Electron-Phonon Renormalization of the Direct Band Gap of Diamond

We calculate from first principles the temperature-dependent renormalization of the direct band gap of diamond arising from electron-phonon interactions. The calculated temperature dependence is in good agreement with spectroscopic ellipsometry measurements, and the zero-point renormalization of the band gap is found to be as large as 0.6 eV. We also calculate the temperature-dependent broadening of the direct absorption edge and find good agreement with experiment. Our work calls for a critical revision of the band structures of other carbon-based materials calculated by neglecting electron-phonon interactions.