Parquet approach to nonlocal vertex functions and electrical conductivity of disordered electrons

Details Parquet approach to nonlocal vertex functions and electrical conductivity of disordered electrons Parquet approach to nonlocal vertex functions and electrical conductivity of disordered electrons

2000-10-03

arxiv.org/abs/cond-mat/0010044v1

Phys. Rev. B64 115115 (2001) 1-16

Physics

Condensed Matter

Strongly Correlated Electrons

REVTeX 19 pages, 9 EPS diagrams, 6 PS figures

Scientific paper

10.1103/PhysRevB.64.115115

A diagrammatic technique for two-particle vertex functions is used to describe systematically the influence of spatial quantum coherence and backscattering effects on transport properties of noninteracting electrons in a random potential. In analogy with many-body theory we construct parquet equations for topologically distinct {\em nonlocal} irreducible vertex functions into which the {\em local} one-particle propagator and two-particle vertex of the coherent-potential approximation (CPA) enter as input. To complete the two-particle parquet equations we use an integral form of the Ward identity and determine the one-particle self-energy from the known irreducible vertex. In this way a conserving approximation with (Herglotz) analytic averaged Green functions is obtained. We use the limit of high spatial dimensions to demonstrate how nonlocal corrections to the $d=\infty$ (CPA) solution emerge. The general parquet construction is applied to the calculation of vertex corrections to the electrical conductivity. With the aid of the high-dimensional asymptotics of the nonlocal irreducible vertex in the electron-hole scattering channel we derive a mean-field approximation for the conductivity with vertex corrections. The impact of vertex corrections onto the electronic transport is assessed quantitatively within the proposed mean-field description on a binary alloy.

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