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.     

Effect of Joule heating on current-induced asymmetries and breakdown of the quantum Hall effect in narrow Hall bars

Recent low-temperature scanning-force-microscopy experiments on narrow Hall bars, under the conditions of the integer quantum Hall effect (IQHE) and its breakdown, have revealed an interesting position dependence of the Hall potential, which changes drastically with the applied magnetic field and the strength of the imposed current through the sample. The present paper shows, that inclusion of Joule heating into an existing self-consistent theory of screening and magneto-transport, which assumes translation invariant Hall bars with a homogeneous background charge due to doping, can explain the experimental results on the breakdown of the IQHE in the so called edge-dominated regime.     

Odd-integer quantum Hall effect in graphene: interaction and disorder effects

We study the competition between the long-range Coulomb interaction, disorder scattering, and lattice effects in the integer quantum Hall effect (IQHE) in graphene. By direct transport calculations, both nu=1 and nu=3 IQHE states are revealed in the lowest two Dirac Landau levels. However, the critical disorder strength above which the nu=3 IQHE is destroyed is much smaller than that for the nu=1 IQHE, which may explain the absence of a nu=3 plateau in recent experiments. While the excitation spectrum in the IQHE phase is gapless within numerical finite-size analysis, we do find and determine a mobility gap, which characterizes the energy scale of the stability of the IQHE. Furthermore, we demonstrate that the nu=1 IQHE state is a Dirac valley and sublattice polarized Ising pseudospin ferromagnet, while the nu=3 state is an xy plane polarized pseudospin ferromagnet.     

Disorder effect on the quantum Hall effect in thin films of three-dimensional topological insulators

We numerically study the quantum Hall effect (QHE) in three-dimensional topological insulator (3DTI) thin film in the presence of the finite Zeeman energy g and the hybridization gap Δ under a strong magnetic field and disorder. For Δ = 0 but g ≠ 0, the Hall conductivity remains to be odd-integer quanti-zed σ _xy = ν(e ²/h) , where ν = 2? + 1 with ? being an integer. In the presence of disorder, the Hall plateaus can be destroyed through the float-up of extended levels toward the band center and the higher plateaus disappear first. The two central plateaus with ν = ± 1 around the band center are strongest against disorder scattering. With the increasing of the disorder strength, Hall plateaus are destroyed faster for the system with a weaker magnetic field. If g = 0 but Δ ≠ 0, there is a splitting of the central (n = 0) Landau level, yielding a new plateau with ν = 0, in addition to the original odd-integer plateaus. In the strong-disorder regime, the QHE plateaus can be destroyed due to the float-up of extended levels toward the band center. The ν = 0 plateau around the band center is strongest against disorder scattering, which eventually disappears. For both g ≠ 0 and Δ ≠ 0, the simultaneous presence of nonzero g and Δ causes the splitting of the degenerating Landau levels, so that all integer Hall plateaus ν = ? appear. The ν = 0,1 plateaus are the most stable ones. In the strong-disorder regime, all QHE states are destroyed by disorder, and the system transits into an insulating phase.     

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.     

Mesoscopic effects in the quantum Hall regime

We report results of a study of (integer) quantum Hall transitions in a single or multiple Landau levels for non-interacting electrons in disordered two-dimensional systems, obtained by projecting a tight-binding Hamiltonian to the corresponding magnetic subbands. In finite-size systems, we find that mesoscopic effects often dominate, leading to apparent non-universal scaling behavior in higher Landau levels. This is because localization length, which grows exponentially with Landau level index, exceeds the system sizes amenable to the numerical study at present. 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 to experimentally observed transitions between quantum Hall states and the insulating phase at low magnetic fields.     

Arithmetic of the Integer Quantum Hall Effect

The integer quantum Hall effect (IQHE) is analysed, considering the degeneracies of localized and extended states separately. Occupied localized and extended states are counted, and their variation is studied as a function of magnetic field. The number of current-carrying electrons is found to have a saw-tooth variation with magnetic field. The analysis addresses certain basic questions in the IQHE, particularly the one about floatation of extended states as the magnetic field tends to zero.     

On the phase boundaries of the integer quantum hall effect

It has been pointed out that, according to the two-parameter scaling theory, the magnetic-field position of the phases of the integer quantum Hall effect (IQHE) at ω_cτ ? 1 is not determined by the filling factor ν = nh/eB. The position of the IQHE phases is given by the bare Hall conductivity σ _xy ⁰ . In this regard, it has been shown that the diagonal resistivity in the magnetic field measured by Sakr et al. [Phys. Rev. B 64, 161308 (2001)] does not exhibit transitions between the σ _xy = 3, 4 and 6 IQHE states on the one hand and the dielectric state on the other hand in contrast to the assertion by Sakr et al.     

High frequency conductivity in the quantum hall regime

We have measured the complex conductivity sigma(xx) of a two-dimensional electron system in the quantum Hall regime up to frequencies of 6 GHz at electron temperatures below 100 mK. Using both its imaginary and real part we show that sigma(xx) can be scaled to a single function for different frequencies and several transitions between plateaus in the quantum Hall effect. Additionally, the conductivity in the variable-range hopping regime is used for a direct evaluation of the localization length xi. Even for large filling factor distances deltanu from the critical point we find xi approximately equals deltanu(-gamma) with a scaling exponent gamma = 2.3.     

Quantum Hall Effect on the Hyperbolic Plane in the Presence of Disorder

We study both the continuous model and the discrete model of the quantum Hall effect (QHE) on the hyperbolic plane in the presence of disorder, extending the results of an earlier paper. Here we model impurities, that is we consider the effect of a random or almost periodic potential as opposed to just periodic potentials. The Hall conductance is identified as a geometric invariant associated to an algebra of observables, which has plateaus at gaps in extended states of the Hamiltonian. We use the Fredholm modules defined in Comm. Math. Phys. 190 (1998), 629–673, to prove the integrality of the Hall conductance in this case. We also prove that there are always only a finite number of gaps in extended states of any random discrete Hamiltonian.     

Spin Polarizations of Electron with Rashba Couplings in T-Shaped Devices: A Finite Element Approach

A generalized finite element formulation is proposed for the study of the spin-dependent ballistic transport of electron through the two-dimensional quantum structures with Rashba spin-orbit interactions (SOI). Thetransmission coefficient, conductance, the total and local polarization are numerically calculated and discussed as the Rashba coefficient, the geometric sizes, and incident energy are changed in the T-shaped devices. Some interesting features are found in the proper parameter regime. The polarization has an enhancement as the Rashba coefficient becomes stronger. The polarization valley is rigid in the regime of the conductance plateaus since the local interference among the polarized multi-wave modes. The Rashba interactions coupling to geometry in sizes could form the structure-induced Fano-Rashba resonance. In the wider stub, the localized spin lattice of electron could be produced. The conductance plateaus correspond to weakpolarizations. Strong polarizations appear when the stub sizes, incident energy, and the Rashba coupling coefficient are matched. The resonances are formed in a wide Fermi energy segment easily.     

Quantum Hall effect in kagomé lattices under staggered magnetic field

The interplay of staggered magnetic field (SMF) and uniform magnetic field (UMF) on the quantum Hall effect (QHE) in kagomé lattices is investigated in the weak UMF limit. The topological band gaps coming from SMF are robust against UMF although the extended bands split into a series of Landau levels. With SMF applied, in the unconventional QHE region, one plateau of Hall conductance becomes wider and the others are compressed. Meanwhile, one of the two series of integer Hall plateaus splits and the resulting two series of Hall plateaus still exhibit the integer behavior. The Hall conductance varies with SMF step by step with the step height being e(2)/h or 2e(2)/h according to the QHE being conventional or unconventional. In the transitional regions, redistribution of Chern numbers happens even in the weak UMF limit.     

Interlayer tunneling in double-layer quantum hall pseudoferromagnets

We show that the interlayer tunneling I-V in double-layer quantum Hall states displays a rich behavior which depends on the relative magnitude of sample size, voltage length scale, current screening, disorder, and thermal lengths. For weak tunneling, we predict a negative differential conductance of a power-law shape crossing over to a sharp zero-bias peak. An in-plane magnetic field splits this zero-bias peak, leading instead to a "derivative" feature at V(B)(B(parallel)) = 2 pi Planck's over 2 pi upsilon B(parallel)d/e phi(0), which gives a direct measurement of the dispersion of the Goldstone mode corresponding to the spontaneous symmetry breaking of the double-layer Hall state.     

Giant mesoscopic spin Hall effect on the surface of topological insulator

We study mesoscopic spin Hall effect on the surface of a topological insulator with a step-function potential by using the McMillan method commonly used in the study of superconductor junctions. In the ballistic transport regime, we predict a giant spin polarization induced by a transverse electric current with parameter suitable to the topological insulator thin film Bi(2)Se(3). The spin polarization oscillates across the potential boundary with no confinement due to the Klein paradox, and should be observable in a spin resolved scanning tunneling microscope.     

Charge and spin Hall conductivity in metallic graphene

Graphene has an unusual low-energy band structure with four chiral bands and half-quantized and quantized Hall effects that have recently attracted theoretical and experimental attention. We study the Fermi energy and disorder dependence of its spin Hall conductivity sigma(xy)(SH). In the metallic regime we find that vertex corrections enhance the intrinsic spin Hall conductivity and that skew scattering can lead to sigma(xy)(SH) values that exceed the quantized ones expected when the chemical potential is inside the spin-orbit induced energy gap. We predict that large spin Hall conductivities will be observable in graphene even when the spin-orbit gap does not survive disorder.     

Integer quantum Hall effect in trilayer graphene

By using high-magnetic fields (up to 60 T), we observe compelling evidence of the integer quantum Hall effect in trilayer graphene. The magnetotransport fingerprints are similar to those of the graphene monolayer, except for the absence of a plateau at a filling factor of ν=2. At a very low filling factor, the Hall resistance vanishes due to the presence of mixed electron and hole carriers induced by disorder. The measured Hall resistivity plateaus are well reproduced theoretically, using a self-consistent Hartree calculations of the Landau levels and assuming an ABC stacking order of the three layers.     

Mesoscopic SNS junctions and their application to SQUIDs and millimeter-wave detectors

Mesoscopic SNS junctions have been studied both in the ballistic and diffusive regimes. SNS junctions in the ballistic regime behave as an ideal Fermion oscillator which is to be compared with the Boson oscillator or the Planck theory of blackbody radiation. The current of mesoscopic SNS junctions in the diffusive regime has the same phase dependence as that of dirty-limit short weak links derived by a transport equation. Recent theories of mesoscopic SNS junctions have successfully unified the theories of the tunnel Josephson junction, the clean-limit short weak link and the dirty-limit short weak link which look very different conceptionally. We can even observe transitions among the three types of junctions when we change the transmission coefficients of the barriers between the superconducting electrodes experimentally. We looked experimentally for the optimum transmission coefficient which gives the minimum low-frequency telegraph noise in order to make a low-noise SQUID magnetometor for brain science. We have observed signals of 5 fT from human brains with a good signal-to-noise ratio using the SQUID magnetometor of the SNS junctions. The 64-channel SQUID magnetometer of SNS junctions has confirmed that mesoscopic SNS junctions are important not only theoretically but also practically. These data could encourage people studying SNS junctions of high-T_c superconductors.     

Effect of dissipation on the properties of surface polaritons in GaAs/AlGaAs heterojunctions in a quantizing magnetic field

A study is reported of nonradiative surface and bulk polaritons in GaAs/Al_xGa_1−x As real heterojunctions under conditions favoring integer-quantum Hall effect (IQHE) and in the presence of dissipation in a two-dimensional electron layer. The conditions of their existence, the spectrum, and damping have been determined. It is shown that under IQHE conditions all aspects of surface and bulk polaritons are quantized. It is found that, as the wave number is varied, surface and bulk polaritons can transform continuously into one another. The possibilities of experimental observation of nonradiative polaritons are discussed. Fiz. Tverd. Tela (St. Petersburg) 41, 705–711 (April 1999)     

Current distribution in the integer quantum Hall effect: The role of bulk states

The role of bulk and edge currents in a two-dimensional electron gas under the conditions of the integer quantum Hall effect (IQHE) was studied by means of an inductive coupling to Hall bar geometry. From this study we conclude that the extended states at the bulk of the sample below the Fermi energy are capable of carrying a substantial amount of Hall current. For Hall bar geometry sample with a back gate we demonstrated that injected current can be pushed from one edge to another by reversing the direction of the external magnetic field.     

From weak to strong pinning I: A finite size study

We have used linear stability analysis to study the depinning of an elastic chain with long range interactions submitted to a random pinning potential. In this paper, we provide, for the first time, evidence of a pronounced change from a strong pinning regime to a weak pinning regime. This change depends on the strength of disorder, and takes place only in finite size systems. For a given disorder, we show a characteristic length separating the weak pinning regime from the strong pinning regime. This length depends on the long range of the algebraic decay of the elastic couplings. The weak pinning regime is very well described by perturbation theory. As an example, we discuss more specifically the case of wetting of heterogeneous surfaces, where the change from a strong to a weak pinning regime could be induced in the wetting front by varying the surface tension of the liquid-air interface.Received: 12 September 2003, Published online: 20 April 2004PACS: 05.10.-a Computational methods in statistical physics and nonlinear dynamics - 68.08.Bc Wetting - 02.50.Fz Stochastic analysis