On Wannier Excitons^*

Groupe de Physique des Solides, Université Pierre et Marie Curie, CNRS URA 17, Tour 23, 2 place Jussieu, 75005 Paris, France

Abstract

We rederive the exciton concept from scratch i.e. from N electrons in the valence and conduction bands. In a first part, we diagonalize the semiconductor Hamiltonian in a restricted N electron subspace having valence electrons and one conduction electron. We show that the introduction of Wannier states is unnecessary and that the main steps of this diagonalization are quite clear in terms of valence and conduction Bloch states only. We also show why the dielectric constant is irremediably lost by the diagonalization inside this restricted subspace, its appearance being then phenomenologically forces as a "reasonable screening of the Coulomb interaction". In a second part, we look for the response function of a semiconductor to a photon field using the standard Green's function procedure. The main advantage of this second approach is to generate in a natural way the appearance of the semiconductor dielectric constant.