Dynamic and charge doping effects on the phonon dispersion of graphene

The phonon dispersion of graphene is calculated using a perturbative approach within a density-functional-based nonorthogonal tight-binding model. In the adiabatic approximation, the LO and the TO phonon branches are found to have a finite slope at the Gamma and K points of the Brillouin zone, respectively. This linear behavior is due to strong electron-phonon coupling for electron wave vector close to the K point and is a signature of the Kohn anomaly. The explicit account of the dynamic effects results in a strong modification of these phonon branches as well as in a significant broadening of their linewidth in the vicinity of the Gamma and K points. In particular, the finite slope of the phonon branches turns to zero. The charge doping of graphene changes the LO and TO branches in the vicinity of the two points and essentially removes the Kohn anomaly with the increase in the doping level. The obtained results are in a good agreement with available experimental data.