Quantum saturation and condensation of excitons in Cu$_2$O: a theoretical study

TL;DR

This theoretical study models high-density excitons in Cu$_2$O, explaining quantum saturation and selective Bose-Einstein condensation of paraexcitons due to decay mechanisms, phonon interactions, and interconversion effects.

Contribution

It introduces a comprehensive model incorporating exciton decay, phonon coupling, and interconversion, revealing the conditions for quantum saturation and selective condensation in Cu$_2$O.

Findings

Orthoexcitons exhibit quantum saturation without crossing the phase boundary.

Paraexcitons condense due to lower Auger recombination rates.

The model matches experimental observations of exciton behavior.

Abstract

Recent experiments on high density excitons in 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 orthoexcitons move along the phase boundary without crossing it (i.e., exhibit a ``quantum saturation''), as a consequence of the balance of entropy changes due to cooling of excitons by phonons and heating by the non-radiative 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 paraexcitons condense while the orthoexcitons fail to do so.