Decay and frequency shift of both intervalley and intravalley phonons in graphene: Dirac-cone migration

By considering analytical expressions for the self-energies of intervalley and intravalley phonons in graphene, we describe the behavior of D, 2D, and D' Raman bands with changes in doping (mu) and light-excitation energy (E-L). Comparing the self-energy with the observed mu dependence of the 2D bandwidth, we estimate the wave vector q of the constituent intervalley phonon at (h) over bar vq similar or equal to E-L/1.6 (v is the electron's Fermi velocity) and conclude that the self-energy makes a major contribution (60%) to the dispersive behavior of the D and 2D bands. The estimate of q is based on a concept of shifted Dirac cones in which the resonance decay of a phonon satisfying q >omega/v (omega is the phonon frequency) into an electron-hole pair is suppressed when mu < (<(h)over bar>vq - h omega)/2. We highlight the fact that the decay of an intervalley (and intravalley longitudinal optical) phonon with q = omega/v is strongly suppressed by electron-phonon coupling at an arbitrary mu. This feature is in contrast with the divergent behavior of an intravalley transverse optical phonon, which bears a close similarity to the polarization function relevant to plasmons.