On Bose-Einstein condensate inside moving exciton-phonon droplets

TL;DR

This paper models a moving Bose-Einstein condensate of excitons interacting with phonons in a crystal, analyzing localized solutions, stability conditions, and potential for stable droplet movement.

Contribution

It introduces a nonlinear field model for exciton-phonon interactions, predicting stable, localized moving condensates in crystals, with conditions for their formation and stability.

Findings

Localized exciton-phonon condensate solutions exist.

Stable moving condensates can occur under certain conditions.

Critical parameters for condensate stability are identified.

Abstract

We explore a nonlinear field model to describe the interplay between the ability of excitons to be Bose condensed and their interaction with other modes of a crystal. We apply our consideration to the long-living paraexcitons in Cu2O. Taking into account the exciton-phonon interaction and introducing a coherent phonon part of the moving condensate, we solve quasi-stationary equations for the exciton-phonon condensate. These equations support localized solutions, and we discuss the conditions for the inhomogeneous condensate to appear in the crystal. Allowable values of the characteristic width of ballistic condensates are estimated. The stability conditions of the moving condensate are analyzed by use of Landau arguments, and Landau critical parameters appear in the theory. It follows that, under certain conditions, the condensate can move through the crystal as a stable droplet. To separate the coherent and non-coherent parts of the exciton-phonon packet, we suggest to turn off the phonon wind by the changes in design of the 3D crystal and boundary conditions for the moving droplet.