Many-body theory for luminescence spectra in high-density electron-hole systems

We present a unified theory for the luminescence spectra in highly excited semiconductors, which is applicable throughout the whole density regime including the electron-hole (e-h) BCS state and the excitonic Bose-Einstein condensate. The calculated spectra clearly show the crossover behavior between the e-h BCS state and the excitonic Bose-Einstein condensate. The analysis is based on the generalized random-phase approximation combined with the Bethe-Salpeter equation. This approach allows us to consider the strong and weak e-h pair correlations on the same basis. In particular, we find that the broad spectral component arising from the carrier recombination in the e-h BCS state splits into the P and P₂ lines with decreasing e-h density. This behavior can be predicted neither by the BCS-like mean-field theory nor by the interacting Boson model. The result agrees with a recent noteworthy experiment for the strongly excited ZnO, where the ultraviolet laser emission was observed at room temperature.