Thermally Activated Deviations from Quantum Hall Plateaus

TL;DR

This paper investigates how thermal activation causes deviations from quantized Hall conductivity in two-dimensional electron systems, revealing temperature-dependent behaviors and extending results to fractional quantum Hall states.

Contribution

It introduces a model describing the thermal activation-induced deviations from quantized Hall plateaus, including temperature dependence and fractional charge considerations.

Findings

Deviation follows an exponential form with temperature.

Prefactor decays as a power law below a characteristic temperature.

Results apply to fractional quantum Hall states with fractional charge.

Abstract

The Hall conductivity $\sigma_{\rm xy}$ 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 $\sigma_{\rm xy}$ 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 $\sigma_{\rm xy}^*\exp(-\Delta/T)$. The prefactor $\sigma_{\rm xy}^*$ is equal to $e^2/h$ at temperatures above a characteristic temperature $T_2$. With the temperature decreasing below $T_2$, $\sigma_{\rm xy}^*$ decays according to a power law: $\sigma_{\rm xy}^* = \frac{e^2}{h}(T/T_2)^\gamma$. Similar results are valid for a fractional Hall plateau near filling factor $p/q$ if $e$ is replaced by the fractional charge $e/q$.