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

Abstract

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.