PACS. 72.15.Rn -Localization effects (Anderson or weak localization). PACS. 71.27.+a -Strongly correlated electron systems; heavy fermions. PACS. 71.30.+h -Metal-insulator transitions and other electronic transitions.Abstract. -We present a self-consistent theory of Anderson localization that yields a simple algorithm to obtain typical local density of states as an order parameter, thereby reproducing the essential features of a phase-diagram of localization-delocalization quantum phase transition in the standard lattice models of disordered electron problem. Due to the local character of our theory, it can easily be combined with dynamical mean-field approaches to strongly correlated electrons, thus opening an attractive avenue for a genuine non-perturbative treatment of the interplay of strong interactions and strong disorder.c EDP Sciences

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.

We discuss the recently discovered two-dimensional metal-insulator transition in zero magnetic field in the light of the scaling theory of localization. We demonstrate that the observed symmetry relating conductivity and resistivity follows directly from the quantum critical behavior associated with such a transition. In addition, we show that very general scaling considerations imply that any disordered twodimensional metal is a perfect metal, but most likely not a Fermi liquid. [S0031-9007 (97)03673-9] PACS numbers: 71.30. + h, 72.15.RnIn an influential 1979 paper [1], simple scaling arguments were put forward which have shaped much of our thinking about metal-insulator transitions (MITs) in disordered systems. Focusing on noninteracting electrons, the authors demonstrated that in two dimensions (2D) even weak disorder is sufficient to localize the electrons, and no true metallic behavior is possible at T 0. Ever since, it has been widely believed that two is the lower critical dimension for MITs in disordered systems, and this prompted much theoretical activity based on expansions around dimension d 2. The scaling ideas were quickly extended to interacting systems, but despite many years of painstaking effort no satisfying theoretical picture has emerged for the interacting case. Nevertheless, the belief that all the states are localized in d 2 has remained largely unquestioned.Recently, a remarkable experiment [2] performed on a 2D electron gas in zero magnetic field suggested that the conventional picture might be incomplete. In this work, fairly convincing evidence was presented which supports the existence of a true MIT in 2D. Despite the beauty and elegance of the data, this work has met considerable resistance, largely due to its apparent conflict with the scaling theory of localization as well as its uniqueness.The major assumption of [1] was based on an earlier idea of Thouless [3] about the length (scale) dependence of the conductance. In [1] it is asserted that the "beta function" b͑ g͒ d͓ln͑ g͔͒͞d͓ln͑L͔͒ is a function of the conductance g itself but not an explicit function of the length scale L. Now b͑ g͒ is known in the two limits of very large and very small disorder, and it is reasonable to assume that it is continuous (smooth) in between. From Ohm's law, b͑ g͒ ͑d 2 2͒ for g ! 1`, while for g small, one expects exponentially localized states, so that b͑ g͒ ! 2`in this limit. Since the metallic behavior is possible only for b͑ g͒ . 0, the form of b͑ g͒ at large g is sufficient to determine the stability of the metallic phase. In particular, for noninteracting electrons, this has a form b͑ g͒ ͑d 2 2͒ 2 1͞g 1 · · · [4], indicating that the metallic phase is unstable in d # 2.However, it is important to emphasize that the last step in this analysis is valid only for noninteracting electrons; the scaling theory is only complete in the absence of electron-electron interaction. In the following, we show that the existence of a 2D transition does not contradict any general scaling principles. However, ...