Mean field solution of the quantum Coulomb glass

We study a mean field model for the Coulomb glass emerging from the interplay of strong interactions and disorder, by considering spinless fermions on the Bethe lattice in the limit of infinite coordination number. We combine quantum Monte-Carlo simulations with self-consistent diagrammatic perturbation theory to show that strong interactions induce a metallic Coulomb glass phase with a pseudogap structure at the Fermi energy. Quantum and thermal fluctuations both melt this glass and lead to a disordered quantum liquid phase. We obtain the complete phase diagram of the model, and characterize its dynamical properties in the replica symmetric liquid phase, as well as in the glassy phase in the presence of full replica symmetry breaking. The spectral function displays an Efros-Shklovskii pseudogap upon decreasing temperatures, but the density of states remains finite at the Fermi energy due to residual quantum fluctuations. Our results bear relevance to the metallic glass phase observed in Si inversion layers.

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