On the regular part of the Bloch Green’s function for the Laplacian: analytical formula and critical points

Abstract

This paper is concerned with the regular part of the Bloch Green’s function in a Wigner–Seitz lattice cell. We first give a new fast converging series expression. Then we derive explicit expression using some Dedekind eta functions when the Bloch vector $$\\mathbf {k}$$ k are some rational numbers. Finally we study its critical points.