Disorder broadening of even-denominator fractional quantum Hall states in the presence of a short-range alloy potential

We study energy gaps of the $\nu=7/2$ and $\nu=5/2$ fractional quantum Hall states in a series of two-dimensional electron gases containing alloy disorder. We found that gaps at these two filling factors have the same suppression rate with alloy disorder. The dimensionless intrinsic gaps in our alloy samples obtained from the model proposed by Morf and d'Ambrumenil are consistent with numerical results, but are larger than those obtained from experiments on pristine samples published in the literature. The disorder broadening parameter has large uncertainties. However, a modified analysis relying on shared intrinsic gaps yields consistent results for both the $\nu=5/2$ and $7/2$ fractional quantum Hall states and establishes a linear relationship between the disorder broadening parameter and alloy concentration. Furthermore, we find that we can separate contributions to the disorder broadening of the long-range and short-range scattering.