Conductivity of disordered electrons: Mean-field approximation containing vertex corrections

Abstract

The electrical {\em dc}-conductivity of disordered, non-interacting electrons is calculated in the asymptotic limit of high lattice dimensions $d\to \infty$. To go beyond the lowest-order contribution in the expansion parameter $1/d$ of the single bubble diagram, vertex corrections are calculated from an asymptotic expression for the two-particle vertex. A mean-field approximation for the dc-conductivity containing the leading high-dimensional vertex corrections is proposed which is free of spurious non-analyticities, i.e. the conductivity is non-negative and shows no unphysical behavior in $d\ge 3$.

REVTeX, 7 pages, 4 EPS figures, submitted to PRB

References in corpus (2)

• Stability of self-consistent solutions for the Hubbard model at intermediate and strong coupling
• Asymptotic limit of high spatial dimensions and thermodynamic consistence

Cited by in corpus (9)

• Critical metal-insulator transition and divergence in a two-particle irreducible vertex in disordered and interacting electron systems
• Anderson localization vs. Mott-Hubbard metal-insulator transition in disordered, interacting lattice fermion systems
• Nonlocal correlations and spectral properties of the Falicov-Kimball model
• Parquet approach to nonlocal vertex functions and electrical conductivity of disordered electrons
• Influence of disorder on the transport properties of heavy-fermion systems
• A mean-field theory of Anderson localization
• Vertex corrections to the mean-field electrical conductivity in strongly disordered electron systems
• On the Analyticity of Solutions in the Dynamical Mean-Field Theory
• Quantum diffusion in a random potential: A consistent perturbation theory