Biexciton as a Feshbach resonance and Bose-Einstein condensation of paraexcitons in Cu$_{2}$O.

Paraexcitons, the lowest energy exciton states in Cu$_{2}$O, have been considered a good system for realizing exciton Bose-Einstein condensation (BEC). The fact that their BEC has not been attained so far is attributed to a collision-induced loss, whose nature remains unclear. To understand collisional properties of cold paraexcitons governing their BEC, we perform here a microscopic consideration of the s-wave paraexciton-paraexciton scattering. We show its two-channel character with incoming paraexcitons coupled to a biexciton, which is a Feshbach resonance producing a paraexciton loss and a diminution of their background scattering length. The former elucidates the mechanism of the long-observed paraexciton loss, which turns out to be inefficient at temperatures near one Kelvin and below, whereas the latter makes the paraexciton scattering length in strain-induced traps negative under stress exceeding a critical value. Our rough estimates give this value of order of one kilobar, hence already moderate stress creates a serious obstacle to attaining a stable paraexciton BEC. Thus our results indicate that BEC of trapped paraexcitons might be achieved at a subkelvin temperature, but only under low stress.