Optical spectra and excitonic BEC–BCS crossover in coherent electron–hole pair condensation

We investigate coherent pair condensation in three-dimensional electron–hole (e–h) systems using the two-band Hubbard model with both repulsion and attraction, especially from the viewpoint of optical properties. Applying the self-consistent t-matrix and local approximations, the crossover behavior between the e–h BCS-like state and the excitonic Bose–Einstein condensation (BEC) at finite temperatures is described as a function of the e–h attraction strength. The changes of absorption and luminescence spectra are also discussed along the excitonic BEC–BCS crossover.