Remarks on the lattice Green's Function for the anisotropic Face Centered Cubic Lattice

TL;DR

This paper analytically and numerically evaluates the Green's function for an anisotropic face centered cubic lattice, providing insights into the density of states, phase shift, and scattering cross section relevant for impurity problems.

Contribution

It introduces an explicit analytical expression for the Green's function of the anisotropic FCC lattice, linking it to elliptic integrals and enabling detailed impurity analysis.

Findings

Green's function expressed via elliptic integrals

Density of states and scattering properties derived

Analytical and numerical methods combined

Abstract

An expression for the Green's function (GF) of anisotropic face centered cubic lattice is evaluated analytically and numerically for a single impurity problem. The density of states (DOS), phase shift and scattering cross section are expressed in terms of complete elliptic integrals of the first kink.