Closed-form solutions to surface Green`s functions

Journal Article · Sat Feb 01 04:00:00 EST 1997 · Physical Review, B: Condensed Matter

DOI:https://doi.org/10.1103/PhysRevB.55.5266· OSTI ID:467373

Umerski, A ^[1]

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1. Department of Mathematics, Imperial College, London SW7 2BZ (United Kingdom)

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 Moebius 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. {copyright} {ital 1997} {ital The American Physical Society}

• OSTI ID: 467373
• Journal Information: Physical Review, B: Condensed Matter, Journal Name: Physical Review, B: Condensed Matter Journal Issue: 8 Vol. 55; ISSN 0163-1829; ISSN PRBMDO
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
ANALYTICAL SOLUTION
BAND THEORY
CALCULATION METHODS
EIGENVALUES
EIGENVECTORS
ELECTRONIC STRUCTURE
ENERGY-LEVEL DENSITY
GREEN FUNCTION
LAYERS
SURFACES