A method for determining surface states by complex extension of tight binding

A method is developed for calculating surface states and the composition of the surface wave functions. The formulation is made for tight-binding Hamiltonians. The present scheme is based on the extension of the bulk bands in the complexk-plane. The surface is viewed as a boundary condition of the Schrodinger difference equation of the infinite crystal. At points of high symmetry of the two-dimensional Brillouin zone, this approach gives analytic expressions for surface states and allows one to determine the composition of real and evanescent waves which make up the wave function of the semi-infinite crystal. It provides an attractive computational method that can also be used to study reconstructed surfaces.