Impact of disorder on frequency scaling in the integer quantum Hall effect

Abstract

We have studied the effect of both long- and short-range disorder on frequency scaling of the diagonal magnetoconductivity ${\ensuremath{\sigma}}_{xx}$ in the integer quantum Hall effect regime of two-dimensional electrons confined to Al${}_{x}$Ga${}_{1\text{\ensuremath{-}}x}$As/Al${}_{0.33}$Ga${}_{0.67}$As single heterostructures for two Al concentrations, $x$. Within the frequency range 100 MHz \ensuremath{\leqslant} $f$ \ensuremath{\leqslant} 20 GHz and for a temperature $T$ = 35 mK, we found that the frequency scaling exponent $c$ changes from 0.6 \ifmmode\pm\else\textpm\fi{} 0.05 for a GaAs/Al${}_{0.33}$Ga${}_{0.67}$As heterostructure, where the disorder is dominated by long-range ionized impurity potentials, to $c$ = 0.42 \ifmmode\pm\else\textpm\fi{} 0.06 for Al${}_{0.015}$Ga${}_{0.985}$As/Al${}_{0.33}$Ga${}_{0.67}$As heterostructures, where the dominant contribution to the disorder is from short-range alloy potential fluctuations. This value of $c$ allows us to estimate the dynamical scaling exponent as $z$ = 1 \ifmmode\pm\else\textpm\fi{} 0.13.