High-temperature resistivity measured at ν=5/2 as a predictor of the two-dimensional electron gas quality in the N=1 Landau level

We report a high-temperature (T = 0.3 K) indicator of the excitation gap Delta(5/2) at the filling factor nu = 5/2 fractional quantum Hall state in ultrahigh-quality AlGaAs/GaAs two-dimensional electron gases. As the lack of correlation between mobility mu and Delta(5/2) has been well established in previous experiments, we define, analyze, and discuss the utility of a different metric rho(5/2), the resistivity at nu = 5/2, as a high-temperature predictor of Delta(5/2). This high-field resistivity reflects the scattering rate of composite fermions. Good correlation between rho(5/2) and Delta(5/2) is observed in both a density-tunable device and in a series of identically structured wafers with similar density but vastly different mobility. This correlation can be explained by the fact that both rho(5/2) and Delta(5/2) are sensitive to long-range disorder from remote impurities, while mu is sensitive primarily to disorder localized near the quantum well.