The role of the biexciton in a dynamic density matrix theory of the semiconductor band edge

We describe the dielectric response of the semiconductor band edge in a dynamic density matrix model. Our treatment is based on a set of ₃-relevant constitutive equations involving two-, four- and six-point density matrices. We demonstrate that under certain conditions all contributions to the third order susceptibility can be expressed in terms of excitonic and biexcitonic transitions. As a first application of these ₃-relevant equations we investigate the influence of the biexciton on the optical Stark effect in CuCl. We calculate shifts and lineshapes. Our results turn out to be in excellent agreement with experiments as well as with other theoretical predictions.