Thermally Activated Deviations from Quantum Hall Plateaus

Abstract

The Hall conductivity $σ_{\rm xy}$ of a two-dimensional electron system is quantized in units of $e^2/h$ when the Fermi level is located in the mobility gap between two Landau levels. We consider the deviation of $σ_{\rm xy}$ from a quantized value caused by the thermal activation of electrons to the extended states for the case of a long range random potential. This deviation is of the form $σ_{\rm xy}^*\exp(-Δ/T)$. The prefactor $σ_{\rm xy}^*$ is equal to $e^2/h$ at temperatures above a characteristic temperature $T_2$. With the temperature decreasing below $T_2$, $σ_{\rm xy}^*$ decays according to a power law: $σ_{\rm xy}^* = \frac{e^2}{h}(T/T_2)^γ$. Similar results are valid for a fractional Hall plateau near filling factor $p/q$ if $e$ is replaced by the fractional charge $e/q$.