Fractional quantum Hall effect energy gap: role of electron layer thickness

TL;DR

This study compares experimental measurements of the fractional quantum Hall effect energy gaps in high-quality GaAs quantum wells with theoretical calculations, highlighting the influence of electron layer thickness and disorder.

Contribution

It provides a systematic, quantitative comparison between measured and calculated FQHE energy gaps considering layer thickness and Landau level mixing.

Findings

Measured gaps are below theoretical predictions.

Increasing layer thickness improves agreement between experiment and theory.

Disorder accounts for some discrepancies.

Abstract

The fractional quantum Hall effect (FQHE) stands as a quintessential manifestation of an interacting two-dimensional electron system. One of FQHE's most fundamental characteristics is the energy gap separating the incompressible ground state from its excitations. Yet, despite nearly four decades of investigations, a quantitative agreement between the theoretically calculated and experimentally measured energy gaps is lacking. Here we report a quantitative comparison between the measured energy gaps and the available theoretical calculations that take into account the role of finite layer thickness and Landau level mixing. Our systematic experimental study of the FQHE energy gaps uses very high-quality two-dimensional electron systems confined to GaAs quantum wells with varying well widths. All the measured energy gaps fall bellow the calculations, but as the electron layer thickness increases, the results of experiments and calculations come closer. Accounting for the role of disorder in a phenomenological manner, we find the measured energy gaps to be in reasonable quantitative agreement with calculations, although some discrepancies remain.