Effective surface potential method for calculating surface states

E. N. Foo, M. F. Thorpe, D Weaire

Research output: Contribution to journalArticle

Abstract

A novel formalism (the effective surface potential method) is developed for calculating surface states. Like the Green function method of Kalkstein and Soven and the transfer matrix method of Falicov and Yndurain, the technique is exact for simple tight binding Hamiltonians. As well as offering an alternative viewpoint, the present method provides a simple analytic expression describing the surface states. At each point ks in the surface Brillouin zone the semi-infinite solid is viewed as an effective linear chain where each element of the chain is a planar layer. The solution to the linear chain problem can be expressed in terms of an effective potential h(ks,E) at each energy E. A number of examples are presented in detail; "spd" Hamiltonians for a linear chain (d = 1), the honeycomb lattice (d = 2), the 111 surface of silicon (d = 3), and a dissected Bethe lattice. Various exact results are given, e.g. the extremities of surface state bands and the surface density of states of p-like (delta function) bands. The results of Kalkstein and Soven for the 100 surface of a simple cubic solid with a perturbation on the surface layer are rederived. © 1976.

Original languageEnglish
Pages (from-to)323-347
Number of pages25
JournalSurface Science
Volume57
Issue number1
Publication statusPublished - 1 Jul 1976

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