High temperature resistivity measured at ν = 5/2 as a predictor of 2DEG quality in the N=1 Landau level

Abstract

We report a high temperature (T = 0.3K) indicator of the excitation gap $\hat{I}{”}_{5/2}$ at the filling factor $\hat{I}½=5/2$ fractional quantum Hall state in ultra-high quality AlGaAs/GaAs two-dimensional electron gases. As the lack of correlation between mobility $\hat{I}¼$ and $\hat{I}{”}_{5/2}$ has been well established in previous experiments, we define, analyze and discuss the utility of a different metric $\ddot{I}{}_{5/2}$, the resistivity at $\hat{I}½=5/2$, as a high temperature predictor of $\hat{I}{”}_{5/2}$. This high-field resistivity reflects the scattering rate of composite fermions. Good correlation between $\ddot{I}{}_{5/2}$ and $\hat{I}{”}_{5/2}$ 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 $\ddot{I}{}_{5/2}$ and $\hat{I}{”}_{5/2}$ are sensitive to long-range disorder from remote impurities, while $\hat{I}¼$ is sensitive primarily to disorder localized near the quantum well.

11 pages, 4 figures