SAW) single-electron transport devices is studied by measuring the current plateau as a function of the SAW power and gate bias as well as a function of perpendicular magnetic filed. Our investigation indicates that the fractional plateau is induced by the tunnelling effect from the dynamic quantum dots (QDs) into a static impurity dot. Rate equations are used to extract the tunnelling rates, which change a lot with the number of electrons in the dynamic QDs, the SAW power and gate bias. In addition, the current plateau evolves into a fractional structure, when a strong perpendicular magnetic field is applied to the system.
Experimental halls workshop summary
International Nuclear Information System (INIS)
Thorndike, A.
1976-01-01
A brief discussion is given of: (1) pros and cons of open areas as compared with enclosed halls; (2) experimental hall needs of ep, anti p p, and other options; (3) hall for the lepton detector; and, (4) hall for the hadron spectrometer
Statistical distribution for generalized ideal gas of fractional-statistics particles
International Nuclear Information System (INIS)
Wu, Y.
1994-01-01
We derive the occupation-number distribution in a generalized ideal gas of particles obeying fractional statistics, including mutual statistics, by adopting a state-counting definition. When there is no mutual statistics, the statistical distribution interpolates between bosons and fermions, and respects a fractional exclusion principle (except for bosons). Anyons in a strong magnetic field at low temperatures constitute such a physical system. Applications to the thermodynamic properties of quasiparticle excitations in the Laughlin quantum Hall fluid are discussed
Experimental halls workshop summary
International Nuclear Information System (INIS)
Thorndike, A.
1976-01-01
On May 26 and 27, 1976, approximately 50 people met for an informal workshop on plans for experimental halls for ISABELLE. Plans as they exist in the May 1976 version of the ISABELLE proposal were presented. Discussions were held on the following four general topics by separate working groups: (1) pros and cons of open areas as compared with enclosed halls; (2) experimental hall needs of ep, anti pp, and other options; (3) hall for the lepton detector; and (4) hall for the hadron spectrometer. The planning for experimental halls at PEP, the hall for the lepton detector, the hadron spectrometer, and open areas are discussed
Quasi-one-dimensional Hall physics in the Harper–Hofstadter–Mott model
Kozarski, Filip; Hügel, Dario; Pollet, Lode
2018-04-01
We study the ground-state phase diagram of the strongly interacting Harper–Hofstadter–Mott model at quarter flux on a quasi-one-dimensional lattice consisting of a single magnetic flux quantum in y-direction. In addition to superfluid phases with various density patterns, the ground-state phase diagram features quasi-one-dimensional analogs of fractional quantum Hall phases at fillings ν = 1/2 and 3/2, where the latter is only found thanks to the hopping anisotropy and the quasi-one-dimensional geometry. At integer fillings—where in the full two-dimensional system the ground-state is expected to be gapless—we observe gapped non-degenerate ground-states: at ν = 1 it shows an odd ‘fermionic’ Hall conductance, while the Hall response at ν = 2 consists of the transverse transport of a single particle–hole pair, resulting in a net zero Hall conductance. The results are obtained by exact diagonalization and in the reciprocal mean-field approximation.
Measurement-only topological quantum computation via anyonic interferometry
International Nuclear Information System (INIS)
Bonderson, Parsa; Freedman, Michael; Nayak, Chetan
2009-01-01
We describe measurement-only topological quantum computation using both projective and interferometrical measurement of topological charge. We demonstrate how anyonic teleportation can be achieved using 'forced measurement' protocols for both types of measurement. Using this, it is shown how topological charge measurements can be used to generate the braiding transformations used in topological quantum computation, and hence that the physical transportation of computational anyons is unnecessary. We give a detailed discussion of the anyonics for implementation of topological quantum computation (particularly, using the measurement-only approach) in fractional quantum Hall systems
Experimental halls workshop summary
International Nuclear Information System (INIS)
Thorndike, A.
1976-01-01
At the experimental halls workshop, discussions were held on: (1) open areas as compared with enclosed halls; (2) the needs of ep, anti pp, and other options; (3) the hall for the lepton detector; and (4) the hall for the hadron spectrometer. The value of different possibilities for the future experimental program was explored. A number of suggestions emerged which will be used as the design of the experimental halls progresses
International Nuclear Information System (INIS)
Hatsugai, Y.; Kohmoto, M.
1992-01-01
We investigate the energy spectrum and the Hall effect of electrons on the square lattice with next-nearest-neighbor (NNN) hopping as well as nearest-neighbor hopping. General rational values of magnetic flux per unit cell φ=p/q are considered. In the absence of NNN hopping, the two bands at the center touch for q even, thus the Hall conductance is not well defined at half filling. An energy gap opens there by introducing NNN hoping. When φ=1/2, the NNN model coincides with the mean field Hamiltonian for the chiral spin state proposed by Wen, Wilczek and Zee (WWZ). The Hall conductance is calculated from the Diophantine equation and the E-φ diagram. We find that gaps close for other fillings at certain values of NNN hopping strength. The quantized value of the Hall conductance changes once this phenomenon occurs. In a mean field treatment of the t-J model, the effective Hamiltonian is the same as our NNN model. From this point of view, the statistics of the quasi-particles is not always semion and depends on the filling and the strength of the mean field. (orig.)
Fractional Charge Definitions and Conditions
Energy Technology Data Exchange (ETDEWEB)
Goldhaber, A.S.
2004-06-04
Fractional charge is known through theoretical and experimental discoveries of isolable objects carrying fractions of familiar charge units--electric charge Q, spin S, and the difference of baryon and lepton numbers B-L. With a few simple assumptions all these effects may be described using a generalized version of charge renormalization for locally conserved charges, in which medium correlations yield familiar adiabatic, continuous renormalization, or sometimes nonadiabatic, discrete renormalization. Fractional charges may be carried by fundamental particles or fundamental solitons. Either picture works for the simplest fractional-quantum-Hall-effect quasiholes, though the particle description is far more general. The only known fundamental solitons in three or fewer space dimensions d are the kink (d = 1), the vortex (d = 2), and the magnetic monopole (d = 3). Further, for a charge not intrinsically coupled to the topological charge of a soliton, only the kink and the monopole may carry fractional values. The same reasoning enforces fractional values of B-L for electrically charged elementary particles.
Fractional Charge Definitions and Conditions
International Nuclear Information System (INIS)
Goldhaber, A.S.
2004-01-01
Fractional charge is known through theoretical and experimental discoveries of isolable objects carrying fractions of familiar charge units--electric charge Q, spin S, and the difference of baryon and lepton numbers B-L. With a few simple assumptions all these effects may be described using a generalized version of charge renormalization for locally conserved charges, in which medium correlations yield familiar adiabatic, continuous renormalization, or sometimes nonadiabatic, discrete renormalization. Fractional charges may be carried by fundamental particles or fundamental solitons. Either picture works for the simplest fractional-quantum-Hall-effect quasiholes, though the particle description is far more general. The only known fundamental solitons in three or fewer space dimensions d are the kink (d = 1), the vortex (d = 2), and the magnetic monopole (d = 3). Further, for a charge not intrinsically coupled to the topological charge of a soliton, only the kink and the monopole may carry fractional values. The same reasoning enforces fractional values of B-L for electrically charged elementary particles
Quantization and hall effect: necessities and difficulties
International Nuclear Information System (INIS)
Ahmed Bouketir; Hishamuddin Zainuddin
1999-01-01
The quantization procedure is a necessary tool for a proper understanding of many interesting quantum phenomena in modern physics. In this note, we focus on geometrical framework for such procedures, particularly the group-theoretic approach and their difficulties. Finally we look through the example of Hall effect as a quantized macroscopic phenomenon with group-theoretic quantization approach. (author)
Nagaosa, Naoto; Sinova, Jairo; Onoda, Shigeki; MacDonald, A. H.; Ong, N. P.
2010-04-01
The anomalous Hall effect (AHE) occurs in solids with broken time-reversal symmetry, typically in a ferromagnetic phase, as a consequence of spin-orbit coupling. Experimental and theoretical studies of the AHE are reviewed, focusing on recent developments that have provided a more complete framework for understanding this subtle phenomenon and have, in many instances, replaced controversy by clarity. Synergy between experimental and theoretical works, both playing a crucial role, has been at the heart of these advances. On the theoretical front, the adoption of the Berry-phase concepts has established a link between the AHE and the topological nature of the Hall currents. On the experimental front, new experimental studies of the AHE in transition metals, transition-metal oxides, spinels, pyrochlores, and metallic dilute magnetic semiconductors have established systematic trends. These two developments, in concert with first-principles electronic structure calculations, strongly favor the dominance of an intrinsic Berry-phase-related AHE mechanism in metallic ferromagnets with moderate conductivity. The intrinsic AHE can be expressed in terms of the Berry-phase curvatures and it is therefore an intrinsic quantum-mechanical property of a perfect crystal. An extrinsic mechanism, skew scattering from disorder, tends to dominate the AHE in highly conductive ferromagnets. The full modern semiclassical treatment of the AHE is reviewed which incorporates an anomalous contribution to wave-packet group velocity due to momentum-space Berry curvatures and correctly combines the roles of intrinsic and extrinsic (skew-scattering and side-jump) scattering-related mechanisms. In addition, more rigorous quantum-mechanical treatments based on the Kubo and Keldysh formalisms are reviewed, taking into account multiband effects, and demonstrate the equivalence of all three linear response theories in the metallic regime. Building on results from recent experiment and theory, a
The Hall module of an exact category with duality
Young, Matthew B.
2012-01-01
We construct from a finitary exact category with duality a module over its Hall algebra, called the Hall module, encoding the first order self-dual extension structure of the category. We study in detail Hall modules arising from the representation theory of a quiver with involution. In this case we show that the Hall module is naturally a module over the specialized reduced sigma-analogue of the quantum Kac-Moody algebra attached to the quiver. For finite type quivers, we explicitly determin...
Electron quantum optics as quantum signal processing
Roussel, B.; Cabart, C.; Fève, G.; Thibierge, E.; Degiovanni, P.
2016-01-01
The recent developments of electron quantum optics in quantum Hall edge channels have given us new ways to probe the behavior of electrons in quantum conductors. It has brought new quantities called electronic coherences under the spotlight. In this paper, we explore the relations between electron quantum optics and signal processing through a global review of the various methods for accessing single- and two-electron coherences in electron quantum optics. We interpret electron quantum optics...
Dynamic response functions, helical gaps, and fractional charges in quantum wires
Meng, Tobias; Pedder, Christopher J.; Tiwari, Rakesh P.; Schmidt, Thomas L.
We show how experimentally accessible dynamic response functions can discriminate between helical gaps due to magnetic field, and helical gaps driven by electron-electron interactions (''umklapp gaps''). The latter are interesting since they feature gapped quasiparticles of fractional charge e / 2 , and - when coupled to a standard superconductor - an 8 π-Josephson effect and topological zero energy states bound to interfaces. National Research Fund, Luxembourg (ATTRACT 7556175), Deutsche Forschungsgemeinschaft (GRK 1621 and SFB 1143), Swiss National Science Foundation.
Hall conductance and topological invariant for open systems.
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.
Cryogenic microsize Hall sensors
International Nuclear Information System (INIS)
Kvitkovic, J.; Polak, M.
1993-01-01
Hall sensors have a variety of applications in magnetic field measurements. The active area of the Hall sensor does not play an important role in measuring of homogeneous magnetic field. Actually Hall sensors are widely used to measure profiles of magnetic fields produced by magnetization currents in samples of HTC superconductors, as well as of LTC ones. Similar techniques are used to measure magnetization of both HTC and LTC superconductors. In these cases Hall sensor operates in highly inhomogeneous magnetic fields. Because of that, Hall sensors with very small active area are required. We developed and tested Hall sensors with active area 100 μm x 100 μm - type M and 50 μm x 50 μm - type V. Here we report on the most imporant parameters of these units, as well as on their properties as differential magnetometer. (orig.)
Developments in Scanning Hall Probe Microscopy
Chouinard, Taras; Chu, Ricky; David, Nigel; Broun, David
2009-05-01
Low temperature scanning Hall probe microscopy is a sensitive means of imaging magnetic structures with high spatial resolution and magnetic flux sensitivity approaching that of a Superconducting Quantum Interference Device. We have developed a scanning Hall probe microscope with novel features, including highly reliable coarse positioning, in situ optimization of sensor-sample alignment and capacitive transducers for linear, long range positioning measurement. This has been motivated by the need to reposition accurately above fabricated nanostructures such as small superconducting rings. Details of the design and performance will be presented as well as recent progress towards time-resolved measurements with sub nanosecond resolution.
Fractional Schroedinger equation
International Nuclear Information System (INIS)
Laskin, Nick
2002-01-01
Some properties of the fractional Schroedinger equation are studied. We prove the Hermiticity of the fractional Hamilton operator and establish the parity conservation law for fractional quantum mechanics. As physical applications of the fractional Schroedinger equation we find the energy spectra of a hydrogenlike atom (fractional 'Bohr atom') and of a fractional oscillator in the semiclassical approximation. An equation for the fractional probability current density is developed and discussed. We also discuss the relationships between the fractional and standard Schroedinger equations
Resonant spin Hall effect in two dimensional electron gas
Shen, Shun-Qing
2005-03-01
Remarkable phenomena have been observed in 2DEG over last two decades, most notably, the discovery of integer and fractional quantum Hall effect. The study of spin transport provides a good opportunity to explore spin physics in two-dimensional electron gas (2DEG) with spin-orbit coupling and other interaction. It is already known that the spin-orbit coupling leads to a zero-field spin splitting, and competes with the Zeeman spin splitting if the system is subjected to a magnetic field perpendicular to the plane of 2DEG. The result can be detected as beating of the Shubnikov-de Haas oscillation. Very recently the speaker and his collaborators studied transport properties of a two-dimensional electron system with Rashba spin-orbit coupling in a perpendicular magnetic field. The spin-orbit coupling competes with the Zeeman splitting to generate additional degeneracies between different Landau levels at certain magnetic fields. It is predicted theoretically that this degeneracy, if occurring at the Fermi level, gives rise to a resonant spin Hall conductance, whose height is divergent as 1/T and whose weight is divergent as -lnT at low temperatures. The charge Hall conductance changes by 2e^2/h instead of e^2/h as the magnetic field changes through the resonant point. The speaker will address the resonance condition, symmetries in the spin-orbit coupling, the singularity of magnetic susceptibility, nonlinear electric field effect, the edge effect and the disorder effect due to impurities. This work was supported by the Research Grants Council of Hong Kong under Grant No.: HKU 7088/01P. *S. Q. Shen, M. Ma, X. C. Xie, and F. C. Zhang, Phys. Rev. Lett. 92, 256603 (2004) *S. Q. Shen, Y. J. Bao, M. Ma, X. C. Xie, and F. C. Zhang, cond-mat/0410169
Enhanced Performance of Cylindrical Hall Thrusters
International Nuclear Information System (INIS)
Raitses, Y.; Smirnov, A.; Fisch, N.J.
2007-01-01
The cylindrical thruster differs significantly in its underlying physical mechanisms from the conventional annular Hall thruster. It features high ionization efficiency, quiet operation, ion acceleration in a large volume-to-surface ratio channel, and performance comparable with the state-of-the-art conventional Hall thrusters. Very significant plume narrowing, accompanied by the increase of the energetic ion fraction and improvement of ion focusing, led to 50-60% increase of the thruster anode efficiency. These improvements were achieved by overrunning the discharge current in the magnetized thruster plasma
Li, Tingxin; Wang, Pengjie; Sullivan, Gerard; Lin, Xi; Du, Rui-Rui
2017-12-01
We report low-temperature transport measurements in strained InAs /G a0.68I n0.32Sb quantum wells, which supports time-reversal symmetry-protected helical edge states. The temperature and bias voltage dependence of the helical edge conductance for devices of various sizes are consistent with the theoretical expectation of a weakly interacting helical edge state. Moreover, we found that the magnetoresistance of the helical edge states is related to the edge interaction effect and the disorder strength.
Energy Technology Data Exchange (ETDEWEB)
Owerre, S. A., E-mail: solomon@aims.ac.za [African Institute for Mathematical Sciences, 6 Melrose Road, Muizenberg, Cape Town 7945, South Africa and Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo, Ontario N2L 2Y5 (Canada)
2016-07-28
Quite recently, the magnon Hall effect of spin excitations has been observed experimentally on the kagome and pyrochlore lattices. The thermal Hall conductivity κ{sup xy} changes sign as a function of magnetic field or temperature on the kagome lattice, and κ{sup xy} changes sign upon reversing the sign of the magnetic field on the pyrochlore lattice. Motivated by these recent exciting experimental observations, we theoretically propose a simple realization of the magnon Hall effect in a two-band model on the honeycomb lattice. The magnon Hall effect of spin excitations arises in the usual way via the breaking of inversion symmetry of the lattice, however, by a next-nearest-neighbour Dzyaloshinsky-Moriya interaction. We find that κ{sup xy} has a fixed sign for all parameter regimes considered. These results are in contrast to the Lieb, kagome, and pyrochlore lattices. We further show that the low-temperature dependence on the magnon Hall conductivity follows a T{sup 2} law, as opposed to the kagome and pyrochlore lattices. These results suggest an experimental procedure to measure thermal Hall conductivity within a class of 2D honeycomb quantum magnets and ultracold atoms trapped in a honeycomb optical lattice.
Hall effect in the two-dimensional Luttinger liquid
International Nuclear Information System (INIS)
Anderson, P.W.
1991-01-01
The temperature dependence of the Hall effect in the normal state is a commom theme of all the cuprate superconductors and has been one of the more puzzling observations on these puzzling materials. We describe a general scheme within the Luttinger liquid theory of these two-dimensional quantum fluids which corrrelates the anomalous Hall and resistivity observations on a wide variety of both pure and doped single crystals, especially the data in the accompanying Letter of Chien, Wang, and Ong
Quantum conductance staircase of holes in silicon nanosandwiches
Directory of Open Access Journals (Sweden)
Nikolay T. Bagraev
2017-03-01
Full Text Available The results of studying the quantum conductance staircase of holes in one-dimensional channels obtained by the split-gate method inside silicon nanosandwiches that are the ultra-narrow quantum well confined by the delta barriers heavily doped with boron on the n-type Si (100 surface are reported. Since the silicon quantum wells studied are ultra-narrow (~2 nm and confined by the delta barriers that consist of the negative-U dipole boron centers, the quantized conductance of one-dimensional channels is observed at relatively high temperatures (T>77 K. Further, the current-voltage characteristic of the quantum conductance staircase is studied in relation to the kinetic energy of holes and their sheet density in the quantum wells. The results show that the quantum conductance staircase of holes in p-Si quantum wires is caused by independent contributions of the one-dimensional (1D subbands of the heavy and light holes. In addition, the field-related inhibition of the quantum conductance staircase is demonstrated in the situation when the energy of the field-induced heating of the carriers become comparable to the energy gap between the 1D subbands. The use of the split-gate method made it possible to detect the effect of a drastic increase in the height of the quantum conductance steps when the kinetic energy of holes is increased; this effect is most profound for quantum wires of finite length, which are not described under conditions of a quantum point contact. In the concluding section of this paper we present the findings for the quantum conductance staircase of holes that is caused by the edge channels in the silicon nanosandwiches prepared within frameworks of the Hall geometry. This longitudinal quantum conductance staircase, Gxx, is revealed by the voltage applied to the Hall contacts, with the plateaus and steps that bring into correlation respectively with the odd and even fractional values.
International Nuclear Information System (INIS)
Buechler, Hans Peter; Calcarco, Tommaso; Dressel, Martin
2008-01-01
The following topics are dealt with: Artificial atoms and molecules, tailored from solids, fractional flux quanta, molecular magnets, controlled interaction in quantum gases, the theory of quantum correlations in mott matter, cold gases, and mesoscopic systems, Bose-Einstein condensates on the chip, on the route to the quantum computer, a quantum computer in diamond. (HSI)
National Oceanic and Atmospheric Administration, Department of Commerce — Salt marsh habitats along the shoreline of Halls Lake are threatened by wave erosion, but the reconstruction of barrier islands to reduce this erosion will modify or...
Spontaneous Hall effect in a chiral p-wave superconductor
Furusaki, Akira; Matsumoto, Masashige; Sigrist, Manfred
2001-08-01
In a chiral superconductor with broken time-reversal symmetry a ``spontaneous Hall effect'' may be observed. We analyze this phenomenon by taking into account the surface properties of a chiral superconductor. We identify two main contributions to the spontaneous Hall effect. One contribution originates from the Bernoulli (or Lorentz) force due to spontaneous currents running along the surfaces of the superconductor. The other contribution has a topological origin and is related to the intrinsic angular momentum of Cooper pairs. The latter can be described in terms of a Chern-Simons-like term in the low-energy field theory of the superconductor and has some similarities with the quantum Hall effect. The spontaneous Hall effect in a chiral superconductor is, however, nonuniversal. Our analysis is based on three approaches to the problem: a self-consistent solution of the Bogoliubov-de Gennes equation, a generalized Ginzburg-Landau theory, and a hydrodynamic formulation. All three methods consistently lead to the same conclusion that the spontaneous Hall resistance of a two-dimensional superconducting Hall bar is of order h/(ekFλ)2, where kF is the Fermi wave vector and λ is the London penetration depth; the Hall resistance is substantially suppressed from a quantum unit of resistance. Experimental issues in measuring this effect are briefly discussed.
Modeling electron fractionalization with unconventional Fock spaces.
Cobanera, Emilio
2017-08-02
It is shown that certain fractionally-charged quasiparticles can be modeled on D-dimensional lattices in terms of unconventional yet simple Fock algebras of creation and annihilation operators. These unconventional Fock algebras are derived from the usual fermionic algebra by taking roots (the square root, cubic root, etc) of the usual fermionic creation and annihilation operators. If the fermions carry non-Abelian charges, then this approach fractionalizes the Abelian charges only. In particular, the mth-root of a spinful fermion carries charge e/m and spin 1/2. Just like taking a root of a complex number, taking a root of a fermion yields a mildly non-unique result. As a consequence, there are several possible choices of quantum exchange statistics for fermion-root quasiparticles. These choices are tied to the dimensionality [Formula: see text] of the lattice by basic physical considerations. One particular family of fermion-root quasiparticles is directly connected to the parafermion zero-energy modes expected to emerge in certain mesoscopic devices involving fractional quantum Hall states. Hence, as an application of potential mesoscopic interest, I investigate numerically the hybridization of Majorana and parafermion zero-energy edge modes caused by fractionalizing but charge-conserving tunneling.
Energy Technology Data Exchange (ETDEWEB)
Gardner, Geoffrey C. [Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907 (United States); School of Materials Engineering, Purdue University, West Lafayette, Indiana 47907 (United States); Watson, John D.; Mondal, Sumit [Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907 (United States); Department of Physics, Purdue University, West Lafayette, Indiana 47907 (United States); Deng, Nianpei; Csathy, Gabor A. [Department of Physics, Purdue University, West Lafayette, Indiana 47907 (United States); Manfra, Michael J. [Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907 (United States); School of Materials Engineering, Purdue University, West Lafayette, Indiana 47907 (United States); Department of Physics, Purdue University, West Lafayette, Indiana 47907 (United States); School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907 (United States)
2013-06-24
We report on the growth and electrical characterization of modulation-doped Al{sub 0.24}Ga{sub 0.76}As/Al{sub x}Ga{sub 1-x}As/Al{sub 0.24}Ga{sub 0.76}As quantum wells with mole fractions as low as x = 0.00057. Such structures will permit detailed studies of the impact of alloy disorder in the fractional quantum Hall regime. At zero magnetic field, we extract an alloy scattering rate of 24 ns{sup -1} per%Al. Additionally, we find that for x as low as 0.00057 in the quantum well, alloy scattering becomes the dominant mobility-limiting scattering mechanism in ultra-high purity two-dimensional electron gases typically used to study the fragile {nu} = 5/2 and {nu} = 12/5 fractional quantum Hall states.
Coulomb drag: a probe of electron interactions in coupled quantum wells
DEFF Research Database (Denmark)
Jauho, Antti-Pekka
1996-01-01
As semiconductor devices shrink in size and in dimensionality, interactions between charge carriers become more and more important. There is a simple physical reason behind this behavior: fewer carriers lead to less effective screening, and hence stronger effective interactions. A point in case...... are one-dimensional systems (quantum wires): there electron-electron interactions may lead to a behavior, which is qualitatively different from the standard Fermi liquid picture (Luttinger liquids). Electron-electron interactions also play a central role in the fractional quantum Hall effect, which...... be the study of quantum wires: there the interactions may lead to even more dramatic effects...
Cooperative ring exchange and quantum melting of vortex lattices in atomic Bose-Einstein condensates
International Nuclear Information System (INIS)
Ghosh, Tarun Kanti; Baskaran, G.
2004-01-01
Cooperative ring exchange is suggested as a mechanism of quantum melting of vortex lattices in a rapidly rotating quasi-two-dimensional atomic Bose-Einstein condensate (BEC). Using an approach pioneered by Kivelson et al. [Phys. Rev. Lett. 56, 873 (1986)] for the fractional quantized Hall effect, we calculate the condition for quantum melting instability by considering large-correlated ring exchanges in a two-dimensional Wigner crystal of vortices in a strong 'pseudomagnetic field' generated by the background superfluid Bose particles. BEC may be profitably used to address issues of quantum melting of a pristine Wigner solid devoid of complications of real solids
Al-Khalili, Jim
2003-01-01
In this lively look at quantum science, a physicist takes you on an entertaining and enlightening journey through the basics of subatomic physics. Along the way, he examines the paradox of quantum mechanics--beautifully mathematical in theory but confoundingly unpredictable in the real world. Marvel at the Dual Slit experiment as a tiny atom passes through two separate openings at the same time. Ponder the peculiar communication of quantum particles, which can remain in touch no matter how far apart. Join the genius jewel thief as he carries out a quantum measurement on a diamond without ever touching the object in question. Baffle yourself with the bizzareness of quantum tunneling, the equivalent of traveling partway up a hill, only to disappear then reappear traveling down the opposite side. With its clean, colorful layout and conversational tone, this text will hook you into the conundrum that is quantum mechanics.
Quantum field theory in 2+1 dimensions
International Nuclear Information System (INIS)
Marino, E.C.
1998-01-01
An introductory review is made of many outstanding features of Quantum Field Theory formulated in three-dimensional spacetime. These include topological properties, the Huygens Principle, the Coulomb potential, topological excitations like vortices and skyrmions, dynamical mass generation, fractional spin and statistics, duality nd bosonization. Theories including the Maxwell-Chern-Simons, Abelian Higgs and C P 1 -Nonlinear Sigma Model are used to illustrate the different features. Applications to High-T c Superconductivity and to the Quantum Hall Effect are also presented. (author)
Can one trust quantum simulators?
International Nuclear Information System (INIS)
Hauke, Philipp; Cucchietti, Fernando M; Tagliacozzo, Luca; Lewenstein, Maciej; Deutsch, Ivan
2012-01-01
Various fundamental phenomena of strongly correlated quantum systems such as high-T c superconductivity, the fractional quantum-Hall effect and quark confinement are still awaiting a universally accepted explanation. The main obstacle is the computational complexity of solving even the most simplified theoretical models which are designed to capture the relevant quantum correlations of the many-body system of interest. In his seminal 1982 paper (Feynman 1982 Int. J. Theor. Phys. 21 467), Richard Feynman suggested that such models might be solved by ‘simulation’ with a new type of computer whose constituent parts are effectively governed by a desired quantum many-body dynamics. Measurements on this engineered machine, now known as a ‘quantum simulator,’ would reveal some unknown or difficult to compute properties of a model of interest. We argue that a useful quantum simulator must satisfy four conditions: relevance, controllability, reliability and efficiency. We review the current state of the art of digital and analog quantum simulators. Whereas so far the majority of the focus, both theoretically and experimentally, has been on controllability of relevant models, we emphasize here the need for a careful analysis of reliability and efficiency in the presence of imperfections. We discuss how disorder and noise can impact these conditions, and illustrate our concerns with novel numerical simulations of a paradigmatic example: a disordered quantum spin chain governed by the Ising model in a transverse magnetic field. We find that disorder can decrease the reliability of an analog quantum simulator of this model, although large errors in local observables are introduced only for strong levels of disorder. We conclude that the answer to the question ‘Can we trust quantum simulators?’ is … to some extent. (key issues reviews)
Can one trust quantum simulators?
Hauke, Philipp; Cucchietti, Fernando M.; Tagliacozzo, Luca; Deutsch, Ivan; Lewenstein, Maciej
2012-08-01
Various fundamental phenomena of strongly correlated quantum systems such as high-Tc superconductivity, the fractional quantum-Hall effect and quark confinement are still awaiting a universally accepted explanation. The main obstacle is the computational complexity of solving even the most simplified theoretical models which are designed to capture the relevant quantum correlations of the many-body system of interest. In his seminal 1982 paper (Feynman 1982 Int. J. Theor. Phys. 21 467), Richard Feynman suggested that such models might be solved by ‘simulation’ with a new type of computer whose constituent parts are effectively governed by a desired quantum many-body dynamics. Measurements on this engineered machine, now known as a ‘quantum simulator,’ would reveal some unknown or difficult to compute properties of a model of interest. We argue that a useful quantum simulator must satisfy four conditions: relevance, controllability, reliability and efficiency. We review the current state of the art of digital and analog quantum simulators. Whereas so far the majority of the focus, both theoretically and experimentally, has been on controllability of relevant models, we emphasize here the need for a careful analysis of reliability and efficiency in the presence of imperfections. We discuss how disorder and noise can impact these conditions, and illustrate our concerns with novel numerical simulations of a paradigmatic example: a disordered quantum spin chain governed by the Ising model in a transverse magnetic field. We find that disorder can decrease the reliability of an analog quantum simulator of this model, although large errors in local observables are introduced only for strong levels of disorder. We conclude that the answer to the question ‘Can we trust quantum simulators?’ is … to some extent.
Zhang, Run-Wu; Liu, Cheng-Cheng; Ma, Da-Shuai; Yao, Yugui
2018-03-01
Two-dimensional (2D) topological insulators (TIs) have attracted tremendous research interest from both the theoretical and the experimental fields in recent years. However, it is much less investigated in realizing node line (NL) semimetals in 2D materials. Combining first-principles calculations and symmetry analysis, we find that NL phases emerge in p -CS2 and p -SiS2 , as well as other pentagonal IVX2 films, i.e., p -IVX2 (IV= C, Si, Ge, Sn, Pb; X=S, Se, Te) in the absence of spin-orbit coupling (SOC). The NLs in p -IVX2 consist of symbolic Fermi loops centered around the Γ point and are protected by mirror reflection symmetry. As the atomic number is downward shifted, the NL semimetals are driven into 2D TIs with the large bulk gap up to 0.715 eV induced by the remarkable SOC effect. The nontrivial bulk gap can be tunable under external biaxial strain and uniaxial strain. Moreover, we also propose a quantum well by sandwiching a p -PbTe2 crystal between two NaI sheets in which p -PbTe2 still keeps its nontrivial topology with a sizable band gap (˜0.5 eV). These findings provide a new 2D material platform for exploring fascinating physics in both NL semimetals and TIs.
Intrinsic superspin Hall current
Linder, Jacob; Amundsen, Morten; Risinggârd, Vetle
2017-09-01
We discover an intrinsic superspin Hall current: an injected charge supercurrent in a Josephson junction containing heavy normal metals and a ferromagnet generates a transverse spin supercurrent. There is no accompanying dissipation of energy, in contrast to the conventional spin Hall effect. The physical origin of the effect is an antisymmetric spin density induced among transverse modes ky near the interface of the superconductor arising due to the coexistence of p -wave and conventional s -wave superconducting correlations with a belonging phase mismatch. Our predictions can be tested in hybrid structures including thin heavy metal layers combined with strong ferromagnets and ordinary s -wave superconductors.
Random operators disorder effects on quantum spectra and dynamics
Aizenman, Michael
2015-01-01
This book provides an introduction to the mathematical theory of disorder effects on quantum spectra and dynamics. Topics covered range from the basic theory of spectra and dynamics of self-adjoint operators through Anderson localization-presented here via the fractional moment method, up to recent results on resonant delocalization. The subject's multifaceted presentation is organized into seventeen chapters, each focused on either a specific mathematical topic or on a demonstration of the theory's relevance to physics, e.g., its implications for the quantum Hall effect. The mathematical chapters include general relations of quantum spectra and dynamics, ergodicity and its implications, methods for establishing spectral and dynamical localization regimes, applications and properties of the Green function, its relation to the eigenfunction correlator, fractional moments of Herglotz-Pick functions, the phase diagram for tree graph operators, resonant delocalization, the spectral statistics conjecture, and rela...
Energy Technology Data Exchange (ETDEWEB)
Kohandani, R; Kaatuzian, H [Photonics Research Laboratory, Electrical Engineering Department, AmirKabir University of Technology, Hafez Ave., Tehran (Iran, Islamic Republic of)
2015-01-31
We report a theoretical study of optical properties of AlGaAs/GaAs multiple quantum-well (MQW), slow-light devices based on excitonic population oscillations under applied external magnetic and electric fields using an analytical model for complex dielectric constant of Wannier excitons in fractional dimension. The results are shown for quantum wells (QWs) of different width. The significant characteristics of the exciton in QWs such as exciton energy and exciton oscillator strength (EOS) can be varied by application of external magnetic and electric fields. It is found that a higher bandwidth and an appropriate slow-down factor (SDF) can be achieved by changing the QW width during the fabrication process and by applying magnetic and electric fields during device functioning, respectively. It is shown that a SDF of 10{sup 5} is obtained at best. (slowing of light)
A model study of present-day Hall-effect circulators
Energy Technology Data Exchange (ETDEWEB)
Placke, B. [RWTH Aachen University, Institute for Quantum Information, Aachen (Germany); Bosco, S. [RWTH Aachen University, Institute for Quantum Information, Aachen (Germany); Juelich-Aachen Research Alliance (JARA), Fundamentals of Future Information Technologiesh, Juelich (Germany); DiVincenzo, D.P. [RWTH Aachen University, Institute for Quantum Information, Aachen (Germany); Juelich-Aachen Research Alliance (JARA), Fundamentals of Future Information Technologiesh, Juelich (Germany); Peter Gruenberg Institute, Theoretical Nanoelectronics, Forschungszentrum Juelich, Juelich (Germany)
2017-12-15
Stimulated by the recent implementation of a three-port Hall-effect microwave circulator of Mahoney et al. (MEA), we present model studies of the performance of this device. Our calculations are based on the capacitive-coupling model of Viola and DiVincenzo (VD). Based on conductance data from a typical Hall-bar device obtained from a two-dimensional electron gas (2DEG) in a magnetic field, we numerically solve the coupled field-circuit equations to calculate the expected performance of the circulator, as determined by the S parameters of the device when coupled to 50Ω ports, as a function of frequency and magnetic field. Above magnetic fields of 1.5 T, for which a typical 2DEG enters the quantum Hall regime (corresponding to a Landau-level filling fraction ν of 20), the Hall angle θ{sub H} = tan{sup -1} σ{sub xy}/σ{sub xx} always remains close to 90 , and the S parameters are close to the analytic predictions of VD for θ{sub H} = π/2. As anticipated by VD, MEA find the device to have rather high (kΩ) impedance, and thus to be extremely mismatched to 50Ω, requiring the use of impedance matching. We incorporate the lumped matching circuits of MEA in our modeling and confirm that they can produce excellent circulation, although confined to a very small bandwidth. We predict that this bandwidth is significantly improved by working at lower magnetic field when the Landau index is high, e.g. ν = 20, and the impedance mismatch is correspondingly less extreme. Our modeling also confirms the observation of MEA that parasitic port-to-port capacitance can produce very interesting countercirculation effects. (orig.)
A model study of present-day Hall-effect circulators
International Nuclear Information System (INIS)
Placke, B.; Bosco, S.; DiVincenzo, D.P.
2017-01-01
Stimulated by the recent implementation of a three-port Hall-effect microwave circulator of Mahoney et al. (MEA), we present model studies of the performance of this device. Our calculations are based on the capacitive-coupling model of Viola and DiVincenzo (VD). Based on conductance data from a typical Hall-bar device obtained from a two-dimensional electron gas (2DEG) in a magnetic field, we numerically solve the coupled field-circuit equations to calculate the expected performance of the circulator, as determined by the S parameters of the device when coupled to 50Ω ports, as a function of frequency and magnetic field. Above magnetic fields of 1.5 T, for which a typical 2DEG enters the quantum Hall regime (corresponding to a Landau-level filling fraction ν of 20), the Hall angle θ_H = tan"-"1 σ_x_y/σ_x_x always remains close to 90 , and the S parameters are close to the analytic predictions of VD for θ_H = π/2. As anticipated by VD, MEA find the device to have rather high (kΩ) impedance, and thus to be extremely mismatched to 50Ω, requiring the use of impedance matching. We incorporate the lumped matching circuits of MEA in our modeling and confirm that they can produce excellent circulation, although confined to a very small bandwidth. We predict that this bandwidth is significantly improved by working at lower magnetic field when the Landau index is high, e.g. ν = 20, and the impedance mismatch is correspondingly less extreme. Our modeling also confirms the observation of MEA that parasitic port-to-port capacitance can produce very interesting countercirculation effects. (orig.)
Fractional Solitons in Excitonic Josephson Junctions
Su, Jung-Jung; Hsu, Ya-Fen
The Josephson effect is especially appealing because it reveals macroscopically the quantum order and phase. Here we study this effect in an excitonic Josephson junction: a conjunct of two exciton condensates with a relative phase ϕ0 applied. Such a junction is proposed to take place in the quantum Hall bilayer (QHB) that makes it subtler than in superconductor because of the counterflow of excitonic supercurrent and the interlayer tunneling in QHB. We treat the system theoretically by first mapping it into a pseudospin ferromagnet then describing it by the Landau-Lifshitz-Gilbert equation. In the presence of interlayer tunneling, the excitonic Josephson junction can possess a family of fractional sine-Gordon solitons that resemble the static fractional Josephson vortices in the extended superconducting Josephson junctions. Interestingly, each fractional soliton carries a topological charge Q which is not necessarily a half/full integer but can vary continuously. The resultant current-phase relation (CPR) shows that solitons with Q =ϕ0 / 2 π are the lowest energy states for small ϕ0. When ϕ0 > π , solitons with Q =ϕ0 / 2 π - 1 take place - the polarity of CPR is then switched.
International Nuclear Information System (INIS)
Avdonin, A.; Skupiński, P.; Grasza, K.
2016-01-01
A simple description of the Hall effect in the hopping regime of conductivity in semiconductors is presented. Expressions for the Hall coefficient and Hall mobility are derived by considering averaged equilibrium electron transport in a single triangle of localization sites in a magnetic field. Dependence of the Hall coefficient is analyzed in a wide range of temperature and magnetic field values. Our theoretical result is applied to our experimental data on temperature dependence of Hall effect and Hall mobility in ZnO. - Highlights: • Expressions for Hall coefficient and mobility for hopping conductivity are derived. • Theoretical result is compared with experimental curves measured on ZnO. • Simultaneous action of free and hopping conduction channels is considered. • Non-linearity of hopping Hall coefficient is predicted.
Energy Technology Data Exchange (ETDEWEB)
Avdonin, A., E-mail: avdonin@ifpan.edu.pl [Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warszawa (Poland); Skupiński, P. [Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warszawa (Poland); Grasza, K. [Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warszawa (Poland); Institute of Electronic Materials Technology, ul. Wólczyńska 133, 01-919 Warszawa (Poland)
2016-02-15
A simple description of the Hall effect in the hopping regime of conductivity in semiconductors is presented. Expressions for the Hall coefficient and Hall mobility are derived by considering averaged equilibrium electron transport in a single triangle of localization sites in a magnetic field. Dependence of the Hall coefficient is analyzed in a wide range of temperature and magnetic field values. Our theoretical result is applied to our experimental data on temperature dependence of Hall effect and Hall mobility in ZnO. - Highlights: • Expressions for Hall coefficient and mobility for hopping conductivity are derived. • Theoretical result is compared with experimental curves measured on ZnO. • Simultaneous action of free and hopping conduction channels is considered. • Non-linearity of hopping Hall coefficient is predicted.
Granberg, Donald; Brown, Thad A.
1995-01-01
Examines people's behavior in the Monty Hall Dilemma (MHD), in which a person must make two decisions to win a prize. In a series of five studies, found that people misapprehend probabilities in the MHD. Discusses the MHD's relation to illusion of control, belief perseverance, and the status quo bias. (RJM)
Laurent Guiraud
2000-01-01
General view of the Isotope-Separator On-Line (ISOLDE) hall. ISOLDE is dedicated to the production of a large variety of radioactive ion beams for many different experiments. Rare isotopes can be produced allowing the study of spectra for neutrino beam production.
Oguntoyinbo, Lekan
2011-01-01
Many urban and commuter universities have their sights set on students who are unlikely to connect with the college and likely to fail unless the right strategies are put in place to help them graduate. In efforts to improve retention rates, commuter colleges are looking to an unusual suspect: residence halls. The author discusses how these…
Czech Academy of Sciences Publication Activity Database
Nagaosa, N.; Sinova, Jairo; Onoda, S.; MacDonald, A. H.; Ong, N. P.
2010-01-01
Roč. 82, č. 2 (2010), s. 1539-1592 ISSN 0034-6861 Institutional research plan: CEZ:AV0Z10100521 Keywords : anomalous Hall effect * spintronics Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 51.695, year: 2010
Giant Planar Hall Effect in the Dirac Semimetal ZrTe5
Li, Peng; Zhang, Chenhui; Zhang, Junwei; Wen, Yan; Zhang, Xixiang
2018-01-01
Exploration and understanding of exotic topics in quantum physics such as Dirac and Weyl semimetals have become highly popular in the area of condensed matter. It has recently been predicted that a theoretical giant planar Hall effect can be induced
Lu, Y. M.; Cai, J. W.; Guo, Zaibing; Zhang, Xixiang
2013-01-01
Pt films. The relationship between electron transport and temperature reveals a quantitatively insignificant Coulomb interaction in these films, while the temperature dependent anomalous Hall conductivity experiences quantum correction from electron
International Nuclear Information System (INIS)
Lederman, L.M.; Carrigan, R.A. Jr.
1987-01-01
This paper estimates the fraction of the economic activity that makes use of quantum mechanical devices. The questionable methodology estimates the fraction of a given economic activity which uses post-atomic technology. The scheme arrives at 23% over a given set of direct activities. Scientist in a curiosity-driven quest for an understanding of what, in 1900, was a dimly conceived exotic concept, stimulated, by their discoveries, economic acitivity amounting to about $1000 billion (in 1987 dollars) of our annual GNP, which is about $4 trillion. One quarter of this part of the GNP, or $280 billion, is paid back to the federal government in taxes annually. This number can be very wrong, but still be an impressive return from science, compared to the $10 billions of federal funding which OMB defines as basic research. 1 figure
Temporal Quantum Fluctuations of Current in Nano-structures
International Nuclear Information System (INIS)
Saminadayar, Laurent
1997-01-01
In a mesoscopic conductor, the transport of current is coherent: the associated wave of the electrons keeps a well-defined phase, so that one can observe interference effects. Transport in this regime has been extensively studied in the last decade, and the main features are well understood. In this thesis, we did focus on another aspect of the quantum transport, the noise. The purpose is to detect the fluctuations of the current around its average value. Our work is divided in three parts: first, we have measured shot noise in a quantum point contact. Shot-noise is due to the granularity of the charge. In a classical conductor, it is directly related to the current. We have shown that in a quantum conductor, such as a quantum point contact, quantum correlation due to the Pauli principle reduce the shot-noise, and that it can even be suppressed under certain conditions. In a second part, we did use the fact that shot-noise is sensitive to the charge of the carriers to detect the fractionally charged quasiparticles of the quantum Hall effect. The existence of the quasiparticles has been predicted since 1983, but no experimental observation has been reported up to now. By inducing a current of quasiparticles between the two edges of a sample in the fractional quantum Hall effect regime, and by measuring the noise associated with this current, we have proved it to be SI=2(e/3)I. This is actually a direct measurement of the charge of the carriers in the fractional quantum Hall regime, which is found to be e*=e/3 as predicted by the theory. Finally, the third part of our work is devoted to a subject closer to the applied physics, namely the measurement of low frequency noise in quantum dots. As quantum systems are more and more studied for potential applications, it is crucial to characterize the low frequency noise ('1/f' noise). We have found that this is due to free charges moving on the substrate around the dot, and that any improvement of the noise of
Sinova, Jairo; Valenzuela, Sergio O.; Wunderlich, J.; Back, C. H.; Jungwirth, T.
2015-10-01
Spin Hall effects are a collection of relativistic spin-orbit coupling phenomena in which electrical currents can generate transverse spin currents and vice versa. Despite being observed only a decade ago, these effects are already ubiquitous within spintronics, as standard spin-current generators and detectors. Here the theoretical and experimental results that have established this subfield of spintronics are reviewed. The focus is on the results that have converged to give us the current understanding of the phenomena, which has evolved from a qualitative to a more quantitative measurement of spin currents and their associated spin accumulation. Within the experimental framework, optical-, transport-, and magnetization-dynamics-based measurements are reviewed and linked to both phenomenological and microscopic theories of the effect. Within the theoretical framework, the basic mechanisms in both the extrinsic and intrinsic regimes are reviewed, which are linked to the mechanisms present in their closely related phenomenon in ferromagnets, the anomalous Hall effect. Also reviewed is the connection to the phenomenological treatment based on spin-diffusion equations applicable to certain regimes, as well as the spin-pumping theory of spin generation used in many measurements of the spin Hall angle. A further connection to the spin-current-generating spin Hall effect to the inverse spin galvanic effect is given, in which an electrical current induces a nonequilibrium spin polarization. This effect often accompanies the spin Hall effect since they share common microscopic origins. Both can exhibit the same symmetries when present in structures comprising ferromagnetic and nonmagnetic layers through their induced current-driven spin torques or induced voltages. Although a short chronological overview of the evolution of the spin Hall effect field and the resolution of some early controversies is given, the main body of this review is structured from a pedagogical
International Nuclear Information System (INIS)
Chwiej, T; Szafran, B
2013-01-01
We study electron transfer across a two-terminal quantum ring using a time-dependent description of the scattering process. For the considered scattering event the quantum ring is initially charged with one or two electrons, with another electron incident to the ring from the input channel. We study the electron transfer probability (T) as a function of the external magnetic field. We determine the periodicity of T for a varied number of electrons confined within the ring. For that purpose we develop a method to describe the wave packet dynamics for a few electrons participating in the scattering process, taking into full account the electron–electron correlations. We find that electron transfer across the quantum ring initially charged by a single electron acquires a distinct periodicity of half of the magnetic flux quantum (Φ 0 /2), corresponding to the formation of a transient two-electron state inside the ring. In the case of a three-electron scattering problem with two electrons initially occupying the ring, a period of Φ 0 /3 for T is formed in the limit of thin channels. The effect of disorder present in the confinement potential of the ring is also discussed. (paper)
Chwiej, T; Szafran, B
2013-04-17
We study electron transfer across a two-terminal quantum ring using a time-dependent description of the scattering process. For the considered scattering event the quantum ring is initially charged with one or two electrons, with another electron incident to the ring from the input channel. We study the electron transfer probability (T) as a function of the external magnetic field. We determine the periodicity of T for a varied number of electrons confined within the ring. For that purpose we develop a method to describe the wave packet dynamics for a few electrons participating in the scattering process, taking into full account the electron-electron correlations. We find that electron transfer across the quantum ring initially charged by a single electron acquires a distinct periodicity of half of the magnetic flux quantum (Φ0/2), corresponding to the formation of a transient two-electron state inside the ring. In the case of a three-electron scattering problem with two electrons initially occupying the ring, a period of Φ0/3 for T is formed in the limit of thin channels. The effect of disorder present in the confinement potential of the ring is also discussed.
Hall Conductivity in a Quasi-Two-Dimensional Disordered Electron System
Institute of Scientific and Technical Information of China (English)
YANG Yong-Hong; WANG Yong-Gang; LIU Mei
2002-01-01
By making use of the diagrammatic techniques in perturbation theory,we have investigated the Hall effect in a quasi-two-dimensional disordered electron system.In the weakly localized regime,the analytical expression for quantum correction to Hall conductivity has been obtained using the Kubo formalism and quasiclassical approximation.The relevant dimensional crossover behavior from three dimensions to two dimensions with decreasing the interlayer hopping energy is discussed.The quantum interference effect is shown to have a vanishing correction t,o the Hall coefficient.
Energy Technology Data Exchange (ETDEWEB)
1984-08-01
This report demonstrates the economic viability of an exterior rewrap retrofit performed on a public community facility for the performing arts. This facility originally consisted of two mess halls built by the American army. The exterior retrofit consisted of constructing a super-insulated passageway to link the two halls as well as completely wrapping the facility with six millimetre polyethylene to provide an airtight barrier. The roofs and walls were reinsulated and insulation levels were increased to RSI 10.5 in the ceilings and RSI 7.7 in the walls. The installation of a propane fuelled furnace was also included in the retrofit package. Prior to the renovations and retrofitting, the Guild Hall facility was almost unusable. The demonstration project transformed the cold, drafty buildings into an attractive, comfortable and functional centre for the performing arts. Heating requirements have been reduced to 500 MJ/m {sup 2} of floor space annually compared to a predicted 1,760 MJ/m{sup 2} of floor space based on HOTCAN analysis of the heating requirements without the energy conservation measures. 9 figs., 10 tabs.
Magnetic anisotrpy in quantum Hall feromagnets
Czech Academy of Sciences Publication Activity Database
Jungwirth, Tomáš; Shlukla, S. P.; Smrčka, Ludvík; Shayegan, M.; MacDonald, A. H.
1998-01-01
Roč. 81, č. 11 (1998), s. 2328-2331 ISSN 0031-9007 R&D Projects: GA ČR GA202/98/0085; GA MŠk ME 104 Grant - others:NSF GRANTS(US) INT-9602140; NSF GRANTS(US) DMR-9623511 Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 6.017, year: 1998
Fractional charge and inter-Landau-level states at points of singular curvature.
Biswas, Rudro R; Son, Dam Thanh
2016-08-02
The quest for universal properties of topological phases is fundamentally important because these signatures are robust to variations in system-specific details. Aspects of the response of quantum Hall states to smooth spatial curvature are well-studied, but challenging to observe experimentally. Here we go beyond this prevailing paradigm and obtain general results for the response of quantum Hall states to points of singular curvature in real space; such points may be readily experimentally actualized. We find, using continuum analytical methods, that the point of curvature binds an excess fractional charge and sequences of quantum states split away, energetically, from the degenerate bulk Landau levels. Importantly, these inter-Landau-level states are bound to the topological singularity and have energies that are universal functions of bulk parameters and the curvature. Our exact diagonalization of lattice tight-binding models on closed manifolds demonstrates that these results continue to hold even when lattice effects are significant. An important technological implication of these results is that these inter-Landau-level states, being both energetically and spatially isolated quantum states, are promising candidates for constructing qubits for quantum computation.
Generic superweak chaos induced by Hall effect
Ben-Harush, Moti; Dana, Itzhack
2016-05-01
We introduce and study the "kicked Hall system" (KHS), i.e., charged particles periodically kicked in the presence of uniform magnetic (B ) and electric (E ) fields that are perpendicular to each other and to the kicking direction. We show that for resonant values of B and E and in the weak-chaos regime of sufficiently small nonintegrability parameter κ (the kicking strength), there exists a generic family of periodic kicking potentials for which the Hall effect from B and E significantly suppresses the weak chaos, replacing it by "superweak" chaos (SWC). This means that the system behaves as if the kicking strength were κ2 rather than κ . For E =0 , SWC is known to be a classical fingerprint of quantum antiresonance, but it occurs under much less generic conditions, in particular only for very special kicking potentials. Manifestations of SWC are a decrease in the instability of periodic orbits and a narrowing of the chaotic layers, relative to the ordinary weak-chaos case. Also, for global SWC, taking place on an infinite "stochastic web" in phase space, the chaotic diffusion on the web is much slower than the weak-chaos one. Thus, the Hall effect can be relatively stabilizing for small κ . In some special cases, the effect is shown to cause ballistic motion for almost all parameter values. The generic global SWC on stochastic webs in the KHS appears to be the two-dimensional closest analog to the Arnol'd web in higher dimensional systems.