Electron-electron interactions and doping dependence of the two-phonon Raman intensity in graphene

Raman spectroscopy is a fast, non-destructive means to characterize graphene samples. In particular, the Raman spectra show a significant dependence on doping. While the change in position and width of the G peak can be explained by the non-adiabatic Kohn anomaly at $\Gamma$, the significant doping dependence of the 2D peak intensity has not been explained yet. Here we show that this is due to a combination of electron-phonon and electron-electron scattering. Under full resonance, the photogenerated electron-hole pairs can scatter not just with phonons, but also with doping-induced electrons or holes, and this changes the intensity. We explain the doping dependence and show how it can be used to determine the corresponding electron-phonon coupling. This is higher than predicted by density-functional theory, as a consequence of renormalization by Coulomb interactions.