Coherent-potential approximation for liquid metals and amorphous solids. II. Modified cumulant theory

Publisher Website
Google Scholar
Abstract
Yonezawa's theory of the modified cumulant method used in the evaluation of the coherent-potential approximation (CPA) for completely random substitutional alloys is extended to develop a CPA-equivalent approximation of electronic properties in structurally disordered systems such as liquids and amorphous solids. The proper self-energy operator for the averaged Green's function is expressed in terms of the cumulant averages of density operators. The atomic distribution functions characterizing the structural randomness (or correlation) in these systems are described by the Kirkwood superposition approximation modified suitably to be consistent with the single-site nature of the CPA theory. A set of equations determining the self-energy of the averaged Green's function is derived and is shown to be equivalent to the effective-medium theory recently proposed by Roth. Analysis of several previous theories proposed as an extension of the original CPA to the liquid case is given to clarify the approximations involved in those theories.