Theory of Current-Induced Breakdown of the Quantum Hall Effect

TL;DR

This paper investigates how high injected currents and electric fields cause the breakdown of the quantum Hall effect, revealing a topological transition at a critical electric field proportional to B^{3/2}.

Contribution

It introduces a theoretical model using von Neumann lattice representation to explain the current-induced breakdown of the quantum Hall effect, emphasizing the role of state broadening and topological invariants.

Findings

Hall conductance remains quantized below critical field

Conductance becomes non-quantized above critical field

Critical electric field scales as B^{3/2}

Abstract

By studying the quantum Hall effect of stationary states with high values of injected current using a von Neumann lattice representation, we found that broadening of extended state bands due to a Hall electric field occurs and causes the breakdown of the quantum Hall effect. The Hall conductance agrees with a topological invariant that is quantized exactly below a critical field and is not quantized above a critical field. The critical field is proportional to $B^{3/2}$ and is enhanced substantially if the extended states occupy a small fraction of the system.