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

Electrons (or holes) confined in two-dimensional (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 (WC) at very low carrier densities in order to optimize their Coulomb potential energy. The ability to tune the carrier density continuously in a fixed sample allows the 2D semiconductor system to go from a high-density metallic Fermi liquid to a low-density disorder dominated Anderson insulator, or, if the sample is particularly clean, to a Coulomb interaction dominated low-density quantum Wigner crystal. Since the disorder in 2D semiconductors is mostly Coulomb disorder arising from random unintentional quenched charged impurities in the environment, 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. In addition, the Wigner crystallization occurs at such low carrier densities, that in most situations the relevant carrier density is comparable to the background charged impurity density even in ultraclean samples. 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 nine different materials, we establish, utilizing the Ioffe-Regel-Mott (IRM) 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 particularly 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 strongly localized AI, which may have short-range WC-like correlations at very low carrier densities. Our theoretically calculated disorder-driven critical MIT density agrees well with experimental findings in all 2D samples, even for the ultraclean samples where the critical density approaches the WC transition density. 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.