Use of Elementary Group Theory in Calculating Band Structure

Summary

In this chapter, we first reviewed elementary group theory and studied the electronic band structure in terms of elementary concepts of the group theory. We have shown that how group theory ideas can be used in obtaining the band structure of a solid. Group representations and characters of twodimensional square lattice are discussed in depth and empty lattice bands of the square lattice are illustrated. Concepts of irreducible representations and compatibility relations are used in discussing the symmetry character of bands connecting different symmetry points and the removal of band degeneracies. We also discussed empty lattice bands of the cubic system and sketched the band calculation of common semiconductors.