  Motivated by recent experiments on Si/SiGe quantum wells with a co-design of
high electron mobility and large valley splitting [B. Paquelet Wuetz, et al.,
Nature Communications 14, 1385 (2023); D. D. Esposti, et al.,
arXiv:2309.02832], suitable for a Si-based spin qubit quantum computing
platform, we examine the role of disorder by theoretically calculating mobility
and quantum mobility from various scattering mechanisms and their dependence on
the electron density. At low electron densities $n_e < 4 \times 10^{11}$
cm$^{-2}$, we find that mobility is limited by remote Coulomb impurities in the
capping layer, whereas interface roughness becomes the significant limiting
factor at higher densities. We also find that alloy disorder scattering is not
a limiting mechanism in the reported high-mobility structures. We estimate the
critical density of the disorder-driven low-density metal-insulator transition
using the Anderson-Ioffe-Regel localization criterion and qualitatively explain
the breakdown of the Boltzmann-Born theory at low densities. We also estimate
the critical density by considering inhomogeneous density fluctuations induced
by long-range Coulomb disorder in the system, and find a larger critical
density compared to the one obtained from the Anderson-Ioffe-Regel criterion.
For quantum mobility, our calculation suggests that remote and distant
background impurities are likely the limiting scattering sources across all
density. Future measurements of quantum mobility should provide more
information on the distribution of background impurities inside the SiGe
barriers. Moreover, we extend our theoretical analysis to the effect of quantum
degeneracy on transport properties and predict the mobility and the critical
density for the metal-insulator transition in spin-polarized high-mobility
structures under an external parallel magnetic field.
