Field-induced breakdown of the quantum Hall effect

TL;DR

This paper presents a numerical analysis of the quantum Hall effect breakdown caused by Hall electric fields, revealing a scaling law that explains the dependence on magnetic and electric fields and aligns with experimental observations.

Contribution

It introduces a simple scaling law describing the breakdown of the quantum Hall effect due to the Hall field's competition with disorder, supported by numerical analysis.

Findings

Localized states decrease exponentially with Hall field

Breakdown fields are of a few hundred V/cm

Magnetic-field dependence follows B^{3/2}

Abstract

A numerical analysis is made of the breakdown of the quantum Hall effect caused by the Hall electric field in competition with disorder. It turns out that in the regime of dense impurities, in particular, the number of localized states decreases exponentially with the Hall field, with its dependence on the magnetic and electric field summarized in a simple scaling law. The physical picture underlying the scaling law is clarified. This intra-subband process, the competition of the Hall field with disorder, leads to critical breakdown fields of magnitude of a few hundred V/cm, consistent with observations, and accounts for their magnetic-field dependence \propto B^{3/2} observed experimentally. Some testable consequences of the scaling law are discussed.