Anharmonic phonon lifetimes in graphene, graphite and carbon nanotubes

We present a density-functional study of anharmonic phonon lifetimes in low-dimensional graphitic structures. Phonon lifetimes are evaluated from the cubic terms in the interatomic potential, using density-functional perturbation theory and the 2n+1 theorem. We show that in graphene and graphite the phonon lifetimes of the $E_{2g}$ LO mode at {\bf $\Gamma$} and the ${A'}_1$ mode at {\bf K} due to phonon-phonon scattering are larger than those due to the electron-phonon interaction. We discuss the relevance of this finding for the transport properties and the implications for carbon nanotubes. We also present the results for the temperature-dependent frequency shift of the Raman G mode, in which third- and fourth-order anharmonic terms contribute equally.