Temperature and magnetization-dependent band-gap renormalization and optical many-body effects in diluted magnetic semiconductors

We calculate the Coulomb interaction induced density, temperature and magnetization dependent many-body band-gap renormalization in a typical diluted magnetic semiconductor GaMnAs in the optimally-doped metallic regime as a function of carrier density and temperature. We find a large (about 0.1 eV) band gap renormalization which is enhanced by the ferromagnetic transition. We also calculate the impurity scattering effect on the gap narrowing. We suggest that the temperature, magnetization, and density dependent band gap renormalization could be used as an experimental probe to determine the valence band or the impurity band nature of carrier ferromagnetism.