Delocalized Coulomb phase in two dimensions

Abstract

Extending finite size scaling theory to the many body ground state, one finds that Coulomb repulsion can drive a system of spinless fermions in a random potential from the Anderson insulator (Fermi glass of localized states) towards a new extended phase in dimension $d=2$. The transition occurs at a Coulomb energy to Fermi energy ratio $r_s \approx 4$, where a change in the nature of the persistent currents has been previously observed. Relevance to the recently observed $2d$ metallic phase is suggested.