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 ($\mu_\mathrm{m} \sim 10^3 \mathrm{cm}^2/Vs$) reported strong localization crossover at $n_c \sim 10^{12} \mathrm{cm}^{-2}$ with $\rho_c \sim 10^3\Omega$ whereas recent experiments (after 1995), using high-quality samples ($\mu_\mathrm{m} >10^4 \mathrm{cm}^2/Vs$), report $n_c \sim 10^{11} \mathrm{cm}^{-2}$ with $\rho_c>10^4\Omega$. 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.