Relativistic Formulation of the Green's Function Method in Periodic Lattices

Abstract

A relativistic formulation of the Kohn-Rostoker Green's function method is developed in the Dirac formalism. The result is very simple. The matrix elements of the secular equa­ tion have the same form as the nonrelativistic matrix elements, and the relativistic structure constant consists of the summation of the products of a nonrelativistic structure constant and a Clebsch-Gordan coefficient over spin ± 1/2. Hence, a calculation of the relativistic matrix elements can be performed as easily as the nonrelativistic calculation, and the only problem is a significant increase in computing time which results from the doubling of the dimensions of the secular equation and the complex property of the matrix elements. The present paper also contains a brief discussion of the relativistic formulation of the APW method, and an expression for the matrix element corresponding to the nonrelativistic matrix element is proposed.