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

Absence of conventional quantum phase transitions in itinerant systems with disorder

Effects of disorder are examined in itinerant systems close to quantum critical points. We argue that spin fluctuations associated with the long-range part of the RKKY interactions generically induce non-Ohmic dissipation due to rare disorder configurations. This dissipative mechanism is found to destabilize quantum Griffiths phase behavior in itinerant systems with arbitrary symmetry of the order parameter, leading to the formation of a "cluster glass" phase preceding uniform ordering.Comment: 4+epsilon pages, 1 figure. Phys. Rev. Lett., in press (2005

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

Spin Liquid Behavior in Electronic Griffiths Phases

We examine the interplay of the Kondo effect and the RKKY interactions in electronic Griffiths phases using extended dynamical mean-field theory methods. We find that sub-Ohmic dissipation is generated for sufficiently strong disorder, leading to suppression of Kondo screening on a finite fraction of spins, and giving rise to universal spin-liquid behavior.Comment: 4 pages, minor changes included, typos correcte

Electronic Griffiths phase of the d=2 Mott transition

We investigate the effects of disorder within the T=0 Brinkman-Rice (BR) scenario for the Mott metal-insulator transition (MIT) in two dimensions (2d). For sufficiently weak disorder the transition retains the Mott character, as signaled by the vanishing of the local quasiparticles (QP) weights Z_{i} and strong disorder screening at criticality. In contrast to the behavior in high dimensions, here the local spatial fluctuations of QP parameters are strongly enhanced in the critical regime, with a distribution function P(Z) ~ Z^{\alpha-1} and \alpha tends to zero at the transition. This behavior indicates a robust emergence of an electronic Griffiths phase preceding the MIT, in a fashion surprisingly reminiscent of the "Infinite Randomness Fixed Point" scenario for disordered quantum magnets.Comment: 4+ pages, 5 figures, final version to appear in Physical Review Letter