Effects of large disorder on the Hofstadter butterfly

TL;DR

This paper investigates how large disorder influences the Hofstadter butterfly spectrum in two-dimensional electron systems under strong magnetic fields, revealing new spectral features and wave function behaviors.

Contribution

It provides a detailed numerical analysis of disorder effects on the Hofstadter butterfly, especially when disorder exceeds periodic potential strength, an area not well addressed by existing theories.

Findings

Disorder significantly alters the Hofstadter spectrum.

Wave functions exhibit localization and extension depending on disorder strength.

New transport phenomena are explained qualitatively.

Abstract

Motivated by the recent experiments on periodically modulated, two dimensional electron systems placed in large transversal magnetic fields, we investigate the interplay between the effects of disorder and periodic potentials in the integer quantum Hall regime. In particular, we study the case where disorder is larger than the periodic modulation, but both are small enough that Landau level mixing is negligible. In this limit, the self-consistent Born approximation is inadequate. We carry extensive numerical calculations to understand the relevant physics in the lowest Landau level, such as the spectrum and nature (localized or extended) of the wave functions. Based on our results, we propose a qualitative explanation of the new features uncovered recently in transport measurements.