Effective Electron-Hole Interaction in Shallow Excitons

Abstract

The Green's function method developed by Mahan for excitons is extended to the case that the interaction is not instantaneous. Energy corrections to the exciton due to recoil effects, retardation effects, renormalization constants and vertex parts arising from the interactions of an electron and a hole forming an exciton with longitudinal optical (LO) phonons, which were treated by Haken in another simplified manner, are explicitly calculated by using the extended method to first order in electron-phonon coupling constant α and in (\(E/\hbar\omega_{l}\)), where E is the binding energy of the exciton and ω l is the LO phonon frequency. It is shown that in these corrections, the recoil effect and the retardation effect cancel out each other and the renormalization effect and the vertex effect cancel out each other, and a resultant effective interaction between the electron and hole is reduced to Haken's result for large electron-hole separations.