Density-tuned effective metal-insulator transitions in two-dimensional semiconductor layers: Anderson localization or Wigner crystallization

Abstract

Electrons (or holes) confined in 2D semiconductor layers have served as model systems for studying disorder and interaction effects for almost 50 years. In particular, strong disorder drives the metallic 2D carriers into a strongly localized Anderson insulator (AI) at low densities whereas pristine 2D electrons in the presence of no (or little) disorder should solidify into a Wigner crystal at low carrier densities. Since the disorder in 2D semiconductors is mostly Coulomb disorder arising from random charged impurities, the applicable physics is complex as the carriers interact with each other as well as with the random charged impurities through the same long-range Coulomb coupling. By critically theoretically analyzing the experimental transport data in depth using a realistic transport theory to calculate the low-temperature 2D resistivity as a function of carrier density in 11 different experimental samples covering 9 different materials, we establish, utilizing the Ioffe-Regel-Mott criterion for strong localization, a direct connection between the critical localization density for the 2D metal-insulator transition (MIT) and the sample mobility deep into the metallic state, which for clean samples could lead to a localization density low enough to make the transition appear to be a Wigner crystallization. We believe that the insulating phase is always an effective Coulomb disorder-induced localized AI, which may have short-range WC-like correlations at low carrier densities. Our theoretically calculated disorder-driven critical MIT density agrees with experimental findings in all 2D samples, even for the ultra-clean samples. In particular, the extrapolated critical density for the 2D MIT seems to vanish when the high-density mobility goes to infinity, indicating that transport probes a disorder-localized insulating ground state independent of how low the carrier density might be.