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

K. Saeed, N. A. Dodoo-Amoo, L. H. Li, S. P. Khanna, E. H. Linfield, A. G. Davies, and J. E. Cunningham

Phys. Rev. B 84, 155324 – Published 31 October 2011

Abstract

We have studied the effect of both long- and short-range disorder on frequency scaling of the diagonal magnetoconductivity $σ_{x x}$ in the integer quantum Hall effect regime of two-dimensional electrons confined to Al $_{x}$ Ga $_{1 − x}$ As/Al $_{0.33}$ Ga $_{0.67}$ As single heterostructures for two Al concentrations, $x$ . Within the frequency range 100 MHz ⩽ $f$ ⩽ 20 GHz and for a temperature $T$ = 35 mK, we found that the frequency scaling exponent $c$ changes from 0.6 ± 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 ± 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 ± 0.13.