Using the Ioffe-Regel-Mott criterion for strong localization crossover in disordered doped two-dimensional (2D) electron systems, we theoretically study the relationships between 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 (MITs) in Si systems over a 50-year period (1970–2020), showing that $n_{\mathrm{c}}$ $\left({\rho }_{\mathrm{c}}\right)$ decreases (increases) with increasing sample quality, explaining why the early experiments in the 1970s, using low-quality samples $[{\mu }_{\mathrm{m}}\sim {10}^3$ ${\mathrm{cm}}^2/\left(\mathrm{V}\mathrm{s}\right)]$, reported strong localization crossover at $n_{\mathrm{c}}\sim {10}^{12}$ ${\mathrm{cm}}^{-2}$ with ${\rho }_{\mathrm{c}}\sim {10}^3$ $\mathrm{\Omega }$ whereas recent experiments (after 1995), using high-quality samples $[{\mu }_{\mathrm{m}}>{10}^4$ ${\mathrm{cm}}^2/\left(\mathrm{V}\mathrm{s}\right)]$, report $n_{\mathrm{c}}\sim {10}^{11}$ ${\mathrm{cm}}^{-2}$ with ${\rho }_{\mathrm{c}}>{10}^4$ $\mathrm{\Omega }$. 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 values, thus unifying Si 2D MIT phenomena over a 50-year period.

Close

PrevNext

View figure in article

• Metal-insulator transition
• Disordered systems
• Boltzmann theory