Interplay of valley selection and helicity exchange of light in Raman scattering for graphene and MoS2

Raman spectra of graphene andMoS(2) are calculated for incident and scattered circularly polarized light. In the case of graphene, the well known G-band Raman spectra have a not well known property that the helicity of the incident circularly polarized light changes to another helicity in the scattered light. Using the electron-photon and electron-phonon matrix elements by first-principles calculation, we calculate resonant Raman spectra of graphene and MoS2 for circularly polarized light which are compared with recent experiments. The Raman intensity for circularly polarized light is relevant to optical valley polarization in the case of MoS2. We also discuss how the helicity- selection rule can be modified by applying stress to graphene.