Quantum Hall Insulator Research Articles

Quantum Hall effect in p-Ge∕Ge1−xSix heterostructures with low hole mobility

The apparent insulator–quantum Hall–insulator (I–QH–I) transition for filling factor ν=1 is investigated in p-type Ge∕Ge1−xSix heterostructures with εFτ∕hbar≈1. Scaling analysis is carried out for both the low- and high-field transition point. In low magnetic fields ωcτ<1, pronounced QH-like peculiarities for ν=1 are also observed in both the longitudinal and Hall resistivities. Such behavior may be evidence of a localization effect in the mixing region of Landau levels and is inherent to two-dimensional structures in the vicinity of a metal–insulator transition.

Observation of the quantized Hall insulator in the quantum critical regime of the two-dimensional electron gas

We have investigated the Hall resistance ${R}_{\mathrm{H}}$ near the plateau-insulator transition of a two-dimensional electron gas in the quantum critical regime. High-field magnetotransport data taken on a low-mobility $\mathrm{In}\mathrm{Ga}\mathrm{As}∕\mathrm{In}\mathrm{P}$ heterostructure with the plateau-insulator transition at a critical field ${B}_{c}$ of $17.2\phantom{\rule{0.3em}{0ex}}\mathrm{T}$ show that the Hall resistance ${R}_{\mathrm{H}}$ is quantized at $h∕{e}^{2}$ near the critical filling fraction $({\ensuremath{\nu}}_{c}=0.55)$ for $T<1\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. By making use of universal scaling functions extracted from the magnetotransport data we show that ${R}_{\mathrm{H}}$ in the insulating phase in the limit $T\ensuremath{\rightarrow}0$ is quantized at $h∕{e}^{2}$ for all values of the scaling parameter $\ensuremath{\Delta}\ensuremath{\nu}∕{(T∕{T}_{0})}^{\ensuremath{\kappa}}$ with $\ensuremath{\Delta}\ensuremath{\nu}=\ensuremath{\nu}\ensuremath{-}{\ensuremath{\nu}}_{c}$. However, as a function of $\ensuremath{\Delta}\ensuremath{\nu}$ (or magnetic field) the Hall resistance diverges in the limit $T\ensuremath{\rightarrow}0$ for all values $\ensuremath{\nu}<{\ensuremath{\nu}}_{c}$.

Quantum tunneling of vortices in two-dimensional condensates

The tunneling rate t_v of a vortex between two pinning sites (of strength V separated by d) is computed using the Bogoliubov expansion of vortex wavefunctions overlap. For BCS vortices, tunneling is suppressed beyond a few Fermi wavelengths. For Bose condensates, t_v = V exp(- pi n_s d^2/2), where n_s is the boson density. The analogy between vortex hopping in a superconducting film and 2D electrons in a perpendicular magnetic field is exploited. We derive the variable range hopping temperature, below which vortex tunneling contributes to magneto-resistance. Using the 'Quantum Hall Insulator' analogy we argue that the -Hall conductivity- (rather than the inverse Hall resistivity) measures the effective carrier density in domains of mobile vortices. Details of vortex wavefunctions and overlap calculations, and a general derivation of the Magnus coefficient for any wavefunction on the sphere, are provided in appendices.

REAL-SPACE RENORMALIZATION-GROUP APPROACH TO THE INTEGER QUANTUM HALL EFFECT

We review recent results based on an application of the real-space renormalization group (RG) approach to a network model for the integer quantum Hall (QH) transition. We demonstrate that this RG approach reproduces the critical distribution of the power transmission coefficients, i.e., two-terminal conductances, Pc(G), with very high accuracy. The RG flow of P(G) at energies away from the transition yields a value of the critical exponent ν that agrees with most accurate large-size lattice simulations. A description of how to obtain other relevant transport coefficients such as RLand RHis given. From the non-trivial fixed point of the RG flow we extract the critical level-spacing distribution (LSD). This distribution is close, but distinctively different from the earlier large-scale simulations. We find that the LSD obeys scaling behavior around the QH transition with ν = 2.37±0.02. Away from the transition it crosses over towards the Poisson distribution. We next investigate the plateau-to-insulator transition at strong magnetic fields. For a fully quantum coherent situation, we find a quantized Hall insulator with RH≈h/e2up to RL~20h/e2when interpreting the results in terms of most probable value of the distribution function P(RH). Upon further increasing RL→∞, the Hall insulator with diverging Hall resistance [Formula: see text] is seen. The crossover between these two regimes depends on the precise nature of the averaging procedure for the distributions P(RL) and P(RH). We also study the effect of long-ranged inhomogeneities on the critical properties of the QH transition. Inhomogeneities are modeled by a smooth random potential with a correlator which falls off with distance as a power law r-α. Similar to the classical percolation, we observe an enhancement of ν with decreasing α. These results exemplify the surprising fact that a small RG unit, containing only five nodes, accurately captures most of the correlations responsible for the localization-delocalization transition.

Microwave resonance of the reentrant insulating quantum Hall phases in the first excited Landau level

We present measurements of the real diagonal microwave conductivity of the reentrant insulating quantum Hall phases in the first excited Landau level at temperatures below 50 mK. A resonance is detected around filling factor $\nu=2.58$ and weaker frequency dependence is seen at $\nu=2.42$ and 2.28. These measurements are consistent with the formation of a bubble phase crystal centered around these $\nu$ at very low temperatures.

TUNNELING BETWEEN TWO QUANTUM HALL DROPLETS

We report on tunneling experiment between two quantum Hall droplets separated by a nearly ideal tunnel barrier. The device is produced by cleaved edge overgrowth that laterally juxtaposes two two-dimensional electron systems across a high quality semi-conductor barrier. The dramatic evolution of the tunneling characteristics is consistent with the magnetic field-dependent tunneling between the coupled edge states of the quantum Hall droplets. We identify a series of quantum critical points between successive strong and weak tunneling regimes that are reminiscent of the plateau-transitions in quantum Hall effect. Scaling analysis shows that the conductance near the critical magnetic fields Bc is a function of a single scaling argument |B-Bc|T-κ, where the exponent κ=0.42. This puzzling resemblance to a quantum Hall-insulator transition points to the significance of interedge correlation in the lateral tunneling of quantum Hall droplets.

THE QUANTIZED HALL INSULATOR: A "QUANTUM" SIGNATURE OF A "CLASSICAL" TRANSPORT REGIME?

Experimental studies of the transitions from a primary quantum Hall (QH) liquid at filling factor ν=1/k (with k an odd integer) to the insulator have indicated a "quantized Hall insulator" (QHI) behavior: while the longitudinal resistivity diverges with decreasing temperature and current bias, the Hall resistivity remains quantized at the value kh/e2. We review the experimental results and the theoretical studies addressing this phenomenon. In particular, we discuss a theoretical approach which employs a model of the insulator as a random network of weakly coupled puddles of QH liquid at fixed ν. This model is proved to exhibit a robust quantization of the Hall resistivity, provided the electron transport on the network is incoherent. Subsequent theoretical studies have focused on the controversy whether the assumption of incoherence is necessary. The emergent conclusion is that in the quantum coherent transport regime, quantum interference destroys the QHI as a consequence of localization. Once the localization length becomes much shorter than the dephasing length, the Hall resistivity diverges. We conclude by mentioning some recent experimental observations and open questions.

A study on the universality of the magnetic-field-induced phase transitions in the two-dimensional electron system in an AlGaAs/GaAs heterostructure

Plateau–plateau (P–P) and insulator–quantum Hall conductor (I–QH) transitions are observed in the two-dimensional electron system in an AlGaAs/GaAs heterostructure. At high fields, the critical conductivities are not of the expected universal values and the temperature-dependence of the width of the P–P transition does not follow the universal scaling. However, the semicircle law still holds, and universal scaling behavior was found in the P–P transition after mapping it to the I–QH transition by the Landau-level addition transformation. We pointed out that in order to get a correct critical exponent, it is essential that the scaling analysis must be performed near the critical point. And with proper analysis, we found that the P–P transition and the insulator quantum Hall conductor are of the same universal class.

On the low-field insulator-quantum Hall conductor transitions

We studied the insulator-quantum Hall conductor transition which separates the low-field insulator from the quantum Hall state of the filling factor ν=4 on a gated two-dimensional GaAs electron system containing self-assembled InAs quantum dots. To enter the ν=4 quantum Hall state directly from the low-field insulator, the two-dimensional system undergoes a crossover from the low-field localization to Landau quantization. The crossover, in fact, covers a wide range with respect to the magnetic field rather than only a small region near the critical point of the insulator-quantum Hall conductor transition.

Cascade of quantum phase transitions in tunnel-coupled edge states.

We report on the cascade of quantum phase transitions exhibited by tunnel-coupled edge states across a quantum Hall line junction. We identify a series of quantum critical points between successive strong and weak tunneling regimes in the zero-bias conductance. Scaling analysis shows that the conductance near the critical magnetic fields B(c) is a function of a single scaling argument /B-B(c)/T(-kappa), where the exponent kappa=0.42. This puzzling resemblance to a quantum Hall-insulator transition points to the importance of interedge correlation between the coupled edge states.

Magnetic-field-induced quantum Hall—insulator transition and persistent photoconductivity in InAs/GaAs quantum dot layers

We have investigated the temperature dependence of resistance in the temperature range T=0.07– 300 K and in magnetic field up to 35 T in InAs/GaAs quantum dot layers. In samples with relatively high carrier concentration quantum Hall effect—insulator transition was observed in high magnetic fields. Two-dimensional Mott variable range hopping conductivity has been observed at low temperatures in samples with low carrier concentration. The length of localization correlates very well with the quantum dot cluster size obtained by atomic force microscope. In all samples a positive persistent photoconductivity was observed.

Insulator-quantum Hall transitions in two-dimensional electron gas containing self-assembled InAs dots

We present a study of magnetotransport properties in two-dimensional electron gases formed in a GaAs/Al 0.33Ga 0.67As quantum well, where self-assembled InAs quantum dots have been inserted into the centre of the GaAs well. In a perpendicular magnetic field there are transitions between quantum Hall liquids at filling factors ν=2 and 1 and the insulating phase from temperature independent points. In the insulating regime we observe ν=4 and 6 quantum Hall states due to Landau quantisation. We are able to construct a phase diagram in which Shubnikov–de Haas oscillations and insulating behaviour coexist.

On the equivalence between magnetic-field-induced phase transitions in the integer quantum Hall effect

Magnetic-field-induced phase transitions in the two-dimensional electron system in a AlGaAs/InGaAs/GaAs heterostructure are studied. Two kinds of magnetic-field-induced phase transitions, plateau–plateau (P–P) and insulator–quantum Hall conductor (I–QH) transitions, are observed in the integer quantum Hall effect regime at high magnetic fields. In the P–P transition, both the semicircle law and the universality of critical conductivities are broken and we do not observe the universal scaling. However, the P–P transition can still be mapped to the I–QH transition by the Landau-level addition transformation, and as the temperature decreases the critical points of these two transitions appear at the same temperature. Our observations indicate that the equivalence between P–P and I–QH transitions can be found by the suitable analysis even when some expected universal properties are invalid.

Insulator-quantum Hall transition in antidot lattices

Localization in antidot lattices subjected to a magnetic field is numerically studied. Oscillations of the localization length with periods of Φ 0 /2 and Φ 0 , where Φ 0 is a flux quantum h/e, as a function of flux passing through a unit cell are obtained and an insulator-quantum Hall transition point where the Fermi level crosses extended states is identified. It is revealed that extended states float up in energy and disappear at a critical magnetic field. The results are in good agreement with recent experiments.

Insulator-quantum Hall conductor transitions at low magnetic field

Insulator-quantum Hall conductor transitions at low magnetic field B were studied with a gated GaAs-AlGaAs heterostructure. A low field disorder-magnetic field phase diagram was constructed based on the experimental results. This phase diagram shows no floating up of the extended state and allows transitions from the insulating state directly to any Landau level states. The critical filling factor can change from 16 to 6 as the disorder in the sample increases. By inspecting the raw data from this and the other samples and analyzing the scaling behaviors near the transition points, we found that the observed transition has the properties of a genuine phase transition.

Insulator–quantum Hall liquid transitions in a two-dimensional electron gas using self-assembled InAs dots

We investigate the transport properties of two-dimensional electron gases (2DEG) formed in a GaAs/AlGaAs quantum well, where self-assembled InAs quantum dots were grown at the center of the GaAs well. Due to the resulting strain fields repulsive short-range scattering is experienced by the conduction electrons in the 2DEG. In a perpendicular magnetic field, there are transitions between quantum Hall liquids at filling factors ν=1 and 2 and the insulating phase. We show that the boundary of insulator–Quantum Hall transitions can be identified either by analysing the temperature-independent points in ρ xx or from the peaks in σ xx at low temperatures and both methods give similar results.

Localization of the Hall resistivity at high magnetic fields: absence of the quantized Hall insulator

We present a real-space renormalization-group study of localization in a two-dimensional hierarchical network model that is designed to represent phase-coherent electron transport in the quantum-Hall regime. Scaling expressions for both the longitudinal and Hall resistivities are derived. In agreement with recent numerical studies, we find that the Hall resistivity is quantized in the metallic phase but diverges in the insulating phase. This suggests that the characteristics of a quantized Hall insulator can occur only in the presence of a strong dephasing mechanism.

Percolation of quantum Hall droplets in intentionally disordered GaAs/GaAlAs heterojunctions

The transition of two-dimensional electron systems (2DES) with intentional disorder in form of a δ-layer doped with beryllium into quantum Hall insulators composed of separate electron droplets is examined by magnetotransport and far-infrared spectroscopy. We observe the percolation threshold at filling factors clearly below ν c = 1 2 that is expected for statistical disorder. The far-infrared excitations bear strong resemblance to magnetoplasmons of density-modulated 2DES and antidot systems in regular arrays. Thus, a perceptible degree of short-range order between the sites of the beryllium acceptors is uncovered.

Evidence for a quantum Hall insulator in an InGaAs/InP heterostructure

We study the quantum critical behavior of the plateau–insulator (PI) transition in a low mobility In 0.53Ga 0.47As/InP heterostructure. By reversing the direction of the magnetic field ( B) we find an averaged Hall resistance ρ xy which remains quantized at the plateau value h/ e 2 throughout the PI transition. We extract a critical exponent κ′=0.57±0.02 for the PI transition which is slightly different from the established value 0.42±0.04 as previously obtained from the plateau–plateau transitions.

Quantum breakdown of the quantized Hall insulator

We present an analytical scaling theory for localization in a two-dimensional hierarchical network model that is designed to represent phase-coherent electron transport in the quantum-Hall regime. Scaling expressions for both the longitudinal and Hall resistivities are derived. In agreement with recent numerical studies, we find that the Hall resistivity is quantized in the metallic phase but diverges in the insulating phase. This suggests that the characteristics of a quantized Hall insulator can occur only in the presence of a strong dephasing mechanism.