Role of bound pairs in the optical properties of highly excited semiconductors: A self-consistent ladder approximation approach

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Abstract
The presence of bound pairs (excitons) in a low-temperature electron-hole plasma is accounted for by including correlation between fermions at the ladder level. Using a simplified one-dimensional model with on-site Coulomb interaction, we calculate the one-particle self-energies, chemical potential, and optical response. The results are compared to those obtained in the Born approximation, which does not account for bound pairs. In the self-consistent ladder approximation the self-energy and spectral function show a characteristic correlation peak at the exciton energy for low temperature and density. In this regime the Born approximation overestimates the chemical potential. Provided the appropriate vertex correction in the interaction with the photon is included, both ladder and Born approximations reproduce the excitonic and free pair optical absorption at low density, and the disappearance of the exciton absorption peak at larger density. However, line shapes and energy shifts of the absorption and photoluminescence peaks with density are drastically different. In particular, the photoluminescence emission peak is much more stable in the ladder approximation. Moreover, even though at low temperature and density a sizable optical gain is produced in both approximations just below the excitonic peak, this gain shows unphysical features in the Born approximation.
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