Disorder broadening of even denominator fractional quantum Hall states in the presence of a short-range alloy potential

TL;DR

This study investigates how alloy disorder affects the energy gaps of fractional quantum Hall states at filling factors 5/2 and 7/2, revealing a linear relationship between disorder and alloy concentration and separating contributions from different scattering types.

Contribution

It introduces a modified analysis method to accurately determine disorder broadening and demonstrates the linear dependence of disorder effects on alloy concentration in quantum Hall states.

Findings

Gaps at 5/2 and 7/2 are suppressed at the same rate by alloy disorder.

Intrinsic gaps from the model are larger than those from pristine experimental samples.

A linear relationship exists between disorder broadening and alloy concentration.

Abstract

We study energy gaps of the $\nu=7/2$ and $\nu=5/2$ fractional quantum Hall states in a series of two-dimensional electron gases containing alloy disorder. We found that gaps at these two filling factors have the same suppression rate with alloy disorder. The dimensionless intrinsic gaps in our alloy samples obtained from the model proposed by Morf and d'Ambrumenil are consistent with numerical results, but are larger than those obtained from experiments on pristine samples published in the literature. The disorder broadening parameter has large uncertainties. However, a modified analysis relying on shared intrinsic gaps yields consistent results for both the $\nu=5/2$ and $7/2$ fractional quantum Hall states and establishes a linear relationship between the disorder broadening parameter and alloy concentration. Furthermore, we find that we can separate contributions to the disorder broadening of the long-range and short-range scattering.