Application of Double Groups to Energy Bands with Spin

Abstract

In this chapter we apply the group theoretical background for the electron spin and the spin–orbit interaction (which is discussed in Chap. 14) to the treatment of electronic energy band models for solids (which is discussed in Chaps. 12 and 13 for the case when the electron spin is neglected). By including the spin–orbit interaction we can also discuss the effective g-factor, which together with the effective mass tensor, characterize the properties of a semiconductor in a magnetic field. We also review the Slater–Koster method for determination of the electronic energy band structure of crystalline solids by interpolation and extrapolation of energy eigenvalues and eigenfunctions that are accurately known at a few high symmetry points in the Brillouin zone either from ab initio calculations or from experiments.