Many-body localization study in low-density electron gases: do metals exist in two dimensions?

Using a combination of ground state quantum Monte Carlo and finite size scaling techniques, we perform a systematic study of the effect of Coulomb interaction on the localization length of a disordered two-dimensional electron gas. We find that correlations delocalize the 2D system. In the absence of valley degeneracy (as in GaAs heterostructures), this delocalization effect corresponds to a finite increase of the localization length. The delocalization is much more dramatic in the presence of valley degeneracy [as in Si metal-oxide-semiconductor field-effect transistors], where the localization length increases drastically. We find that a simple mechanism accounts for the main features of the metallic behavior observed in two-dimensional gases. Our findings support the claim that this behavior is a genuine effect of the presence of interactions, yet that the system is not a "true" metal in the thermodynamic sense.