2000/10/03 by V. Janiš, V. Janis · 6 citations
Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Born approximation #Combinatorics #Electron #Mathematical physics #Mathematics #Physics #Physics of Superconductivity and Magnetism #Propagator #Quantum and electron transport phenomena #Quantum mechanics #Scattering #Vertex (graph theory) #cond-mat.dis-nn #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.64.115115
published as Phys. Rev. B64 115115 (2001) 1-16 · REVTeX 19 pages, 9 EPS diagrams, 6 PS figures
arxiv created 2000/10/03 · openalex publication_date 2001/08/31 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 nonlocal irreducible vertex functions into which the 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=\ensuremath∞ (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.