Mean Field Theory of the Mott-Anderson Transition

Abstract

We present a theory for disordered interacting electrons that can describe both the Mott and Anderson transitions in the respective limits of zero disorder and zero interaction. We use it to investigate the $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ Mott-Anderson transition at a fixed electron density, as the disorder strength is increased. Surprisingly, we find two critical values of disorder ${W}_{\mathrm{nfl}}$ and ${W}_{c}$. For $W>{W}_{\mathrm{nfl}}$, the system enters a ``Griffiths'' phase, displaying metallic non-Fermi liquid behavior. At even stronger disorder, ${W\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}W}_{c}>{W}_{\mathrm{nfl}}$ the system undergoes a metal-insulator transition, characterized by the linear vanishing of both the typical density of states and the typical quasiparticle weight.