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 equation 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.