Memory effects in ac hopping conductance in the quantum Hall effect regime: Possible manifestation of DX$^-$ centers

Abstract

Using simultaneous measurements of the attenuation and velocity of surface acoustic waves propagating along GaAs/Al$_{0.3}$Ga$_{0.7}$As heterostructures, complex ac conductance of the latters has been determined. In the magnetic fields corresponding to the middles of the Hall plateaus both the ac conductance, $σ(ω)$, and the sheet electron density, $n_s$, in the two-dimensional conducting layer turn out to be dependent on the samples' cooling rate. As a result, the sample ``remembers'' the cooling conditions. The complex conductance is strongly dependent on an infrared illumination which also changes both $σ(ω)$ and $n_s$. Remarkably, the correlation between $σ(ω)$ and $n_s$ is \emph{universal}, i.e. it is independent of the way to change these quantities. The results are attributed to two-electron defects (so-called $DX^-$ centers) located in the Si doped layer.