Quantum saturation and condensation of excitons inCu2O: A theoretical study

Abstract

Recent experiments on high density excitons in ${\mathrm{Cu}}_2$O provide evidence for degenerate quantum statistics and Bose-Einstein condensation of this nearly ideal gas. We model the time dependence of this bosonic system including exciton decay mechanisms, energy exchange with phonons, and interconversion between ortho (triplet-state) and para (singlet-state) excitons, using parameters for the excitonic decay, the coupling to acoustic and low-lying optical phonons, Auger recombination, and ortho-para interconversion derived from experiment. The single adjustable parameter in our model is the optical-phonon cooling rate for Auger and laser-produced hot excitons. We show that the ortho excitons move along the phase boundary without crossing it (i.e., they exhibit a ‘‘quantum saturation’’), as a consequence of the balance of entropy changes due to cooling of excitons by phonons and heating by the nonradiative Auger two-exciton recombination process. The Auger annihilation rate for para-para collisions is much smaller than that for ortho-para and ortho-ortho collisions, explaining why, under the given experimental conditions, the para excitons condense while the ortho excitons fail to do so. © 1996 The American Physical Society.