Crossover of optical spectra from an excitonic feature to the Fermi-edge singularity Original Research Article

Interband optical absorption spectra of many-body electronic systems with free carriers are investigated theoretically. We examine how the optical spectra depend on the carrier concentration to understand in detail the crossover between a normal exciton-peak structure in the low-density limit and the Fermi-edge singularity (FES) in the high-density case. We show clearly that the threshold behavior depends on the electron-spin degrees of freedom and that when a bound state exists there are always four thresholds in the absorption spectrum; two of which are degenerate. We derive an exact expression of the FES exponents as a function of the phase shift at these four thresholds, which are in agreement with the Hopfieldʹs rule of thumb. In order to calculate the absorption spectra we adopt the time-dependent coupled-cluster expansion, which enables us to include straightforwardly dynamical responses of the Fermi sea.