High-frequency hopping conductivity in the quantum Hall effect regime: Acoustical studies

The high-frequency conductivity of Si $\ensuremath{\delta}$-doped GaAs/AlGaAs heterostructures is studied in the integer quantum Hall effect (QHE) regime, using acoustic methods. Both the real and the imaginary parts of the complex conductivity are determined from the experimentally observed magnetic field and temperature dependencies of the velocity and the attenuation of a surface acoustic wave. It is demonstrated that in structures with carrier density $(1.3\ensuremath{-}2.8)\ifmmode\times\else\texttimes\fi{}{10}^{11}{\mathrm{cm}}^{\ensuremath{-}2}$ and mobility $(1\ensuremath{-}2)\ifmmode\times\else\texttimes\fi{}{10}^{5}{\mathrm{cm}}^{2}/\mathrm{V}\mathrm{}\mathrm{s}$ the mechanism of low-temperature conductance near the QHE plateau centers is hopping. It is also shown that at magnetic fields corresponding to filling factors 2 and 4, the doped Si $\ensuremath{\delta}$ layer efficiently shunts the conductance in the two-dimensional electron gas (2DEG) channel. A method to separate the two contributions to the real part of the conductivity is developed, and the localization length in the 2DEG channel is estimated within the context of a nearest-neighbor hopping model.