Abstract
We calculate the Coulomb interaction induced density, temperature and magnetization-dependent many-body band-gap renormalization in a typical diluted magnetic semiconductor ${\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{As}$ in the optimally doped metallic regime as a function of carrier density and temperature. We find a large $(\ensuremath{\sim}0.1\phantom{\rule{0.3em}{0ex}}\mathrm{eV})$ 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.
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