Lattice Green's Function for the Diatomic Lattices

Abstract

Attention is called to the fact that the lattice Green's function for a diatomic alternating lattice (regular or irregular) can be calculated from the lattice Green's function for the corresponding monatomic lattice. The definition of the lattice Green's function is given in such a fashion that the imaginary part of the trace of the function gives the level density. The values at the origin are shown by graphs for the square, sc, and bcc diatomic lattices; the sc and bcc diatomic lattices are of the sodium-chloride and cesium-chloride type crystal structures, respectively. Discussions are given of the analytic behaviors and symmetry properties. The real part of the lattice Green's function is used to discuss the localized state of the one-impurity problem in the diatomic lattices. Some symmetry properties for the monatomic alternating lattice are given in the Appendix.