We consider spin-polarized electrons in a single Landau level on a cylinder as the circumference of the cylinder goes to infinity. This gives a model of interacting electrons on a circle where the momenta of the particles are restricted and there is no kinetic energy. Quantum Hall states are exact ground states for appropriate short range interactions, and there is a gap to excitations. These states develop adiabatically from this one-dimensional quantum Hall circle to the bulk quantum Hall states and further on into the Tao-Thouless states as the circumference goes to zero. For low filling fractions a gapless state is formed which we suggest is connected to the Wigner crystal expected in the bulk.
Low-energy transport measurements in Quantum Hall systems have been argued to be governed by emergent modular symmetries whose predictions are robust against many of the detailed microscopic dynamics. We propose the recently-observed quantum Hall effect in graphene as a test of these ideas, and identify to this end a class of predictions for graphene which would follow from the same modular arguments. We are led to a suite of predictions for high mobility samples that differs from those obtained for the conventional quantum Hall effect in semiconductors, including: predictions for the location…
There is considerable experimental evidence for the existence in Quantum Hall systems of an approximate emergent discrete symmetry, $Γ_0(2) \subset SL(2,Z)$. The evidence consists of the robustness of the tests of a suite a predictions concerning the transitions between the phases of the system as magnetic fields and temperatures are varied, which follow from the existence of the symmetry alone. These include the universality of and quantum numbers of the fixed points which occur in these transitions; selection rules governing which phases may be related by transitions; and the semi-circular t…
The mapping between the metal-insulator transition of the quantum Hall system and a superfluid-to-insulator transition is revisited based on a disordered anyon model. The one-parameter scaling of the superfluid-to-insulator transition is employed for the analysis of the scaling behavior of the integer quantum Hall transitions. The analysis reveals the direct transition from a quantum Hall plateau to the insulator in weak disorder limit, and a float-down transition for strong disorders. In either cases, the transition corresponds to a non-chirality superfluid-to-insulator transition, with the l…
We derive the classical counterpart of a previously obtained quantum mechanical covariant ``continuitylike'' equation for the spin density, and present an intuitive picture for elucidating the non-conservation of the spin current. This reveals the equations of motion for a particle with spin under the Yang-Mills field (in certain semiconductors) as well as the Maxwell field, from which the condition for an infinite spin relaxation time is drawn out directly. As a concrete example, we discuss the procession of the spin orientation in spin Hall effect with the so called ReD field, which undergoe…
Graphene quantum dot with Maxwell fish eye potential energy profile is studied. A quasiclassical approximation is used given that potential energy is a slowly varying function of coordinates. Near the zero energy the spectrum of electron macroscopically degenerates. All the electron trajectories are closed circles that are classified by angular momentum and an additional integral of motion. Provided the complete filling of the lower Dirac zone, a universal value for Hall conductivity is found.
We investigate the role of quantum fluctuations in topological quantum phase transitions of quantum spin Hall insulators and quantum anomalous Hall insulators. Employing the variational cluster approximation to obtain the single-particle Green's function of the interacting many-body system, we characterize different phases by direct calculation of the recently proposed topological order parameter for interacting systems. We pinpoint the influence of quantum fluctuations on the quantum spin Hall to Mott insulator transition in several models. Furthermore, we propose a general mechanism by which…
We derive the low-energy theory of semi-quantized quantum Hall states, a recently observed class of gapless bilayer fractional quantum Hall states. Our theory shows these states to feature gapless quasiparticles of fractional charge coupled to an emergent Chern-Simons gauge field. These gapless quasiparticles can be understood as composites of electrons and Laughlin-like quasiparticles. We show that semi-quantized quantum Hall states exhibit perfect interlayer drag, host non-Fermi liquid physics, and serve as versatile parent states for fully gapped topological phases hosting anyonic excitatio…
We construct a family of holomorphic $β$-functions whose RG flow preserves the $Γ(2)$ modular symmetry and reproduces the observed stability of the Hall plateaus. The semi-circle law relating the longitudinal and Hall conductivities that has been observed experimentally is obtained from the integration of the RG equations for any permitted transition which can be identified from the selection rules encoded in the flow diagram. The generic scale dependance of the conductivities is found to agree qualitatively with the present experimental data. The existence of a crossing point occuring in the …
We show that, for the transition between any two quantum Hall states, the semi-circle law and the existence of a duality symmetry follow solely from the consistency of the law of corresponding states with the two-dimensional scaling flow. This puts these two effects on a sound theoretical footing, implying that both should hold exactly at zero temperature, independently of the details of the microscopic electron dynamics. This derivation also shows how the experimental evidence favours taking the two-dimensional flow seriously for the whole transition, and not just near the critical points.
The use of ultra-low temperature cooling and of high hydrostatic pressure techniques has significantly expanded our understanding of the two-dimensional electron gas confined to GaAs/AlGaAs structures. This chapter reviews a selected set of experiments employing these specialized techniques in the study of the fractional quantum Hall states and of the charged ordered phases, such as the reentrant integer quantum Hall states and the quantum Hall nematic. Topics discussed include a successful cooling technique used, novel odd denominator fractional quantum Hall states, new transport results on e…
We discuss quantum Hall effect in the presence of arbitrary pair interactions between electrons. It is shown that irrespective of the interaction strength the Hall conductivity is given by the filling fraction of Landau levels averaged over the ground state of the system. This conclusion remains valid for both integer and fractional quantum Hall effect.
We study the tunable quantum Hall effects in a non-Abelian honeycomb optical lattice which is a many-Dirac-points system. We find that the quantum Hall effects present different features as change as relative strengths of several perturbations. Namely, a gauge-field-dressed next-nearest-neighbor hopping can induce the quantum spin Hall effect and a Zeeman field can induce a so-called quantum anomalous valley Hall effect which includes two copies of quantum Hall states with opposite Chern numbers and counter-propagating edge states. Our study extends the borders of the field of quantum Hall eff…
Quantum Geometric Origin of Hall Viscosity and Nonlocal Hall Conductivity in Lattice Bands
Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences（中国科学院大学理论物理研究所）；Institute of Solid State Physics, University of Tokyo（东京大学固体物理研究所）；Department of Physics, Nagoya University（名古屋大学物理学系）；Center for Spintronics Research Network, Keio University（庆应义塾大学自旋电子学研究网络中心）；CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences（中国科学院大学拓扑量子计算卓越创新中心）；RIKEN Center for Emergent Matter Science (CEMS)（理化学研究所新兴物质科学中心）；Advanced Science Research Center, Japan Atomic Energy Agency（日本原子能研究开发机构先进科学研究中心）
We calculate a topological invariant, whose value would coincide with the Chern number in case of integer quantum Hall effect, for fractional quantum Hall states. In case of Abelian fractional quantum Hall states, this invariant is shown to be equal to the trace of the K-matrix. In case of non-Abelian fractional quantum Hall states, this invariant can be calculated on a case by case basis from the conformal field theory describing these states. This invariant can be used, for example, to distinguish between different fractional Hall states numerically even though, as a single number, it cannot…
We demonstrate the existance of ferrimagnetic and ferromagnetic phases in a spin phase diagram of coupled lateral quantum dot molecules in the quantum Hall regime. The spin phase diagram is determined from Hartree-Fock Configuration Interaction method as a function of electron numbers N, magnetic field B, Zeeman energy, and tunneling barrier height. The quantum Hall ferrimagnetic phase corresponds to spatially imbalanced spin droplets resulting from strong inter-dot coupling of identical dots. The quantum Hall ferromagnetic phases correspond to ferromagnetic coupling of spin polarization at fi…
We present a phase diagram for a double quantum well bilayer electron gas in the quantum Hall regime at total filling factor $ν=1$, based on exact numerical calculations of the topological Chern number matrix and the (inter-layer) superfluid density. We find three phases: a quantized Hall state with pseudo-spin superfluidity, a quantized Hall state with pseudo-spin ``gauge-glass'' order, and a decoupled composite Fermi liquid. Comparison with experiments provides a consistent explanation of the observed quantum Hall plateau, Hall drag plateau and vanishing Hall drag resistance, as well as the …
We present a comprehensive study of the effective Conformal Field Theory (CFT) describing the low energy excitations of a gas of spinless interacting fermions on a circle in the gapless regime (Luttinger liquid). Functional techniques and modular transformation properties are used to compute all correlation functions in a finite size and at finite temperature. Forward scattering disorder is treated exactly. Laughlin experiments on charge transport in a Quantum Hall Fluid on a cylinder are reviewed within this CFT framework. Edge excitations above a given bulk excitation are described by a twis…
Using the hierarchy picture of the fractional quantum Hall effect, we study the the ground state periodicity of a finite size quantum Hall droplet in a quantum Hall fluid of a different filling factor. The droplet edge charge is periodically modulated with flux through the droplet and will lead to a periodic variation in the conductance of a nearby point contact, such as occurs in some quantum Hall interferometers. Our model is consistent with experiment and predicts that superperiods can be observed in geometries where no interfering trajectories occur. The model may also provide an experimen…
We consider the quantum Hall effect induced by magnetic field and rotation, which can drive the Hall samples into the quantum Hall regime and induce fractional excitations. Both the mass and the charge of the Laughlin quasiparticles are predicted to be fractionally quantized. The observable effects induced by rotation are discussed. Based on the usual Hall samples under rotation, we propose an experimental setup for detecting the macroscopic quantization phenomena and the fractional mass of the Laughlin quasiparticles.
We study spin wave relaxation in quantum Hall ferromagnet regimes. Spin-orbit coupling is considered as a factor determining spin nonconservation, and external random potential as a cause of energy dissipation making spin-flip processes irreversible. We compare this relaxation mechanism with other relaxation channels existing in a quantum Hall ferromagnet.
We present experimental results on the quantized Hall insulator in two dimensions. This insulator, with vanishing conductivities, is characterized by the quantization (within experimental accuracy) of the Hall resistance in units of the quantum unit of resistance, h/e^2. The measurements were performed in a two dimensional hole system, confined in a Ge/SiGe quantum well, when the magnetic field is increased above the nu=1 quantum Hall state. This quantization leads to a nearly perfect semi-circle relation for the diagonal and Hall conductivities. Similar results are obtained with a higher mobi…
The Lagrangian (action) formulation of the Chalker-Coddington network model for plateau-plateau transitions in quantum Hall effect is presented based on a model of fermions hopping on Manhattan Lattice ($ML$). The dimensionless Landauer resistance is considered and its average is calculated over the random U(1) phases with constant distribution on the circle. The Lagrangian of the resultant model on $ML$ is found and the corresponding $R$-matrix is written down. It appeared, that this model is integrable, rising hope to investigate physics of plateau- plateau transitions by the exact method of…
We explore the consequences of introducing a complex conductivity into the quantum Hall effect. This leads naturally to an action of the modular group on the upper-half complex conductivity plane. Assuming that the action of a certain subgroup, compatible with the law of corresponding states, commutes with the renormalisation group flow, we derive many properties of both the integer and fractional quantum Hall effects, including: universality; the selection rule $|p_1q_2 - p_2q_1|=1$ for quantum Hall transitions between filling factors $ν_1=p_1/q_1$ and $ν_2=p_2/q_2$; critical values for the c…
Fractional quantum Hall (FQH) states are topologically ordered which indicates that their essential properties are insensitive to smooth deformations of the manifold on which they are studied. Their microscopic Hamiltonian description, however, strongly depends on geometrical details. Recent work has shown how this dependence can be exploited to generate effective models that are both interesting in their own right and also provide further insight into the quantum Hall system. We review and expand on recent efforts to understand the FQH system close to the solvable thin-torus limit in terms of…
We propose a electron-pumping mechanism called Chern pump to explain the integer quantum Hall effect(IQHE) in the Chern insulator. By using the parallel transport gauge in the hybrid Wannier representation we establish the bulk and edge states correspondence in the Chern insulator. The same correspondence can also be established in two dimensional(2D) topological insulator(TI). So we can consider 2D TI as two time reversal(TR) related CIs put together. The quantum spin Hall effect(QSHE) can be viewed as two TR related Chern pumps pumping electrons to opposite directions. Compared with the Z2 s…
Both quantum spin Hall and quantum anomalous Hall states are novel states of quantum matter with promising applications. We propose junction quantum wells comprising II-VI, III-V or IV semiconductors as a large class of new materials realizing the quantum spin Hall state. Especially, we find that the bulk band gap for the quantum spin Hall state can be as large as 0.1 eV. Further more, magnetic doping would induce the ferromagnetism in these junction quantum wells due to band edge singularities in the band-inversion regime and to realize the quantum anomalous Hall state.
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 …
We engineer quantum anomalous Hall effect in silicene via doping 3d transition metals. We show that there exists a stable quantum anomalous Hall effect in Vanadium doped silicene using both analytical model and Wannier interpolation. We also predict the quantum valley Hall effect and electrically tunable topological states could be realized in certain transition metal doped silicene where the energy band inversion occurs. Our finding provides new scheme for the realization of quantum anomalous Hall effect and platform for electrically controllable topological states.
We find that mesoscopic conductance fluctuations in the quantum Hall regime in silicon MOSFETs display simple and striking patterns. The fluctuations fall into distinct groups which move along lines parallel to loci of integer filling factor in the gate voltage-magnetic field plane. Also, a relationship appears between the fluctuations on quantum Hall transitions and those found at low densities in zero magnetic field. These phenomena are most naturally attributed to charging effects. We argue that they are the first unambiguous manifestation of interactions in dc transport in the integer quan…
The quantum spin Hall (QSH) states discovered in an inverted band of InAs/GaSb and HgTe/CdTe quantum wells categorize them among the very superior candidates for topological insulators. In the presence of a magnetic field, these QSH states persist up to a magnetic field equal to the critical field, beyond which the edge states would consist of normal quantum Hall (QH) states. We provide the expression of this critical field which is found consistent with some previous literature. The critical field partitioned the spectrum into two types of quantum states, \textit{viz}. , the Quantum spin Hall…
Recent experiments in the integer quantum Hall regime seem to find direct transitions from a quantum Hall state with Hall conductance $σ_{xy} = n e^2/h $ with integer $n > 1$, to an insulating state in weak magnetic fields. We study this issue using a variation of the tight-binding lattice model for non-interacting electrons. Although quantum Hall transitions with change in Hall conductance $n e^2/ h$ with $n > 1$ do exist in our model for special tuning of parameters, they generically split into quantum Hall transitions with the Hall conductance changing by $e^2 / h$ at each transition. This …
We demonstrate a new quantum state of matter---valley-polarized quantum anomalous Hall effect in monolayer silicene. In the presence of extrinsic Rashba spin-orbit coupling and exchange field, monolayer silicene can host a quantum anomalous-Hall state with Chern number C=2. We find that through tuning Rashba spin-orbit coupling, a topological phase transition gives rise to a valley polarized quantum anomalous Hall state, i.e. a quantum state which exhibits electronic properties of both quantum valley-Hall effect (valley Chern number C_V=3) and quantum anomalous Hall effect with C=-1.
We describe a new phase transition of the bilayer quantum Hall ferromagnet at filling fraction $ν= 1$. In the presence of static disorder (modeled by a periodic potential), bosonic $S=1/2$ spinons can undergo a superfluid-insulator transition while preserving the ferromagnetic order. The Mott insulating phase has an emergent U(1) photon, and the transition is between Higgs and Coulomb phases of this photon. Physical consequences for charge and counterflow conductivity, and for interlayer tunneling conductance in the presence of quenched disorder are discussed.
In time-reversal invariant systems, all charge Hall effects predicted so far are extrinsic effects due to the dependence on the relaxation time. We explore intrinsic Hall signatures by studying quantum noise spectrum of the Hall current in time-reversal invariant systems, and discover intrinsic thermal Hall noises in both linear and nonlinear regimes. As the band geometric characteristics, quantum geometric tensor and Berry curvature play critical roles in various Hall effects, so are their quantum fluctuations. It is found that the thermal Hall noise in linear order of the electric field is p…
The distribution of the Hall voltage induced by low-frequency AC current is studied theoretically in the incoherent linear transport of quantum Hall systems. It is shown that the Hall-voltage distribution makes a crossover from the uniform distribution to a concentrated-near-edges distribution as the frequency is increased or the diagonal conductivity is decreased. This crossover is also reflected in the frequency dependence of AC magnetoresistance.
We examine the magnetic field driven insulator-quantum Hall-insulator transitions of the two dimensional hole gas in a Ge/SiGe quantum well. We observe direct transitions between low and high magnetic field insulators and the $ν=1$ quantum Hall state. With increasing magnetic field, the transitions from insulating to quantum Hall and quantum Hall to insulating are very similar with respect to their transport properties. We address the temperature dependence around the transitions and show that the characteristic energy scale for the high field transition is larger.
The quantum magnetotransport properties of a monolayer of molybdenum disulfide are derived using linear response theory. Especially, 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 conductivity 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.
We show that in the limit of zero temperature, double layer quantum Hall systems exhibit a novel phenomena called Hall drag, namely a current driven in one layer induces a voltage drop in the other layer, in the direction perpendicular to the driving current. The two-by-two Hall resistivity tensor is quantized and proportional to the ${\bf K}$ matrix that describes the topological order of the quantum Hall state, even when the ${\bf K}$ matrix contains a zero eigenvalue, in which case the Hall conductivity tensor does not exist. Relation between the present work and previous ones is also discu…
We obtain a ``mean field'' scaling flow of the longitudinal and the Hall conductivities in the fractional quantum Hall regime. Using the composite fermion picture and assuming that the composite fermions follow the Khmelnitskii-Pruisken scaling flow for the integer quantum Hall effect, the unstable fixed points which govern the transitions between different fractional quantum Hall states are identified. Distributions of the critical longitudinal and Hall conductivities at the unstable fixed points are obtained and implications of the results for the experiments on mesoscopic quantum Hall syste…
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 explicitely the Hall conductivity from a Kubo formula.
We give a brief introduction to the phenomenon of the Fractional Quantum Hall effect, whose discovery was awarded the Nobel prize in 1998. We also explain the composite fermion picture which describes the fractional quantum Hall effect as the integer quantum Hall effect of composite fermions.
A dynamical group for the single-particle (non-interacting) Quantum Hall Effect is found, and used to describe the Landau levels and determine the transverse (Hall) current.
We report on the dramatic evolution of the quantum Hall ferromagnet in the fractional quantum Hall regime at $ν= 2/5$ filling. A large enhancement in the characteristic timescale gives rise to a dynamical transition into a novel quantized Hall state. The observed Hall state is determined to be a zero-temperature phase distinct from the spin-polarized and spin-unpolarized $ν= 2/5$ fractional quantum Hall states. It is characterized by a strong temperature dependence and puzzling correlation between temperature and time.
We study the influences of antidot-induced bound states on transport properties of two- dimensional quantum spin Hall insulators. The bound statesare found able to induce quantum percolation in the originally insulating bulk. At some critical antidot densities, the quantum spin Hall phase can be completely destroyed due to the maximum quantum percolation. For systems with periodic boundaries, the maximum quantum percolationbetween the bound states creates intermediate extended states in the bulk which is originally gapped and insulating. The antidot in- duced bound states plays the same role a…
We constructed a Hall resistance formula for the fractional quantum Hall effect by analyzing the experimental data reported in [J. P. Eisenstein and H. L. Stormer, {Science} {\bf 248}, 1510 (1990)]. The formula is given as a function of magnetic induction, chemical potential and temperature. The Hall resistance function contains a single-electron energy spectrum, which has phenomenological perturbation terms with three tunable parameters. The formula yields 12 plateaus that are consistent with the experiment. The perturbations can be interpreted as precession or nutation of a Landau orbital in…
The discovery of the quantum Hall effect in 2D systems opens the door to topological phases of matter. A quantum Hall effect in 3D is a long-sought phase of matter and has inspired many efforts and claims. In the perspective, we review our proposal that guarantees a 3D quantum Hall effect. The proposal employs the topologically-protected Fermi arcs and the "wormhole" tunneling via the Weyl nodes in a 3D topological semimetal. The 1D edge states in this 3D quantum Hall effect show an example of (d-2)-dimensional boundary states. Possible signatures of the 3D quantum Hall effect have been observ…
The quantum anomalous Hall effect is defined as a quantized Hall effect realized in a system without external magnetic field. Quantum anomalous Hall effect is a novel manifestation of topological structure in many-electron systems, and may have potential applications in future electronic devices. In recent years, quantum anomalous Hall effect has been proposed theoretically and realized experimentally. In this review article, we provide a systematic overview of the theoretical and experimental developments in this field.
The original motivation of great interest to topological insulators was the hope to observe the quantum spin Hall effect. Therefore if a material is in the topological insulator state they frequently call it the quantum spin Hall state. However, despite impressive experimental results confirming the existence of the quantum spin Hall state, the quantum spin Hall effect has not yet been detected. After a short overview of what was originally suggested as the quantum spin Hall effect (quantum spin conductance determined by the topological Chern number) the paper analyzes the crucial role of the …
A device is proposed that is similar in spirit to the electron turnstile except that it operates within a quantum Hall fluid. In the integer quantum Hall regime, this device pumps an integer number of electrons per cycle. In the fractional regime, it pumps an integer number of fractionally charged quasiparticles per cycle. It is proposed that such a device can make an accurate measurement of the charge of the quantum Hall effect quasiparticles.
We show the inconsistency of the argument linking the integral quantum Hall effect to gauge invariance. The inconsistency mainly consists of equating gauge and real vector potential transformations for a particular system geometry. Correct handling gives no Hall quantization.
The possibility of using quantum Hall systems for thermoelectric energy conversion is investigated. It is shown that the massive degeneracy and the metallicity of a partially-filled Landau level enable thermoelectric cooling and power generation with unprecedented efficiency at low temperature. The figure of merit is explicitly derived for a transverse thermoelectric device using the $ν=0$ quantum Hall state of Dirac materials at charge neutrality, where due to electron-hole symmetry electrical Hall effect vanishes but thermoelectric Hall effect peaks.
We report an intriguing transition from the quantum spin Hall phase to the spin Hall effect upon segregation of thallium adatoms adsorbed onto a graphene surface. Landauer-Büttiker and Kubo-Greenwood simulations are used to access both edge and bulk transport physics in disordered thallium-functionalized graphene systems of realistic sizes. Our findings not only quantify the detrimental effects of adatom clustering in the formation of the topological state, but also provide evidence for the emergence of spin accumulation at opposite sample edges driven by spin-dependent scattering induced by t…
In a two-dimensional electron gas, the quantized Hall conductance can be induced by a strong magnetic field, known as the quantum Hall effect, and it can also result from the strong exchange coupling of magnetic ions, dubbed as the "quantum anomalous Hall effect". The quantum Hall effect requires the out-of-plane magnetic field, and similarly, it is commonly believed that the magnetization should be out-of-plane for the quantum anomalous Hall effect. In the present work, we find this condition is not necessary and predict that the quantum anomalous Hall effect can also be induced by the purely…
We report on the formation of critical states in disordered graphene, at the origin of variable and unconventional transport properties in the quantum Hall regime, such as a zero-energy Hall conductance plateau in the absence of an energy bandgap and Landau level degeneracy breaking. By using efficient real-space transport methodologies, we compute both the dissipative and Hall conductivities of large size graphene sheets with random distribution of model single and double vacancies. By analyzing the scaling of transport coefficients with defect density, system size and magnetic length, we elu…
We study a nonadiabatic effect on the conductances in the quantum Hall effect of two-dimensional electrons with a periodic potential. We found that the Hall and longitudinal conductances oscillate in time with a very large frequencies due to quantum fluctuation.
The ground states of electrons in two vertically coupled quantum dots in the presence of an external magnetic field have been studied within the density functional theory. A phase diagram of the transition to the quantum Hall state in double quantum dots has been plotted for the Landau level filling factor $ν= 1$. It has been shown that the quantum Hall state can be stable for a zero tunnel splitting. The influence of the impurity potential on the stability condition for the quantum Hall state has been analyzed.
We consider the problem of quantum and classical phase transitions in double-layer quantum Hall systems at $ν=1/m$ (m odd integers) from a long-wavelength statistical mechanics viewpoint. We derive an explicit mapping of the long-wavelength Lagrangian of the quantum Hall system into that of a three-dimensional isotropic classical XY model whose coupling constant depends on the quantum fluctuation in the original quantum Hall Hamiltonian. Universal properties of the quantum phase transition at the critical layer separation are completely determined by this mapping. The dependence of the Kosterl…
