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

TL;DR

This paper unifies 50 years of experimental data on 2D metal-insulator transitions in silicon systems by theoretically linking critical localization parameters to sample quality, showing the transition is driven by Coulomb disorder and varies with sample conditions.

Contribution

The study provides a theoretical framework that explains the variation in critical density and resistance in 2D Si systems over decades, unifying experimental observations under a Coulomb disorder-driven localization crossover.

Findings

Critical density decreases with improved sample quality.

Critical resistance increases with improved sample quality.

The 2D MIT is primarily a Coulomb disorder-driven localization crossover.

Abstract

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.