The lifetime of excitons in ${\mathrm{Cu}}_2\mathrm{O}$ 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 $2\overline{C}n$ where $\overline{C}$ is a capture coefficient averaged over orthoexcitons and paraexcitons. Analysis of our photoluminescence data between 2 and $212\mathrm{K}$ 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 $\varphi$ roughly in the range $8–15\mathrm{meV}$ and a biexciton Auger rate ${\tau }_A^{-1}=0.5T{\mathrm{ns}}^{-1}{\mathrm{K}}^{-1}$, 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.

• Received 7 April 2006

DOI:https://doi.org/10.1103/PhysRevB.74.045211