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Motivated by recent experiments on Si/SiGe quantum wells with a co-design ofhigh 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 computingplatform, we examine the role of disorder by theoretically calculating mobilityand quantum mobility from various scattering mechanisms and their dependence onthe 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 thecapping layer, whereas interface roughness becomes the significant limitingfactor at higher densities. We also find that alloy disorder scattering is nota limiting mechanism in the reported high-mobility structures. We estimate thecritical density of the disorder-driven low-density metal-insulator transitionusing the Anderson-Ioffe-Regel localization criterion and qualitatively explainthe breakdown of the Boltzmann-Born theory at low densities. We also estimatethe critical density by considering inhomogeneous density fluctuations inducedby long-range Coulomb disorder in the system, and find a larger criticaldensity compared to the one obtained from the Anderson-Ioffe-Regel criterion.For quantum mobility, our calculation suggests that remote and distantbackground impurities are likely the limiting scattering sources across alldensity. Future measurements of quantum mobility should provide moreinformation on the distribution of background impurities inside the SiGebarriers. Moreover, we extend our theoretical analysis to the effect of quantumdegeneracy on transport properties and predict the mobility and the criticaldensity for the metal-insulator transition in spin-polarized high-mobilitystructures under an external parallel magnetic field.

Understanding disorder in Silicon quantum computing platforms: Scattering mechanisms in Si/SiGe quantum wells