Graphene band structure and its 2D Raman mode

High-precision simulations are used to generate the 2D Raman mode of graphene under a range of screening conditions and laser energies E_L. We reproduce the decreasing trend of the 2D mode FWHM vs E_L and the nearly linearly increasing dispersion ∂_ω2D/∂E_L seen experimentally in freestanding (unscreened) graphene, and propose relations between these experimentally accessible quantities and the local, two-dimensional gradients |∇ | of the electronic and TO phonon bands. In light of state-of-the-art electronic structure calculations that acutely treat the long-range e-e interactions of isolated graphene and its experimentally observed 2D Raman mode, our calculations determine a 40% greater slope of the TO phonons about K than given by explicit phonon measurements performed in graphite or GW phonon calculations in graphene. We also deduce the variation of the broadening energy γ [E_L] for freestanding graphene and find a nominal value γ ∼140 meV, showing a gradually increasing trend for the range of frequencies available experimentally.