Excitons in a semi-infinite insulator in the tight-binding approximation

Publisher Website
Google Scholar
Abstract
The non-local susceptibility is calculated for a semi-infinite, simple cubic insulator with two narrow bands: the conduction ( alpha ) band and valence ( beta ) band. The electrons in the conduction band and the holes in the valence band hop between nearest-neighbour atoms only. The interactions between electron-hole pairs on the same lattice site and on nearest-neighbour lattice sites are also included. As a model for the surface the authors ignore interactions between electron-hole pairs on opposite sides of a plane which bisects the crystal but contains no atoms itself. The hopping integrals of the electrons and holes across this plane are neglected as well. It is shown that the Coulomb interaction between two electron-hole pairs on the same lattice site never produces excitons (bound electron-hole pairs). Excitons are produced by the nearest-neighbour exchange interaction. The equation of motion of the exciton green function is solved analytically. Under suitable conditions, surface excitons localised on the surface of the insulator may be produced.