Symmetry Properties of the Energy Bands of the Zinc Blende Structure

The symmetry properties of the one-electron energy bands of a crystal of the zinc blende structure are studied by means of group theory. This is done both with and without the inclusion of spin-orbit coupling. The character tables and compatability tables are obtained for the various irreducible representations of the space group ${T_d}^2$ associated with the zinc blende structure. The degeneracies and the gradients of the various possible energy bands are studied at lines and points of symmetry in the Brillouin zone. These results are compared with those for the equivalent energy bands in a crystal of the diamond structure.