Exciton Bose condensation : the ground state of an electron-hole gas - I. Mean field description of a simplified model

Abstract

We consider an electron-hole gas in a simple model semiconductor, with direct gap and isotropic, non degenerate bands. We study the Bose condensed ground state of that system as a function of density, using a mean field variational ansatz. In a first stage, we ignore screening as well as the spin structure of the carriers. We thus describe the smooth transition between Bose condensation of atomic excitons at low densities, and the « excitonic insulator » state and ultimately electron-hole plasma at high densities. As compared to previous treatments, our approach includes the effect of electron-hole pairing on the ground state, within a simple realistic ansatz.