Transition dynamics in the electrical breakdown of the quantum Hall effect

Abstract

We investigate the dynamic properties of the breakdown of integer quantum Hall states (QHSs). The critical field of QHS breakdown that occurs at a filling factor of $\ensuremath{\nu}\ensuremath{\sim}2$ is found to depend on the scan rate of the applied Hall field ${E}_{H}$ and to fluctuate stochastically; in contrast, a smooth breakdown is observed at $\ensuremath{\nu}\ensuremath{\sim}4$. The histogram of the critical values of ${E}_{H}$ can be used to derive the escape and relaxation time, ranging from a few seconds to 10 $\ensuremath{\mu}$s between the low-dissipation QHS and the dissipation state. The increase of the escape rate between the low-dissipative QHS and the dissipative state is accompanied by a decrease of the relaxation rate and vice versa, indicating the bistable nature of the breakdown phenomena. The observed results agree well with the calculated results based on the basis of the bootstrap electron heating model. We conclude that the dynamic behaviors of QHS breakdown are governed by the transition probability that resides in the thermal bistable regime between the QHS and the dissipation states.