Closed-form solutions to surface Green's functions

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Abstract
We obtain closed-form analytic solutions for surface Green's functions within arbitrary multiorbital models. The formulation is completely general, and is equally valid for empirical tight binding, linear-muffin-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 applicable to finite or semi-infinite surface systems, with quite general substrate and overlayers, or even to superlattices. This is achieved by solving Dyson's equations by means of a matrix-valued extension of the Möbius 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 obtained. The numerical calculation of the surface Green's function (or of observable quantities such as the density of states) using this closed form is compared with previously known iterative procedures. We find that it is far faster, far more stable, and more accurate than the best iterative method.