Reentrant ν=1 quantum Hall state in a two-dimensional hole system

We report the observation of a reentrant quantum Hall state at the Landau level filling factor ν=1 in a two-dimensional hole system confined to a 35-nm-wide (001) GaAs quantum well. The reentrant behavior is characterized by a weakening and eventual collapse of the ν=1 quantum Hall state in the presence of a parallel magnetic field component B(∥), followed by a strengthening and reemergence as B(∥) is further increased. The robustness of the ν=1 quantum Hall state during the transition depends strongly on the charge distribution symmetry of the quantum well, while the magnitude of B(∥) needed to invoke the transition increases with the total density of the system.     

Fractionalization via Z(2) gauge fields at a cold-atom quantum Hall transition

We study a single species of fermionic atoms in an "effective" magnetic field at total filling factor ν(f)=1, interacting through a p-wave Feshbach resonance, and show that the system undergoes a quantum phase transition from a ν(f)=1 fermionic integer quantum Hall state to ν(b)=1/4 bosonic fractional quantum Hall state as a function of detuning. The transition is in the (2+1)D Ising universality class. We formulate a dual theory in terms of quasiparticles interacting with a Z(2) gauge field and show that charge fractionalization follows from this topological quantum phase transition. Experimental consequences and possible tests of our theoretical predictions are discussed.     

Evolution of the 7/2 fractional quantum Hall state in two-subband systems

We report the evolution of the fractional quantum Hall state (FQHS) at a total Landau level (LL) filling factor of ν=7/2 in wide GaAs quantum wells in which electrons occupy two electric subbands. The data reveal subtle and distinct evolutions as a function of density, magnetic field tilt angle, or symmetry of the charge distribution. At intermediate tilt angles, for example, we observe a strengthening of the ν=7/2 FQHS. Moreover, in a well with asymmetric change distribution, there is a developing FQHS when the LL filling factor of the symmetric subband ν(S) equals 5/2 while the antisymmetric subband has a filling factor of 1<ν(A)<2.     

Signatures of non-Abelian statistics in nonlinear Coulomb blockade transport

Signatures of the non-Abelian statistics of quasiparticles in the ν=5/2 quantum Hall state are predicted to be present in the current-voltage characteristics of tunneling through one or two quantum Hall puddles of Landau filling ν(a) embedded in a bulk of filling ν(b) with (ν(a),ν(b))=(2,5/2) and (ν(a),ν(b))=(5/2,2).     

Fractional quantum Hall effect at high fillings in a two-subband electron system

Magnetotransport measurements in a clean two-dimensional electron system confined to a wide GaAs quantum well reveal that, when the electrons occupy two electric subbands, the sequences of fractional quantum Hall states observed at high fillings (ν>2) are distinctly different from those of a single-subband system. Notably, when the Fermi energy lies in the ground state Landau level of either of the subbands, no quantum Hall states are seen at the even-denominator ν=5/2 and 7/2 fillings; instead, the observed states are at ν=[i+p/(2p±1)], where i=2, 3, 4 and p=1, 2, 3, and include several new states at ν=13/5, 17/5, 18/5, 25/7, and 14/3.     

Spin-polarized to valley-polarized transition in graphene bilayers at ν=0 in high magnetic fields

We investigate the transverse electric field (E) dependence of the ν=0 quantum Hall state (QHS) in dual-gated graphene bilayers in high magnetic fields. The longitudinal resistivity ρ(xx) measured at ν=0 shows an insulating behavior which is strongest in the vicinity of E=0, as well as at large E fields. At a fixed perpendicular magnetic field (B), the ν=0 QHS undergoes a transition as a function of the applied E, marked by a minimum, temperature-independent ρ(xx). This observation is explained by a transition from a spin-polarized ν=0 QHS at small E fields to a valley- (layer-)polarized ν=0 QHS at large E fields. The E field value at which the transition occurs follows a linear dependence on B.     

Josephson tunneling in bilayer quantum Hall system

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$\nu =1$. 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.     

Low-field phase diagram of the spin Hall effect in the mesoscopic regime

When a mesoscopic two dimensional four-terminal Hall cross bar with spin-orbit interaction (SOI) is subjected to a perpendicular uniform magnetic field B, both integer quantum Hall effect (IQHE) and mesoscopic spin Hall effect (MSHE) may exist when disorder strength W in the sample is weak. We have calculated the low field "phase diagram" of MSHE in the (B,W) plane for disordered samples in the IQHE regime. For weak disorder, MSHE conductance G(sH) and its fluctuations rms(G(sH)) vanish identically on even numbered IQHE plateaus, they have finite values on those odd numbered plateaus induced by SOI, and they have values G(sH)=1/2 and rms(G(sH))=0 on those odd numbered plateaus induced by Zeeman energy. At larger disorders, the system crosses over into a regime where both G(sH) and rms(G(sH)) are finite, a chaotic regime, and finally a localized regime.     

Levitation of Extended States in a Random Magnetic Field with a Finite Mean

We study the localization properties of electrons in a two-dimensional system in a random magnetic field B(r)=B₀+δB(r) with the average B₀ and the amplitude of the magnetic field fluctuations δB. The localization length of the system is calculated by using the finite-size scaling method combined with the transfer-matrix technique. In the case of weak δB, we find that the random magnetic field system is equivalent to the integer quantum Hall effect system, namely, the energy band splits into a series of disorder broadened Landau bands, at the centers of which states are extended with the localization length exponent ν=2.34±0.02. With increasing δB, the extended states float up in energy, which is similar to the levitation scenario proposed for the integer quantum Hall effect.     

Manifestation of the bulk phase transition in the edge energy spectrum in a two-dimensional bilayer electron system

We use a quasi-Corbino sample geometry with independent contacts to different edge states in the quantum Hall effect regime to investigate the edge energy spectrum of a bilayer electron system at a total filling factor of ν=2. By analyzing nonlinear I–V curves in normal and tilted magnetic fields, we conclude that the edge energy spectrum is in a close connection with the bulk one. At the bulk phase transition spin-singlet-canted antiferromagnetic phase, the I–V curve becomes linear, indicating the disappearance or strong narrowing of the ν=1 incompressible strip at the edge of the sample.     

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.     

Temperature-dependent magnetotransport around ν=1/2 in ZnO heterostructures

The sequence of prominent fractional quantum Hall states up to ν=5/11 around ν=1/2 in a high-mobility two-dimensional electron system confined at oxide heterointerface (ZnO) is analyzed in terms of the composite fermion model. The temperature dependence of R(xx) oscillations around ν=1/2 yields an estimation of the composite fermion effective mass, which increases linearly with the magnetic field. This mass is of similar value to an enhanced electron effective mass, which in itself arises from strong electron interaction. The energy gaps of fractional states and the temperature dependence of R(xx) at ν=1/2 point to large residual interactions between composite fermions.     

Non-Abelian braiding of lattice bosons

We report on a numerical experiment in which we use time-dependent potentials to braid non-Abelian quasiparticles. We consider lattice bosons in a uniform magnetic field within the fractional quantum Hall regime, where ν, the ratio of particles to flux quanta, is near 1/2, 1, or 3/2. We introduce time-dependent potentials which move quasiparticle excitations around one another, explicitly simulating a braiding operation which could implement part of a gate in a quantum computation. We find that different braids do not commute for ν near 1 and 3/2, with Berry matrices, respectively, consistent with Ising and Fibonacci anyons. Near ν=1/2, the braids commute.     

Intrinsic gap of the nu=5/2 fractional quantum Hall state

The fractional quantum Hall effect is observed at low magnetic field where the cyclotron energy is smaller than the Coulomb interaction energy. The nu=5/2 excitation gap at 2.63 T is measured to be 262+/-15 mK, similar to values obtained in samples with twice the electronic density. Examining the role of disorder on the 5/2 state, we find that a large discrepancy remains between theory and experiment for the intrinsic gap extrapolated from the infinite mobility limit. The observation of a 5/2 state in the low-field regime suggests that inclusion of nonperturbative Landau level mixing may be necessary to fully understand the energetics of half-filled fractional quantum Hall liquids.     

From quantum Hall ferromagnetism to huge longitudinal resistance at the 2/3 fractional quantum Hall state

We observe the transition from a spin-unpolarized to a polarized nu=2/3 fractional quantum Hall state at low currents (<5 nA), recently described in terms of quantum Hall ferromagnetism, versus density and parallel magnetic field. At larger currents the time and current dependent huge longitudinal resistance (HLR) is always initiated at the transition. Transport in the HLR regime is linear and the amount of current-induced nuclear polarization in the HLR is comparable to the thermal nuclear polarization at approximately 20 mK and 10 T. A current-induced disorder in the nuclear polarization is speculated to cause the enhanced resistance in the HLR regime.     

Imaging of Coulomb-driven quantum Hall edge states

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.     

Charge neutral counterflow transport at filling factor 1 in GaAs hole bilayers

Interacting bilayers placed in perpendicular magnetic field exhibit a peculiar quantum Hall state (QHS) at total filling factor ν=1, owing to the carrier-carrier interaction in the two layers. The physics of the ν=1 QHS is similar to that of the many-particle ground state of a superconductor. Unlike conventional superconductors, however, in the ν=1 QHS carriers in one layer pair with vacancies in the opposite layer forming charge neutral particles which flow without dissipation at the lowest temperatures. Here we review the experimental evidence supporting this picture, with an emphasis on magnetotransport in interacting GaAs hole bilayers in a configuration where equal and opposite currents are passed in the two layers.     

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 superfluids in topological insulator thin films

Three-dimensional topological insulators have protected Dirac-cone surface states. In this Letter we argue that gapped excitonic superfluids with spontaneous coherence between top and bottom surfaces can occur in the topological insulator (TI)-thin-film quantum Hall regime. We find that the large dielectric constants of TI materials increase the layer separation range over which coherence survives and decrease the superfluid sound velocity, but have little influence on the superfluid density or on the charge gap. The coherent state at total Landau-level filling factor νT=0 is predicted to be free of edge modes, qualitatively altering its transport phenomenology compared to the widely studied case of νT=1 in GaAs double-quantum wells.