Despite the lack of translational symmetry in random substitutional alloys, their description in terms of single Bloch states has been used in most phenomenological models and spectroscopic practices. We present a new way of analyzing the alloy electronic structures based on a “majority representation” phenomenon of the reciprocal space spectrum $P\left(\mathbf{k}\right)$ of the wave function. This analysis provides a quantitative answer to the questions: When can an alloy state be classified according to the crystal Bloch state symmetry, and under what circumstances are the conventional theoretical alloy models applicable.

• Received 9 October 1997

DOI:https://doi.org/10.1103/PhysRevLett.80.4725