Revisiting excitation gaps in the fractional quantum Hall effect

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.