Critical currents and self organization in quantum Hall bilayers

TL;DR

This paper develops a theory for the critical interlayer tunneling current in disordered quantum Hall bilayers, explaining experimental observations and predicting how the critical current varies with sample size, density, and other parameters.

Contribution

It introduces a model accounting for static vortices and disorder, explaining the area dependence of the critical current and predicting a crossover behavior and density-dependent peaks.

Findings

Critical current proportional to sample area, matching experiments.

Prediction of a crossover to square-root area dependence at smaller sizes or densities.

Identification of a peak in critical current as electron density varies.

Abstract

We present a theory of the critical interlayer tunneling current in a disordered quantum Hall bilayer at total filling factor one, allowing for the effect of static vortices. In agreement with recent experiments [Phys. Rev. B 80, 165120 (2009); ibid. 78, 075302 (2008)], we find that this critical current is proportional to the area of the sample and is comparable in magnitude to observed values. This reflects the formation of a Bean critical state as a result of current injection at the boundary. We predict a crossover to a critical current proportional to the square-root of area as either sample size or electron density decreases. We also predict a peak in the critical current as the electron density varies at fixed layer separation.