Resonance Raman intensities including excitonic effects from first-principles: application to 2D materials

Recent advances in Resonance Raman (RR) spectroscopy on 2D semiconductors such as monolayer MoS$_2$ and ReS$_2$ discovered a rich variety of frequency- and polarization-dependent Raman signatures. Although the theory for RR has been well developed for the case of graphene, strong excitonic effects present in 2D semiconductors call for further scrutiny on Raman intensities based on first-principle calculations. Compared to existing methods of calculating RR intensities based on finite differences where the Bethe-Salpeter equation (BSE) was solved twice for each degree of freedom, we present a perturbational approach in which the BSE is only solved once statically and can be implemented to model first- and second-order resonance Raman processes. Comparisons with experimental results are discussed, as well as the connection between the finite differences and perturbational approaches.