QHE Regime Research Articles

Acoustic studies of ac conductivity mechanisms inn-GaAs/AlxGa1−xAs in the integer and fractional quantum Hall effect regime

For the heterostructure $n$-GaAs/Al${}_{x}$Ga${}_{1\ensuremath{-}x}$As with a sheet density $n=2\ifmmode\times\else\texttimes\fi{}{10}^{11}$cm${}^{\ensuremath{-}2}$ and mobility $\ensuremath{\mu}\ensuremath{\approx}2\ifmmode\times\else\texttimes\fi{}{10}^{6}$ cm${}^{2}$/V$ $s with integer and fractional quantum Hall effects (IQHE and FQHE, respectively) we demonstrate the wide applicability of acoustic methods for determining the general conduction parameters of a two-dimensional electron gas. We also examine the mechanisms of low-temperature conductivity in the minima of oscillations of high-frequency conductivity in the IQHE and FQHE regimes. In the magnetic field region where electrons are delocalized, the parameters determined by the acoustic technique do not differ from those determined by a direct current. However, the acoustic measurements do not require Hall bars and electrical contacts to be fabricated. In the minima of IQHE and FQHE oscillations, electrons are localized, and ac conductivity occurs via hopping. An analysis of the high-frequency conductivity in the QHE regime has been carried out within a ``two-site'' model. Furthermore, measurements of acoustoelectric effects in a tilted magnetic field were used to determine how the activation energy of the $\ensuremath{\nu}=2/3$ fractional quantum Hall effect gap varies with magnetic field.

Effective Maxwell equations for finite planar samples in QHE regime

Effective Maxwell equations for the mean quantum electromagnetic field in planar samples in QHE regime are investigated. Boundary conditions to be satisfied by the mean field intensities at the filamentary boundaries (edges) are determined. For ideal strictly 2D samples embedded in real 3D space, these constraints imply that the total filamentary charge at the boundaries (the free plus polarization terms) and current densities identically vanish at all times. In the static limit the exact quantization of the Hall resistance of samples of arbitrary form, directly follows from the boundary condition. The equations for the electromagnetic response in a neighborhood of the edge of a half-plane in QHE regime are solved. The system exhibits a weak diamagnetic response and inhomogeneous charge and current distributions develop in the sample.

IQHE and FQHE in a wire with incompressible and compressible strips

We report the study of the longitudinal (RL) and Hall (RH) resistances in a wide ballistic wire (LH⪡W⪡l, l is mean free path, W is the width of wire, LH is the magnetic length in QHE regime) in the IQHE and FQHE regimes. It was observed a partial suppression of the RL minima in the IQHE and their practically total disappearance in the FQHE while the Hall resistance plateaus corresponding to these minima remained well pronounced in both the IQHE and FQHE regimes. At lower filling factors (ν<1/3) we have observed a quantum Hall liquid–quantized Hall insulator transition that takes place at a certain critical magnetic field Bc and a critical resistance value close to h/e2. Finally, at ν<1/2 and at the lowest experimental temperatures T<0.3K there have been observed correlated fluctuations in the longitudinal and in the Hall resistance both as a function of magnetic field and gate voltage. It is supposed that the observed features are due to interplay between wide compressible and narrow incompressible strips in the wire.

Oscillations of 2D electron density in GaAs/Ga0.67Al0.33As heterostructures in the QHE regime

Cyclotron resonance (CR) and quantum transport measurements are performed on three GaAs/Ga0.67Al0.33As heterostructures in the quantum Hall regime at T = 2 K. The relaxation time and the 2D electron density Ns are determined fitting the CR transmission curves by the Drude-type model. In all samples the density Ns exhibits oscillations as a function of magnetic field. The dc quantum transport is also studied on the same structures and, assuming that the Hall resistance determines the electron density at all fields, one obtains density oscillations similar to those measured by CR. This density behaviour is modelled using a reservoir hypothesis.

Influence of infrared illumination on the accuracy of the quantized hall resistance

The influence of infrared radiation on the accuracy of the quantized Hall resistance devices used in metrology is investigated. Samples exhibiting anomalous quantized Hall resistances due to large contact resistances resulting from a partially depleted electron gas can be brought back to a normal behavior by illumination with short pulses of infrared light. In addition, the critical current in the QHE regime can be considerably increased by the same illumination method.

Conductance of a 2D Corbino disk under QHE conditions in the presence of contact phenomena

It is noted that contacts of a two-dimensional (2DEG) electronic system with “external” metallic electrodes destroy the spatial uniformity of the density of the system. This gives rise to specific dimensional effects for the conductance of an unscreened Corbino disk in a magnetic field sufficient for the appearance of local regions with an integer-valued filling factor in the electron density profile. The overall pattern of the transport voltage distribution along the disk is seriously transformed. It becomes possible to explain the large (compared with the cyclotron energy) values of the critical transport voltage, leading to breakdown of the QHE regime. The experiment qualitatively confirms the predictions of the theory.

Surface Waves and Forced Oscillations in QHE Planar Samples

Dispersion relations and polarizations for surface waves in infinite planar samples in the QHE regime are explicitly determined in the small wavevector limit in which the dielectric tensor can be considered local. The wavelength and frequency regions of applicability of the results extends to the infrared region for typical experimental conditions. Then, standard samples with millimetric sizes seem to be able to support such excitations. Forced oscillations are also determined which should be generated in the 2DEG by external electromagnetic sources. They show an almost frequency independent wavelength which decreases with the magnetic field. A qualitative model based in these solutions is also presented to describe a recently found new class of resonances appearing near the edge of a 2DEG in the QHE regime.

Influence of infrared illumination on the accuracy of the quantized Hall resistance

The influence of infrared radiation on the accuracy of the quantized Hall resistance devices used in metrology is investigated. Samples exhibiting anomalous quantized Hall resistances due to large contact resistances resulting from a partially depleted electron gas can be brought back to a normal behavior by illumination with short pulses of infrared light. In addition, the critical current in the QHE regime can be considerably increased by the same illumination method.

Low temperature magnetotransport of 2D electron and hole systems in high-mobility Si [sbnd]Si 1 − xGe x heterostructures

Low-temperature magnetotransport measurements of 2D electron and hole systems (2DES, 2DHS) in high quality n- and p-type modulation-doped Si Si 1 − x Ge x heterostructures (respectively) have been extended to high magnetic fields (50 T) and low temperatures (30 mK). For the high-mobility 2DES in n-Si, a two-valley system, signatures of the fractional quantum Hall effect (FQHE) in the region v < 1 (one valley occupied, lowest spin state) usually observed in GaAs AlGaAs are replicated out to v = 2/5 at B ≈ 48T. For 1 < v < 2, however, (both valleys occupied, lowest spin state), prominent FQHE states such as v = 5/3 are absent, indicative of the importance of valley occupation. For the 2DHS in p-Si 1 − x Ge x , in addition to the QHE, two low-temperature insulating phases (IP) are identified at v = 1.5 and v ≲ 0.5 (B ≈ 30T), with re-entrance to the QHE regime at v = 1 ( B ≈ 15T). The IP centred at v = 1.5 has the characteristics of a Hall insulator but is unanticipated by the global phase diagram for 2D systems. The important physics associated with the IP is related to an energy degeneracy of adjacent Landau levels of opposite spin.

Measurements and modeling of nonlocal resistance in the fractional quantum Hall effect.

Recently, we have reported the observation of nonlocal resistance in the regime of the fractional quantum Hall effect (FQHE) that clearly demonstrates edge-state conduction over macroscopic distances. In this paper we present measurements of nonlocal resistance with variations of sample geometry, magnetic-field direction, temperature, and applied current. From our results we formulate a picture of transport in the FQHE regime via coexisting edge and bulk states. Scattering of edge currents is largely suppressed over distances of \ensuremath{\sim}1 mm at low temperatures. Edge currents are partially redistributed into the bulk at Ohmic contacts on the sample periphery. This results in potential drops between Ohmic contacts far from the bulk-only current path, i.e., nonlocal resistances. For analysis of our data, we introduce a FQHE extension of the bulk-edge transport model successfully applied by Szafer et al. in the integer QHE regime. We discuss the current and temperature dependence of the data in terms of temperature-dependent scattering between edge and bulk currents, increasing with increasing current or temperature.

Low-frequency edge magnetoplasmons in the quantum Hall regime under conditions of reduced Coulomb interaction

The authors have measured edge magnetoplasmon oscillations (EMP) in a high-mobility GaAs-GaAlAs heterostructure in the quantum Hall regime. By placing a ground plane close to the two-dimensional electron gas the electrostatic field far from the edge is screened. By varying the separation of the ground plane from the 2DEG the distance that the electrostatic fields penetrates from the edge can be varied. The relative importance of the edge and bulk contributions to the EMP are thus deduced and one is able to estimate the width of the EMP charge distribution in the QHE regime as 1 mu m. The authors attribute this width as being due to the characteristic site of the random potential near the edge of the 2DEG.

Magneto-photoluminescence studies of a 2D electron system: Signatures of the fractional quantum Hall effect and Wigner solid

The anticipated transition from a liquid to a magnetically-induced Wigner solid (MIWS) ground state in a two-dimensional electron system is investigated by bandgap photoluminescence (electron-valence band hole recombination) in two GaAs single heterojunctions of different densities and intersubband spacings. For Landau level filling factors ν< 1 5 the photoluminescence spectra are dominated by a new line, the temperature dependence of which is used to map a phase boundary which is situated close to the boundary associated with a pinned MIWS phase mapped by a variety of other techniques. A weak peak, split off to lower energy from the main PL emission, may also be of relevance to the MIWS. Comparison is made with optical data that probes this transition by electron-neutral acceptor recombination in Be δ-doped samples. In our higher density sample (∼ 10 11cm −2), a temperature-dependent laser-induced 2D electron density depletion effect observed at high magnetic fields and low temperatures is investigated systematically. It has also been possible to study 2D electron to acceptor-bound hole recombination in this sample associated with residual, low concentration carbon impurity levels as a further probe of the QHE regime. Additionally, a definitive optical signature of the ν= 1 3 FQHE hierarchy is reported.

High-frequency conductivity of a 2D electron channel of the GaAs/AlGaAs heterostructure in the QHE regime

We have measured the diagonal conductivity σ xx(ω) of a 2DEG at magnetic fields up to 8T over a range of frequencies from 50 to 600 MHz. At integer filling factors, where QHE is observed, a.c. conductivity exceeds its d.c. value by several orders of magnitude. It increases with frequency and exhibits slow temperature dependence in the range from 1.7 to 4.2 K.