Non-adiabatic exciton-phonon coupling in Raman spectroscopy of layered materials

We present an ab initio computational approach for the calculation of resonant Raman intensities, including both excitonic and non-adiabatic effects. Our diagrammatic approach, which we apply to two prototype, semiconducting layered materials, allows a detailed analysis of the impact of phonon-mediated exciton-exciton scattering on the intensities. In the case of bulk hexagonal boron nitride, this scattering leads to strong quantum interference between different excitonic resonances, strongly redistributing oscillator strength with respect to optical absorption spectra. In the case of MoS$_2$, we observe that quantum interference effects are suppressed by the spin-orbit splitting of the excitons.