Phase diagram of the metal-insulator transition in two-dimensional electronic systems

We investigated the interdependence of the effects of disorder and carrier correlations on the metal-insulator transition in two-dimensional electronic systems. We present a quantitative metal-insulator phase diagram. Depending on the carrier density we find two different types of metal-insulator transition---a continuous localization for ${r}_{s}\ensuremath{\lesssim}8$ and a discontinuous transition at higher ${r}_{s}.$ The critical level of disorder at the transition decreases with decreasing carrier density. At very low carrier densities we find that the system is always insulating. The value of the conductivity at the transition is consistent with recent experimental measurements. The self-consistent method that we have developed includes the effects of both disorder and correlations on the transition using a density relaxation theory, with the Coulomb correlations determined from numerical simulation data.