Dynamical mean-field theories of correlation and disorder

We provide a review of recently-develop dynamical mean-field theory (DMFT) approaches to the general problem of strongly correlated electronic systems with disorder. We first describe the standard DMFT approach, which is exact in the limit of large coordination, and explain why in its simplest form it cannot capture either Anderson localization or the glassy behavior of electrons. Various extensions of DMFT are then described, including statistical DMFT, typical medium theory, and extended DMFT, methods specifically designed to overcome the limitations of the original formulation. We provide an overview of the results obtained using these approaches, including the formation of electronic Griffiths phases, the self-organized criticality of the Coulomb glass, and the two-fluid behavior near Mott-Anderson transitions. Finally, we outline research directions that may provide a route to bridge the gap between the DMFT-based theories and the complementary diffusion-mode approaches to the metal-insulator transition.Comment: 78 pages, 19 figures; To be published in "Conductor Insulator Quantum Phase Transitions", edited by V. Dobrosavljevic, N. Trivedi, and J.M. Valles Jr., Oxford University Press, 2013, ISBN 978019959259

Disorder-Driven Non-Fermi Liquid Behavior of Correlated Electrons

Systematic deviations from standard Fermi-liquid behavior have been widely observed and documented in several classes of strongly correlated metals. For many of these systems, mounting evidence is emerging that the anomalous behavior is most likely triggered by the interplay of quenched disorder and strong electronic correlations. In this review, we present a broad overview of such disorder-driven non-Fermi-liquid behavior, and discuss various examples where the anomalies have been studied in detail. We describe both their phenomenological aspects as observed in experiment, and the current theoretical scenarios that attempt to unravel their microscopic origin.Comment: Final version, as published in the Reports on Progress in Physic

Strong correlations generically protect d-wave superconductivity against disorder

We address the question of why strongly correlated d-wave superconductors, such as the cuprates, prove to be surprisingly robust against the introduction of non-magnetic impurities. We show that, very generally, both the pair-breaking and the normal state transport scattering rates are significantly suppressed by strong correlations effects arising in the proximity to a Mott insulating state. We also show that the correlation-renormalized scattering amplitude is generically enhanced in the forward direction, an effect which was previously often ascribed to the specific scattering by charged impurities outside the copper-oxide planes.Comment: 4+e page