Theoretical polarization dependence of the two-phonon double-resonant Raman spectra of graphene

The experimental Raman spectra of graphene exhibit a few intense two-phonon bands, whichare enhanced through double-resonant scattering processes. Though there are manytheoretical papers on this topic, none of them predicts the spectra within a single model.Here, we present results for the two-phonon Raman spectra of graphene calculated by meansof the quantum-mechanical perturbation theory. The electronic and phonon dispersions,electronic lifetime, electron-photon and electron-phonon matrix elements, are all obtainedwithin a density-functional-theory-based non-orthogonal tight-binding model. We studysystematically the overtone and combination two-phonon Raman bands, and, in particular,the energy and polarization dependence of their Raman shift and intensity. We find thatthe ratio of the integrated intensities for parallel and cross polarized light for alltwo-phonon bands is between 0.33 and 0.42. Our results are in good agreement with theavailable experimental data.