Mobility gap in fractional quantum Hall liquids: Effects of disorder and layer thickness

TL;DR

This paper investigates how disorder and layer thickness affect the stability of fractional quantum Hall states by calculating mobility gaps and comparing them with experimental data, clarifying the nature of gap collapse.

Contribution

It introduces a generalized Chern number approach for many-body systems to accurately determine mobility gaps considering disorder and layer thickness effects.

Findings

Excellent agreement between calculated mobility gaps and experimental activation gaps.

Disorder and layer thickness significantly influence the stability of fractional quantum Hall states.

The study clarifies the distinction between mobility gap and spectral gap in these systems.

Abstract

We study the behavior of two-dimensional electron gas in the fractional quantum Hall regime in the presence of finite layer thickness and correlated disordered potential. Generalizing the Chern number calculation to many-body systems, we determine the mobility gaps of fractional quantum Hall states based on the distribution of Chern numbers in a microscopic model. We find excellent agreement between experimentally measured activation gaps and our calculated mobility gaps, when combining the effects of both disordered potential and layer thickness. We clarify the difference between mobility gap and spectral gap of fractional quantum Hall states and explain the disorder-driven collapse of the gap and the subsequent transitions from the fractional quantum Hall states to insulator.