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

Raman spectroscopy is a fast and nondestructive means to characterize graphene samples. In particular, the Raman spectra are strongly affected by doping. While the resulting change in position and width of the G peak can be explained by the nonadiabatic Kohn anomaly at Gamma, the significant doping dependence of the 2D peak intensity has not been understood 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.