Evaluation of Quantum Scattering Time in Ultra-High Quality GaAs Quantum Wells

We present a critical analysis of the extraction of quantum scattering time from Shubnikov-de Haas oscillations in ultra-high quality GaAs quantum wells. In the regime of temperature and magnetic field study here (T{$\sim$}0.3K, B{$\leq$}0.3T) we find the canonical method for determination of quantum scattering time yields unreliable results (cf. Coleridge, Phys. Rev. B \textbf{44}, 3793). We elaborate a formalism that allows extraction of the quantum scattering time in a regime in which the normalized modulation of the density of states $\Delta g/ g_0$ is greater than unity. This approach describes well low-field data for samples that display very large excitation gaps for fragile fractional quantum Hall states at large magnetic field.