From Electric Field Dependent Particle Dynamics to Bistability in the Breakdown of the Quantum Hall Effect

Abstract

Abstract The integer quantum Hall effect (IQHE) and its breakdown (onset of dissipation) reflect general properties of the solutions of the time-dependent Schrödinger equation, where the macroscopic elec­tric field E is properly included. In particular, the dynamics of an electron in a broadened Landau band not only depends on the disorder potential but also on the value of |E|. This leads to an I n ­ dependence of the conductivities σxx and σxy, which implies that the IQHE breaks down if |E| is sufficiently high. We show that the general form of the | El-dependence of σxx and σxy can lead to jumps in the longitudinal resistance at the breakdown of the IQHE, as observed in recent experiments.