Motivated by recent breakthroughs in molecular beam epitaxy of GaAs/AlGaAs quantum wells [Y. J. Chung et al., Nat. Mater. 20, 632 (2021)], we examine contributions to mobility and quantum mobility from various scattering mechanisms and their dependencies on the electron density. We find that at lower electron densities, $n_e\lesssim 1\times {10}^{11}{\mathrm{cm}}^{-2}$, both transport and quantum mobility are limited by unintentional background impurities and follow a power-law dependence, $\propto n_e^{\alpha }$, with $\alpha \approx 0.85$. Our predictions for quantum mobility are in reasonable agreement with an estimate obtained from the resistivity at filling factor $\nu =1/2$ in a sample of Y. J. Chung et al. with $n_e=1\times {10}^{11}{\mathrm{cm}}^{-2}$. Consideration of other scattering mechanisms indicates that interface roughness (remote donors) is likely a limiting factor of transport (quantum) mobility at higher electron densities. Future measurements of quantum mobility should yield information on the distribution of background impurities in GaAs and AlGaAs.

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• Electrical conductivity
• Roughness
• Disordered alloys
• Semiconductors
• Two-dimensional electron system
• Random phase approximation