CLOSED-FORM SOLUTIONS TO SURFACE GREENS-FUNCTIONS

We obtain closed-form analytic solutions for surface Green's functions within arbitrary multiorbital models. The formulation is completely g eneral, and is equally valid for empirical tight binding, linear-muffi n-tin-orbital tight binding, screened Korringa-Kohn-Rostoker and other Green's-function equivalent formalisms, where the Hamiltonian can be put into a localized (i.e., block-band) form. The solutions are applic able to finite or semi-infinite surface systems, with quite general su bstrate and overlayers, or even to superlattices. This is achieved by solving Dyson's equations by means of a matrix-valued extension of the Mobius transformation. The analytical properties of the solutions are discussed, and by considering their asymptotic limit, a simple closed form for the exact (semi-infinite) surface Green's function is obtain ed. The numerical calculation of the surface Green's function (or of o bservable quantities such as the density of states) using this closed form is compared with previously known iterative procedures. We find t hat it is far faster, far more stable, and more accurate than the best iterative method.