Symmetry analysis of surface band structures in magnetic fields

The method of invariants is used to study the structure of the surface electronic energy bands in the vicinity of symmetry points in the Brillouin zone (BZ). Each of the 17 surface groups has been examined both in the presence and in the absence of spin-orbit coupling. The symmetry points for spinless particles follow a parabolic law while conic “neutrino-like” shape turns out to be the usual shape for spin −1/2 particles. Compulsory Herring degeneracy is found to occur at the sides of the BZ normal to the glide planes. The possibility of cubic rather then linear splitting in the dispersion law in the center of the BZ for groups containing 3- and 6-fold axes is demonstrated. The electron Hamiltonian for all 17 surface groups in the presence of external magnetic fields has been derived and the splitting of the degenerate energy levels in this situation has been discussed.