Acoustic Studies of AC Conductivity Mechanisms in $n$-GaAs/AlGaAs in the Integer and Fractional Quantum Hall Effect Regime

Abstract

In case of a of the heterostructure n-GaAs/AlGaAs with sheet density $n=2 \times 10^{11}$cm$^{-2}$ and mobility $μ\approx 2 \times 10^6$ cm$^2$/V$\cdot$s with integer and fractional quantum Hall effect (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 turns to be 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 provided the dependence of the activation energy on magnetic field in the fractional quantum Hall effect regime at $ν$=2/3.