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

V. Janis·D. Vollhardt
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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 $d\geq 3$.

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V. Janis, D. Vollhardt. 2000-08-25. Conductivity of disordered electrons: Mean-field approximation containing vertex corrections. https://doi.org/10.1103/physrevb.63.125112

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