Ab initioGreen-function formulation of the transfer matrix: Application to complex band structures

A method for the first-principles calculation of the transfer matrix is presented. The method is based on a Green-function formulation and allows one to relate the wave functions and their derivatives on boundaries at opposite sides of a film or junction of finite thickness. Both the underlying theory and an actual implementation in the full-potential linearized augmented plane wave method are described. Currently the embedding method is used to evaluate the Green-function matrix elements and in turn we show that the transfer matrix can be used to construct the embedding potential. Some possible applications of the transfer-matrix method such as the calculations of the complex band structure or the calculation of the transmission and reflection coefficients for ballistic transport are discussed. As a first example, complex band structures of Cu, Fe, and Si are presented.