Auger recombination and biexcitons in Cu2O:: A case for dark excitonic matter

The lifetime of excitons in Cu2O decreases significantly at high gas densities. This effect has been attributed to an Auger recombination process between two excitons, resulting in a loss rate given by tau(-1)=An, where A is the Auger constant and n is the exciton gas density. Previous time- and space-resolved photoluminescence measurements, however, yielded an Auger constant that is orders of magnitude larger than theoretical calculations. In addition, the experimental Auger constant varied inversely with temperature, in contrast to the linear-T dependence predicted for direct Auger recombination of two free excitons. To resolve these discrepancies, we propose that excitons form biexcitons that rapidly decay by the Auger process. In this case, the lifetime of excitons is limited by exciton-exciton capture which occurs more frequently at low temperature. The instantaneous decay rate of excitons due to the capture process is given by 2 (C) over barn where (C) over bar is a capture coefficient averaged over orthoexcitons and paraexcitons. Analysis of our photoluminescence data between 2 and 212 K is consistent with a paraexciton capture coefficient that depends inversely with gas temperature. Detailed analysis of the exciton transients following short-pulse excitation yields a biexciton binding energy phi roughly in the range 8-15 meV and a biexciton Auger rate tau(-1)(A)=0.5T ns(-1) K-1, where T is the gas temperature. Due to their short lifetimes, the density of biexcitons is predicted to be considerably lower than the density of excitons, and it is likely that the ground state of a biexciton is optically inactive. Consequently, it is not surprising that photoluminescence of biexcitons has not been observed in this crystal. The existence of such dark matter would explain the long-standing difficulties in achieving Bose-Einstein condensation of excitons in this system.