Band gap renormalization in photoexcited semiconductor quantum wire structures in the GW approximation

We investigate the dynamical self-energy corrections of the electron-hole plasma due to electron-electron and electron-phonon interactions at the band edges of a quasi-one dimensional (1D) photoexcited electron-hole plasma. The leading-order $GW$ dynamical screening approximation is used in the calculation by treating electron-electron Coulomb interaction and electron-optical phonon Fr\"{o}hlich interaction on an equal footing. We calculate the exchange-correlation induced band gap renormalization (BGR) as a function of the electron-hole plasma density and the quantum wire width. The calculated BGR shows good agreement with existing experimental results, and the BGR normalized by the effective quasi-1D excitonic Rydberg exhibits an approximate one-parameter universality.