First-principles calculations of excitons including radiative recombination and polaritonic effects: the retarded Bethe-Salpeter equation

Recent research in 2D materials has revealed a host of phenomena only present in low-dimensional systems, such as the presence of strongly bound excitons due to the electronic confinement and weak dielectric screening in such systems. The electronic and optical properties in such systems have been largely captured with success through first-principles techniques based on interacting Green's function formalisms, such as the ab initio GW and Bethe-Salpeter equation approaches, respectively. However, these methods are typically derived assuming instantaneous many-electron interactions. Here, we describe a formalism to include retardation effects into the Bethe-Salpeter equation that is computationally efficient and gauge invariant. While previous efforts have focused on the effect of retardation effects in the direct (screened) electron-hole interactions, we find here that retardation effects in the (bare) exchange interactions dominate in low dimensions. Our work predicts a renormalization of the exciton dispersion and a broadening of the exciton dispersion when retardation effects are included. More broadly, our approach can be applied to the study of polaritonic effects directly from standard interacting Green's-function formalisms.