# High temperature resistivity measured at {\nu} = 5/2 as a predictor of 2DEG quality in the N=1 Landau level

## TL;DR

This study demonstrates that the resistivity at filling factor 5/2 at high temperature can predict the excitation gap of the fractional quantum Hall state, providing a new metric for assessing 2DEG quality beyond mobility.

## Contribution

It introduces resistivity at ν=5/2 as a novel high-temperature predictor of the excitation gap, highlighting its correlation with long-range disorder effects.

## Key findings

- Resistivity at ν=5/2 correlates with the excitation gap Δ_{5/2}.
- Resistivity reflects long-range disorder, unlike mobility.
- Resistivity at ν=5/2 is a reliable predictor across different samples.

## Abstract

We report a high temperature (T = 0.3K) indicator of the excitation gap $\Delta_{5/2}$ at the filling factor $ \nu=5/2$ fractional quantum Hall state in ultra-high 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.