Revisiting excitation gaps in the fractional quantum Hall effect

TL;DR

This paper provides improved theoretical calculations of excitation gaps in fractional quantum Hall states, accounting for finite width and Landau level mixing, and discusses deviations from experimental data possibly due to disorder effects.

Contribution

It offers more accurate theoretical gap estimates including finite width and LL mixing effects, and explores the nonzero broadening parameter even without disorder.

Findings

Theory captures width dependence of gaps

Deviations suggest disorder influences gaps

Broadening parameter may be nonzero without disorder

Abstract

Recent systematic measurements of the quantum well width dependence of the excitation gaps of fractional quantum Hall states in high mobility samples [Villegas Rosales {\it et al.}, Phys. Rev. Lett. {\bf 127}, 056801 (2021)] open the possibility of a better quantitative understanding of this important issue. We present what we believe to be accurate theoretical gaps including the effects of finite width and Landau level (LL) mixing. While theory captures the width dependence, there still remains a deviation between the calculated and the measured gaps, presumably caused by disorder. It is customary to model the experimental gaps of the $n/(2n\pm 1)$ states as $\Delta_{n/(2n\pm 1)} = Ce^2/[(2n\pm 1)\varepsilon l]-\Gamma$, where $\varepsilon$ is the dielectric constant of the background semiconductor and $l$ is the magnetic length; the first term is interpreted as the cyclotron energy of composite fermions and $\Gamma$ as a disorder-induced broadening of composite-fermion LLs. Fitting the gaps for various fractional quantum Hall states, we find that $\Gamma$ can be nonzero even in the absence of disorder.