Energy Gap in Weakly Disordered Fractional Quantum Hall Liquids: Quantitative Comparison to GaAs Quantum Well Experiments at ν = 1/3

Based on a recent experiment in high-quality GaAs quantum wells Phys. Rev. Lett. 127, 056801 (2021), we present a microscopic study of the energy gap in two-dimensional electron gases at filling factor ν = 1/3 on the torus geometry, explicitly incorporating both finite layer thickness and disorder effects. The finite layer thickness is modeled by solving the Poisson-Schrödinger equations for the experimental devices, yielding the electron wave functions in the perpendicular direction. Using these wave functions and the disorder strengths calibrated from the experiment, we estimate the charge gap and the mobility gap at ν = 1/3 in the weakly disordered lowest Landau level. Remarkably, both gap estimates show semiquantitative agreement with the experimentally measured activation gap. These results indicate that realistic finite thickness and disorder are essential ingredients for bringing the theoretically estimated energy gaps toward those measured experimentally. Our work also establishes the charge gap as a computationally efficient estimate of the energy-gap scale in weakly disordered samples.