Application of a complex band structure to compute the surface states by the Green's function method

By using the analytical properties of the band energies and wave functions in the complex quasi-momentum domain, a procedure is constructed for the calculation of the Green's function (G_{k_parallel }) . The function (G_{k_parallel }) is represented as the sum of components dependent on complex wave vectors. If such a representation is used for (G_{k_parallel }) in the calculation of the surface Green's function [2], then the equation to determine the surface state spectrum in a model with a potential jump agrees with that obtained in [3] by the method of merging the wave functions.