# Quantum Lifetime in Ultra-High Quality GaAs Quantum Wells: Relationship to $\Delta_{5/2}$ and Impact of Density Fluctuations

## TL;DR

This study investigates the quantum lifetime in high-quality GaAs quantum wells, revealing that density inhomogeneities significantly affect measurements and that quantum lifetime does not directly correlate with the fractional quantum Hall gap at 5/2 filling.

## Contribution

It demonstrates the impact of density fluctuations on quantum lifetime measurements and clarifies the relationship between quantum lifetime and fractional quantum Hall state quality.

## Key findings

- Density inhomogeneities affect Shubnikov-de Haas oscillation amplitudes.
- Quantum lifetime estimates are underestimated without considering inhomogeneities.
- Quantum lifetime does not strongly correlate with the 5/2 fractional quantum Hall gap.

## Abstract

We consider quantum lifetime derived from low-field Shubnikov-de Haas oscillations as a metric of quality of the two-dimensional electron gas in GaAs quantum wells that expresses large excitation gaps in the fractional quantum Hall states of the N=1 Landau level. Analysis indicates two salient features: 1) small density inhomogeneities dramatically impact the amplitude of Shubnikov-de Haas oscillations such that the canonical method (cf. Coleridge, Phys. Rev. B \textbf{44}, 3793) for determination of quantum lifetime substantially underestimates $\tau_q$ unless density inhomogeneity is explicitly considered; 2) $\tau_q$ does not correlate well with quality as measured by $\Delta_{5/2}$, the excitation gap of the fractional quantum Hall state at 5/2 filling.