Vertex corrections to the mean-field electrical conductivity in disordered electron systems

The mean-field theory for noninteracting disordered electron systems is widely and successfully used to describe equilibrium properties of alloys over the whole range of disorder strengths. However, it fails to take into account the effects of quantum coherence and localizing backscattering effects when applied to transport phenomena. Vertex corrections due to multiple backscatterings may turn the electrical conductivity negative and make expansions around the mean field in strong disorder problematic. We show how to stabilize such an expansion with the inverse of the number of nearest neighbors on hypercubic lattices as a small parameter and how to include vertex corrections to the mean-field approximation in such a way that the conductivity remains non-negative in all disorder regimes.