Electronic State of Metal Surface with Random Distribution of Atoms

Abstract

A formulation is proposed to treat the electronic state of metals with a plane surface on which two kinds of atoms are randomly distributed. The method is a combination of the Kalkstein-Soven theory of :ourface state and the J\1atsubara-Y onezawa cumulant expansion technique. Numerical culculation of partial surface state density is performed for a two­ dimensional model. § l. Introduction Recent development of the techniques in LEED and in producing clean solid surfaces has revealed many interesting phenomena taking place on the surfaces of metals and semi-conductors.n. 2 J For example, reconstruction of the surface layers of metals and rearrangement of the atoms adsorbed on solid surfaces above a certain critical temperature appear to be some sort of phase transition in two dimen­ swn. When the relevant forces between atoms involved in the surface modification are known, we can hope to work out fairly accurate theories for these problems. It seems that there exists an evidence suggesting that the reconstruction or rearrange­ ment of atoms is mediated by some effective long range forces, and thus we are led to a conjecture that surface electronic states may play an important role in such surface phenomena. The theory of surface states has been discussed by many authors making use of two methods. One approach is to extend orthogonalized plane wave and pseudo potential methods to deal -vvith surface states 3