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

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 $\ddot{I}{„}_q$ unless density inhomogeneity is explicitly considered; 2) $\ddot{I}{„}_q$ does not correlate well with quality as measured by $\hat{I}{”}_{5/2}$, the excitation gap of the fractional quantum Hall state at 5/2 filling.

12 pages, 4 figures