Mean-field theories for disordered electrons: Diffusion pole and Anderson localization

Abstract

We discuss conditions to be put on mean-field-like theories to be able to describe fundamental physical phenomena in disordered electron systems. In particular, we investigate options for a consistent mean-field theory of electron localization and for a reliable description of transport properties. We argue that a mean-field theory for the Anderson localization transition must be electron-hole symmetric and self-consistent at the two-particle (vertex) level. We show that such a theory with local equations can be derived from the asymptotic limit to high spatial dimensions. The weight of the diffusion pole, i. e., the number of diffusive states at the Fermi energy, in this mean-field theory decreases with the increasing disorder strength and vanishes in the localized phase. Consequences of the disclosed behavior for our understanding of vanishing of electron diffusion are discussed.

REVTeX4, 11 pages, no figures

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• Tiling with triangles: parquet and $GW\gamma$ methods unified
• Universality of vertex corrections to the electrical conductivity in models with elastically scattered electrons
• Integrability of the diffusion pole in the diagrammatic description of noninteracting electrons in a random potential
• Character of eigenstates of the 3D disordered Anderson Hamiltonian
• Vertex corrections to the mean-field electrical conductivity in strongly disordered electron systems
• Quantum diffusion in a random potential: A consistent perturbation theory