Anderson localization crossover in 2D Si systems: The past and the present

Using Ioffe-Regel-Mott (IRM) criterion for strong localization crossover in disordered doped 2D electron systems, we theoretically study the relationships among the three key experimentally determined localization quantities: critical density ($n_{\mathrm{c}}$), critical resistance (${\rho }_{\mathrm{c}}$), and sample quality defined by the effective impurity density (as experimentally diagnosed by the sample mobility, ${\mu }_{\mathrm{m}}$, at densities much higher than critical densities). Our results unify experimental results for 2D metal-insulator transitions (MIT) in Si systems over a 50-year period (1970-2020), showing that $n_{\mathrm{c}}$ (${\rho }_{\mathrm{c}}$) decrease (increase) with increasing sample quality, explaining why the early experiments in the 1970s, using low-quality samples (${\mu }_{\mathrm{m}}\sim {10}^3{\mathrm{c}\mathrm{m}}^2\mathrm{/}Vs$) reported strong localization crossover at $n_c\sim {10}^{12}{\mathrm{c}\mathrm{m}}^{-2}$ with ${\rho }_c\sim {10}^3\mathrm{\Omega }$ whereas recent experiments (after 1995), using high-quality samples (${\mu }_{\mathrm{m}}>{10}^4{\mathrm{c}\mathrm{m}}^2\mathrm{/}Vs$), report $n_c\sim {10}^{11}{\mathrm{c}\mathrm{m}}^{-2}$ with ${\rho }_c>{10}^4\mathrm{\Omega }$. Our theory establishes the 2D MIT to be primarily a screened Coulomb disorder-driven strong localization crossover phenomenon, which happens at different sample-dependent critical density and critical resistance, thus unifying Si 2D MIT phenomena over a 50-year period.