Temperature effects on Fermi-edge absorption spectra

We present an extension to finite temperatures of the Mahan-Nozières-De Dominicis framework to study both the many-body and temperature effects in absorption spectra of doped semiconductors. The method is used to study magnetoabsorption spectra of modulation-doped quantum wells with a weak periodic lateral modulation. In our scheme, temperature effects in the electronic part of the correlation function characterize the absorption spectra. We treat the valence-hole contribution to the absorption correlation function in second-order perturbation. The time-dependent hole self-energy to second order, $F_2\mathrm{}\left(t\right),$ and the creation rate of a conduction electron-hole pair $R\left(\omega \right),$ are carefully discussed. The temperature dependence of such quantities as well as their influence on the absorption spectra is analyzed. As a practical application, we investigate the effect of the hole position on the absorption spectra.