Evolution of individual quantum Hall edge states in the presence of disorder

By using the Bloch eigenmode matching approach, we numerically study the evolution of individual quantum Hall edge states with respect to disorder. As demonstrated by the two-parameter renormalization group flow of the Hall and Thouless conductances, quantum Hall edge states with high Chern number n are completely different from that of the n = 1 case. Two categories of individual edge modes are evaluated in a quantum Hall system with high Chern number. Edge states from the lowest Landau level have similar eigenfunctions that are well localized at the system edge and independent of the Fermi energy. On the other hand, at fixed Fermi energy, the edge state from higher Landau levels exhibit larger expansion, which results in less stable quantum Hall states at high Fermi energies. By presenting the local current density distribution, the effect of disorder on eigenmode-resolved edge states is distinctly demonstrated.     

Quantum Hall effect in intentionally disordered two‐dimensional electron systems

In this work intentionally disordered two‐dimensional electron systems in modulation doped GaAs/GaAlAs heterostructures are studied by magnetotransport experiments. The disorder is provided by a δ‐doped layer of negatively charged beryllium acceptors. In low magnetic fields a strong negative magnetoresistance is observed that can be ascribed to magnetic‐field‐induced delocalization. At increased magnetic fields the quantum Hall effect exhibits broad Hall plateaus whose centers are shifted to higher magnetic fields, i.e. lower filling factors. This shift can be explained by an asymmetric density of states. Consistently, the transition into the insulating state of quantum Hall droplets in high magnetic fields occurs at critical filling factors around ν_c=0.4, i.e. well below the value 1/2 that is expected for symmetric disorder potentials. The insulator transition is characterized by the divergence of both the longitudinal resistance as well as the Hall resistance. This is contrary to other experiments which observe a finite Hall resistance in the insulating regime and has not been observed previously. According to recent theoretical studies the divergence of the Hall resistance points to quantum coherent transport via tunneling between quantum Hall droplets. The magnetotransport experiments are supplemented by simulations of potential landscapes for random and correlated distributions of repulsive scatterers, which enable the determination of percolation thresholds, densities of states, and oscillator strengths for far‐infrared excitations. These simulations reveal that the strong shift of the Hall plateaus and the observed critical filling factor for the insulator transition in high magnetic fields require an asymmetric density of states that can only be generated by a strongly correlated beryllium distribution. Cyclotron resonance on the same samples also indicates the possibility of correlations between the beryllium acceptors.     

Levitation of current carrying states in the lattice model for the integer quantum Hall effect

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.     

Quantum Hall effect of massless dirac fermions in a vanishing magnetic field

The effect of strong long-range disorder on the quantization of the Hall conductivity sigma{xy} in graphene is studied numerically. It is shown that increasing Landau-level mixing progressively destroys all plateaus in sigma{xy} except the plateaus at sigma{xy}=-/+e{2}/2h (per valley and per spin). The critical state at the Dirac point is robust to strong disorder and belongs to the universality class of the conventional plateau transitions in the integer quantum Hall effect. We propose that the breaking of time-reversal symmetry by ripples in graphene can realize this quantum critical point in a vanishing magnetic field.     

Critical width of Hall incompressible strips in regularly nonuniform 2D electron systems

A formalism for determining the critical width of Hall incompressible strips, which arise in regularly nonuniform 2D electron systems in the presence of a magnetic field, is proposed. Under equilibrium conditions, this width is determined by competition between the cyclotron and Coulomb energies at distances of about the critical width of a channel with integer filling factor. The calculations are applied to interpretation of available experimental data.     

Correlation of eigenstates in the critical regime of quantum Hall systems

We extend the multifractal analysis of the statistics of critical wave functions in quantum Hall systems by calculating numerically the correlations of local amplitudes corresponding to eigenstates at two different energies. Our results confirm multifractal scaling relations which are different from those occurring in conventional critical phenomena. The critical exponent corresponding to the typical amplitude, [Formula: see text], gives an almost complete characterization of the critical behaviour of eigenstates, including correlations. Our results support the interpretation of the local density of states being an order parameter of the Anderson transition.     

Redistributing Chern numbers of Landau subbands: tight-binding electrons under staggered modulated magnetic fields

We investigate the magnetotransport properties of electrons on a square lattice under a magnetic field with the alternate flux strength phi+/-Deltaphi in neighboring plaquettes. A new peculiar behavior of the Hall conductance has been found and is robust against weak disorder: if phi=(p/2N)2pi (p and 2N are coprime integers) is fixed, the Chern numbers of Landau subbands will be redistributed between neighboring pairs and hence the total quantized Hall conductance exhibits a direct transition by +/-Ne2/h at critical fillings when Deltaphi is increased from 0 up to a critical value Deltaphi_{c}. This effect can be an experimental probe of the staggered-flux phase.     

Quantum Hall ferromagnetism in the presence of tunable disorder

In this Letter, we report our recent experimental results on the energy gap of the ν=1 quantum Hall state (Δ(ν=1)) in a quantum antidot array sample, where the effective disorder potential can be tuned continuously. Δ(ν=1) is nearly constant at small effective disorders, and collapses at a critical disorder. Moreover, in the weak disorder regime, Δ(ν=1) shows a B(total)(1/2) dependence in tilted magnetic field measurements, while in the strong disorder regime, Δ(ν=1) is linear in B(total), where B(total) is the total magnetic field at ν=1. We discuss our results within several models involving the quantum Hall ferromagnetic ground state and its interplay with sample disorder.     

On the quantum phase transition of a quantum Hall liquid

It is shown that, in the absence of disorder, a quantum Hall liquid undergoes a second-order quantum phase transition as function of the applied magnetic field. The analysis is carried out in the framework of the Chem-Simons-Ginzburg-Landau theory which is shown to exhibit a nontrivial infrared stable fixed point. The corresponding critical exponents are found to be gaussian, and thus universal and independent of the filling fraction.     

Magneto-transport of graphene and quantum phase transitions in the quantum Hall regime

In this paper we show the electronic transport and the quantum phase transitions that characterize the quantum Hall regime in graphene placed on SiO(2) substrates at magnetic fields up to 28 T and temperatures down to 4 K. The analysis of the temperature dependence of the Hall and longitudinal resistivity reveals intriguing non-universalities of the critical exponents of the plateau-insulator transition. These exponents depend on the type of disorder that governs the electrical transport and its characterization is important for the design and fabrication of novel graphene nano-devices.     

Impurity Effects at Surfaces of a Photon-Dressed Bi_2Se_3 Thin Film

We investigate the impurity effects on surfaces of a thin film topological insulator, applied by an off-resonant circular polarized light. It is found that the off-resonant driving induces a quantized total Hall conductivity, when the driving strength is larger than a critical value and the Fermi level lies in the band gap, indicating that our system is converted into the topological phase. We also find that with the increasing disorder strength, the Dirac masses of top and bottom surfaces are renormalized and then fixed to half of their initial values, respectively,which will shrink the widths of the half-integer plateau of anomalous Hall conductivities.     

Observation of reentrant integer quantum Hall States in the lowest landau level

Measurements on very low disorder two-dimensional electrons confined to relatively wide GaAs quantum well samples with tunable density reveal a close competition between the electron liquid and solid phases near the Landau level filling factor ν=1. As the density is raised, the fractional quantum Hall liquid at ν=4/5 suddenly disappears at a well-width dependent critical density, and then reappears at higher densities with insulating phases on its flanks. These insulating phases exhibit reentrant ν=1 integer quantum Hall effects and signal the formation of electron Wigner crystal states. Qualitatively similar phenomena are seen near ν=6/5.     

Localization in a quantum spin Hall system

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.     

Finite-temperature density instability at high landau level occupancy

We study here the onset of charge density wave instabilities in quantum Hall systems at finite temperature for Landau level filling nu>4. Specific emphasis is placed on the role of disorder as well as on an in-plane magnetic field. Beyond some critical value, disorder is observed to suppress the charge density wave melting temperature to zero. In addition, we find that a transition from perpendicular to parallel stripes (relative to the in-plane magnetic field) exists when the electron gas thickness exceeds approximately 60 A. The perpendicular alignment of the stripes is in agreement with the experimental finding that the easy conduction direction is perpendicular to the in-plane field.     

Dissipation and criticality in the lowest Landau level of graphene

The lowest Landau level of graphene is studied numerically by considering a tight-binding Hamiltonian with disorder. The Hall conductance sigma_{xy} and the longitudinal conductance sigma_{xx} are computed. We demonstrate that bond disorder can produce a plateaulike feature centered at nu=0, while the longitudinal conductance is nonzero in the same region, reflecting a band of extended states between +/-E_{c}, whose magnitude depends on the disorder strength. The critical exponent corresponding to the localization length at the edges of this band is found to be 2.47+/-0.04. When both bond disorder and a finite mass term exist the localization length exponent varies continuously between approximately 1.0 and approximately 7/3.     

Effect of random on-site energies on the critical temperature of a lattice Bose gas

We study the effect of random on-site energies on the critical temperature of a non-interacting Bose gas on a lattice. In our derivation the on-site energies are distributed according a Gaussian probability distribution function having vanishing average and variance ν ₀ ² . By using the replicated action obtained by averaging on the disorder, we perform a perturbative expansion for the Green functions of the disordered system. We evaluate the shift of the chemical potential induced by the disorder and we compute, for ν ₀ ² ? 1, the critical temperature for condensation. We find that, for large filling, disorder slightly enhances the critical temperature for condensation.     

Interplay of Rashba spin orbit coupling and disorder in the conductance properties of a four terminal junction device

We report a thorough theoretical investigation on the quantum transport of a disordered four terminal device in the presence of Rashba spin orbit coupling (RSOC) in two dimensions. Specifically we compute the behaviour of the longitudinal (charge) conductance, spin Hall conductance and spin Hall conductance fluctuation as a function of the strength of disorder and Rashba spin orbit interaction using the Landauer Büttiker formalism via Green’s function technique. Our numerical calculations reveal that both the conductances diminish with disorder. At smaller values of the RSOC parameter, the longitudinal and spin Hall conductances increase, while both vanish in the strong RSOC limit. The spin current is more drastically affected by both disorder and RSOC than its charge counterpart. The spin Hall conductance fluctuation does not show any universality in terms of its value and it depends on both disorder as well as on the RSOC strength. Thus the spin Hall conductance fluctuation has a distinct character compared to the fluctuation in the longitudinal conductance. Further one parameter scaling theory is studied to assess the transition to a metallic regime as claimed in literature and we find no confirmation about the emergence of a metallic state induced by RSOC.     

Universal critical exponent in class D superconductors

We study a physical system consisting of noninteracting quasiparticles in disordered superconductors that have neither time-reversal nor spin-rotation invariance. This system belongs to class D within the recent classification scheme of random matrix ensembles, and its phase diagram contains three different phases: metallic and two distinct localized phases with different quantized thermal Hall conductances. We find that critical exponents describing different transitions (insulator-to-insulator and insulator-to-metal) are identical within the error of numerical calculations and also find that critical disorder of the insulator-to-metal transition is energy-independent.     

Anomalous Hall Effect in Spin-Polarized Two-Dimensional Hole Gas with Cubic-Rashbsa Spin-Orbit Interaction

Based on the Kubo formalism, the anomalous Hall effect in a magnetic two-dimensional hole gas with cubic-Rashba spin-orbit coupling is studied in the presence of δ-function scattering potential. When the weak, short-ranged disorder scattering is considered in the Born approximation, we find that the self-energy becomes diagonal in the helicity basis and its value is independent of the wave number, and the vertex correction to the anomalous Hall conductivity due to impurity scattering vanishes when both subbandsare occupied. That is to say, the anomalous Hall effect is not vanishing or influenced by the vertex correction for two-dimensional heavy-hole system, which is in sharp contrast to the case of linear-Rashba spin-orbit coupling in the electron band when the short-range disorder scattering is considered and the extrinsic mechanism as well as the effect of external electric field on the SO interaction are ignored.     

Tunable anomalous Hall effect in a nonferromagnetic system

We measure the low-field Hall resistivity of a magnetically doped two-dimensional electron gas as a function of temperature and electrically gated carrier density. Comparing these results with the carrier density extracted from Shubnikov-de Haas oscillations reveals an excess Hall resistivity that increases with decreasing temperature. This excess Hall resistivity qualitatively tracks the paramagnetic polarization of the sample, in analogy to the ferromagnetic anomalous Hall effect. The data are consistent with skew scattering of carriers by disorder near the crossover to localization.