Unified theory of optical absorption and luminescence including both direct and phonon-assisted processes

Most semiconductors and insulators exhibit indirect band gaps, but no theory is currently available to calculate light absorption and emission spectra of these systems over a wide spectral range with predictive accuracy. The standard textbook theory of indirect absorption becomes ill-defined and yields infinite absorption strength when a photon can promote both direct and phonon-assisted transitions. As a result, state-of-the-art ab initio methods for calculating optical spectra of solids are unable to describe direct and phonon-assisted transitions on the same footing. Here, we develop a rigorous first-principles approach that overcomes this limitation by including electron-phonon correlations via many-body quasidegenerate perturbation theory. Our present formalism enables accurate calculations of the optical spectra of materials with direct, indirect, and quasidirect band gaps, and reduces to the standard theories of direct-only absorption and indirect-only absorption in the appropriate limits. We demonstrate this methodology by investigating the optical absorption spectra of silicon, germanium, gallium arsenide, and diamond. In all cases, we obtain spectra in excellent agreement with experiments. As a more ambitious test, we investigate the temperature-dependent photoluminescence of germanium, and we obtain quantitative agreement with experiments.