Excitons

Abstract

The general procedure to account for many-body effects in optical and energy-loss spectra consists of three steps, (i) preparation of a starting electronic structure, (ii) its improvement due to quasiparticle effects, and (iii) the inclusion of electron-hole attraction and exchange. Their combination gives rise to novel quasiparticles, the excitons. Singlet and triplet states differ by twice the electron-hole exchange. Instructive exciton models are derived studying only pairs of conduction and valence bands. For large distances of electron and hole in real space the effective mass approximation and a constant screening can be employed. The resulting pairs are hydrogen-like Wannier-Mott excitons, which give rise to Rydberg series below the ionization edge and a Coulomb enhancement, the Sommerfeld factor, of the pair density of states above the edge. Localized excitons such as Frenkel and charge-transfer excitons possess larger binding energies and electron-hole distances of the order of atomic or molecular distances. Exciton binding is increased by spatial confinement as demonstrated for two-dimensional systems. Electron-Hole Pairs: Top-Down Approach TerminologyIn the previous Chaps. 18-20 we have described in detail the response of an electronic system to an external perturbation, which however leaves this system neutral. Especially perturbations which are related to the real or virtual absorption of photons with energy ω or the inelastic scattering of high-energy particles with energy losses of energy ω have been considered as examples. Thereby we have learnt that the many-electron interactions mediated by the Coulomb potential play a central role. We found that the treatment of their influence can be nearly divided into a three-step procedure that is schematically illustrated in Fig. 21.1 for a non-metal. In a first step an electron-hole pair may be actually or virtually excited by a photon of energy ω in the reference electronic structure derived from a Kohn-Sham or generalized Kohn-Sham problem. In the second step the formation of quasiparticles is taken into account. As a consequence an energy shift of the bands is considered resulting in an