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arXiv:cond-mat/0412590 · Physical Review B

Metal-insulator transitions in the Falicov-Kimball model with disorder

Krzysztof Byczuk

Published May 6, 2005• 37 citations
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Abstract

The ground-state phase diagrams of the Falicov-Kimball model with local disorder are derived within the dynamical mean-field theory and using the geometrically averaged (``typical'') local density of states. Correlated metal, Mott insulator, and Anderson insulator phases are identified. The metal-insulator transitions are found to be continuous. The interaction and disorder compete with each other stabilizing the metallic phase against the occurring one of the insulators. The Mott and Anderson insulators are found to be continuously connected.

DOI
10.1103/physrevb.71.205105

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The ground-state phase diagrams of the Falicov-Kimball model with local disorder are derived within the dynamical mean-field theory and using the geometrically averaged (``typical'') local density of states. Correlated metal, Mott insulator, and Anderson insulator phases are identified. The metal-insulator transitions are found to be continuous. The interaction and disorder compete with each other stabilizing the metallic phase against the occurring one of the insulators. The Mott and Anderson insulators are found to be continuously connected.
The statistical dynamical mean field theory is used to study the metal-insulator transition in the two-dimensional Falicov-Kimball model with local disorder. Within the theory, the local density of states and its distributions are calculated. As a measure of the metal-insulator transition driven by correlation and disorder, the most probable value of the local density of states is determined. The most probable value of the local density of states is found to exhibit a discontinuity when the system crosses from extended states to localization. A phase diagram is also presented.
The phase diagram of correlated, disordered electron systems is calculated within dynamical mean-field theory using the H\"older mean local density of states. A critical disorder strength is determined in the Anderson-Falicov-Kimball model, and the arithmetic and the geometric averages are found to be just particular means used, respectively, to detect or not the Anderson localization. Correlated metal, Mott insulator, and Anderson insulator phases, as well as coexistence and crossover regimes, are analyzed in this perspective.
We investigate the stability of ``magnetic'' ordering against band-filling changes and Anderson-like disorder in the Falicov-Kimball model, within dynamical mean-field theory (DMFT). The one-particle density of states is obtained by both arithmetic and geometric averages over disorder, allowing us to detect the localization transition. Varying the Coulomb interaction and disorder strength, we construct phase diagrams where we identify metallic and insulating regions, with or without magnetic ordering, and determine how these phases are affected by band filling.
Statistics of the local density of states in the two-dimensional Falicov-Kimball model with local disorder is studied by employing the statistical dynamical mean-field theory. Within the theory, the local density of states and its distributions are calculated through stochastic self-consistent equations. The most probable value of the local density of states is used to monitor the metal-insulator transition driven by correlation and disorder. Nonvanishing of the most probable value of the local density of states at the Fermi energy indicates the existence of extended states in the two-dimensional disordered interacting system. It is also found that the most probable value of the local density of states exhibits a discontinuity when the system crosses from extended states to the Anderson localization. A phase diagram is also presented.
Statistics of the local density of states in the two-dimensional Falicov-Kimball model with local disorder is studied by employing the statistical dynamical mean-field theory. Within the theory the local density of states and its distributions are calculated through stochastic self-consistent equations. The most probable value of the local density of states is used to monitor the metal-insulator transition driven by correlation and disorder. Nonvanishing of the most probable value of the local density of states at the Fermi energy indicates the existence of extended states in the two-dimensional disordered interacting system. It is also found that the most probable value of the local density of states exhibits a discontinuity when the system crosses from extended states to the Anderson localization. A phase diagram is also presented.