Correlated quantum percolation in the lowest Landau level

TL;DR

This paper investigates how power-law correlated disorder affects electron localization in the lowest Landau level, predicting new quantum critical points in the integer quantum Hall effect through numerical analysis.

Contribution

It introduces a numerical study of correlated disorder in quantum Hall systems, applying the extended Harris criterion to predict novel localization critical points.

Findings

Extended Harris criterion applies to quantum localization.

Prediction of new quantum critical points with correlated disorder.

Critical points are stable against short-range disorder.

Abstract

Our understanding of localization in the integer quantum Hall effect is informed by a combination of semi-classical models and percolation theory. Motivated by the effect of correlations on classical percolation we study numerically electron localization in the lowest Landau level in the presence of a power-law correlated disorder potential. Careful comparisons between classical and quantum dynamics suggest that the extended Harris criterion is applicable in the quantum case. This leads to a prediction of new localization quantum critical points in integer quantum Hall systems with power-law correlated disorder potentials. We demonstrate the stability of these critical points to addition of competing short-range disorder potentials, and discuss possible experimental realizations.