Quantum Lifetime in Ultra-High Quality GaAs Quantum Wells: Relationship to ${\Delta }_{5/2}$ 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 ${\tau }_q$ 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.

12 pages, 4 figures

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• The effect of oscillating Fermi energy on the line shape of the Shubnikov-de Haas oscillation in a two dimensional electron gas
• The longitudinal resistance of a quantum Hall system with a density gradient
• Low-temperature illumination and annealing of ultra-high quality quantum wells
• High temperature resistivity measured at ν = 5/2 as a predictor of 2DEG quality in the N=1 Landau level

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