Electron correlation effects in the Si(111)-$7\times 7$ surface

Local-density approximation calculations have been performed for determining the electronic properties and the surface band structure of the Si(111)-$7\times 7$ surface. From these bands, a two-dimensional model is introduced to describe the correlation properties of the electrons localized in the surface adatom dangling bonds. The analysis of this model shows that the Si(111)-$7\times 7$ surface has a metallic character and exhibits important correlation effects that arise from the localization of electrons on some elementary structures having a hexagonal ring geometry.