Green's-function calculation of the surface properties of a two-band crystal

Abstract

The electronic properties of the clean (001) surface of three model crystals with the CsCl structure have been calculated. One model results in no surface states, the second model yields Shockley surface states, and the third model yields Tamm surface states. Analytic expressions for both the bulk-crystal Green's function and the (001)-surface Green's function are derived. Using the resolvent technique, the surface-state bands are presented. Using the phase-shift technique, the change in the total density of states (both inside and outside of the bands) due to the creation of the surface are calculated. From this, the change in the specific heat due to the surface and the surface entropy are found. Finally, the local densities of states for the layers near the surface are obtained from the surface Green's function and compared with the local density of states in the bulk. Our results, which can be used to understand the properties of both semi-conductor and insulator surfaces, are contrasted with previous results for one-band crystal surfaces which are appropriate only for metals. © 1975 The American Physical Society.