High temperature resistivity measured at ν = 5/2 as a predictor of 2DEG quality in the N=1 Landau level
We report a high temperature (T = 0.3K) indicator of the excitation gap $Δ_{5/2}$ at the filling factor $ ν=5/2$ fractional quantum Hall state in ultra-high quality AlGaAs/GaAs two-dimensional electron gases. As the lack of correlation between mobility $μ$ and $Δ_{5/2}$ has been well established in previous experiments, we define, analyze and discuss the utility of a different metric $ρ_{5/2}$, the resistivity at $ν=5/2$, as a high temperature predictor of $Δ_{5/2}$. This high-field resistivity reflects the scattering rate of composite fermions. Good correlation between $ρ_{5/2}$ and $Δ_{5/2}$ 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 $ρ_{5/2}$ and $Δ_{5/2}$ are sensitive to long-range disorder from remote impurities, while $μ$ is sensitive primarily to disorder localized near the quantum well.