Controlled mean-field theory for disordered electronic systems: Single-particle properties

A self-consistent, conserving mean-field theory for one-particle properties of disordered electronic systems is presented. It is based on a systematic perturbation expansion in 1/Z, where Z is the coordination number of the lattice. To obtain a nontrivial limit for large Z, it is crucial to rescale the hopping integral t according to t∼1/ √Z . In the limit Z→∞, the well-known coherent-potential approximation (CPA) is found to become IexactP for any lattice. Explicit proofs are presented within the locator and propagator formalism. This explains why CPA often yields quantitatively correct results even for values of the disorder not accessible by conventional perturbation theory. Exact results are presented for the Bethe lattice, with the disorder given by a box and a binary-alloy distribution, respectively. Explicit 1/Z corrections to the results for Z=∞ are calculated and the additional effects are discussed.