Criterion of applicability of coherent-potential approximation at low impurity concentrations

Criterion of applicability of the coherent-potential approximation (CPA) in the case of three-dimensional systems is suggested. The energy range in which the CPA remains valid is determined. Its bounding energy agrees closely with the expected position of the mobility edge in the disordered system previously confirmed by extensive numerical simulations. The spectrum’s rearrangement with increasing impurity concentration is described in detail.