Energy Gap in Weakly Disordered Fractional Quantum Hall Liquids: Quantitative Comparison to GaAs Quantum Well Experiments at $\nu= 1/3$
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 $\nu=1/3$, explicitly incorporating both finite layer thickness and disorder effects. The finite layer thickness is modeled by solving the Poisson-Schr\"odinger equations for the experimental devices, yielding the electron wave functions in the perpendicular direction. Using these and the disorder energy extracted from the experiment, we estimate the charge gap and the mobility gap at $\nu=1/3$ in the weakly disordered lowest Landau level. Remarkably, both gaps show good quantitative agreement with the activation gap measured from the experiment in narrow quantum wells. Our results also indicate the potential need of incorporating higher subbands to make accurate theoretical predictions of the energy gap in wide quantum wells.