Quantum Lifetime in Ultrahigh Quality GaAs Quantum Wells: Relationship to Δ5/2 and Impact of Density Fluctuations

We consider the quantum lifetime derived from low-field Shubnikov-de Haas oscillations as a metric of the quality of the two- dimensional electron gas in GaAs quantum wells that expresses large excitation gaps of the.nu= 5/2 fractional quantum Hall state in the N = 1 Landau level. In high quality samples, small density inhomogeneities dramatically impact the amplitude of Shubnikov- de Haas oscillations such that the canonical method [cf. Coleridge, Phys. Rev. B 44, 3793 (1991)] for determination of the quantum lifetime substantially underestimates tq unless density inhomogeneity is explicitly considered. We have developed a method that can be used to determine density inhomogeneity and extract the intrinsic tq by analyzing the Shubnikov-de Haas oscillations. However, even after accounting for inhomogeneity, t(q) does not correlate well with sample quality as measured by Delta(5/2,) the excitation gap of the fractional quantum Hall state at 5/ 2 filling.