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Optical properties of a two-dimensional electron gas: Evolution of spectra from excitons to Fermi-edge singularities.

The evolution of the absorption and emission spectrum from an exciton to a Fermi-edge singularity as a function of a quasi-two-dimensional electron-gas density is examined. Band-gap renormalization, screening, shake up of the Fermi sea, and the effect of the finite hole mass are included. The real-time response of the Fermi sea to the creation and annihilation of the hole in the valence band is treated nonperturbatively. The time evolution of the self-energy and vertex corrections is shown to be governed by a set of nonlinear differential equations, which allows for a very efficient numerical solution. The effect of the finite hole mass is to wash out the Fermi-edge singularity in absorption.