Symmetry criterion for surface states in solids

A general symmetry criterion is derived for establishing the existence of surface states in solids. Two kinds of surfaces in solids are distinguished: those coinciding with symmetry planes (or symmetry centers in one dimension) and those in general positions. The symmetry criterion applies to surface states in solids terminating at symmetry planes (or symmetry centers in one dimension). A detailed discussion is given for one-dimensional crystals. The application of the symmetry criterion is demonstrated on the Kronig-Penney, nearly-free-electron, tight-binding, and Mathieu potentials. In particular, it is shown that the Maue and Shockley existence conditions for surface states follow from the general symmetry criterion.