Quantitative Analysis of the Disorder Broadening and the Intrinsic Gap for the $\nu =5\mathrm{/}2$ Fractional Quantum Hall State

We report a reliable method to estimate the disorder broadening parameter from the scaling of the gaps of the even and major odd denominator fractional quantum Hall states of the second Landau level. We apply this technique to several samples of vastly different densities and grown in different MBE chambers. Excellent agreement is found between the estimated intrinsic and numerically obtained energy gaps for the $\nu =5\mathrm{/}2$ fractional quantum Hall state. Futhermore, we quantify, for the first time, the dependence of the intrinsic gap at $\nu =5\mathrm{/}2$ on Landau level mixing.