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We have implemented a generic method, based on the 2n+1 theorem withindensity functional perturbation theory, to calculate the anharmonic scatteringcoefficients among three phonons with arbitrary wavevectors. The method is usedto study the phonon broadening in graphite and graphene mono- and bi-layer. Thebroadening of the high-energy optical branches is highly nonuniform andpresents a series of sudden steps and spikes. At finite temperature, the twolinearly dispersive acoustic branches TA and LA of graphene have nonzerobroadening for small wavevectors. The broadening in graphite and bi-layergraphene is, overall, very similar to the graphene one, the most remarkablefeature being the broadening of the quasi acoustical ZO' branch. Finally, westudy the intrinsic anharmonic contribution to the thermal conductivity of thethree systems, within the single mode relaxation time approximation. We findthe conductance to be in good agreement with experimental data for theout-of-plane direction but to underestimate it by a factor 2 in-plane.

Anharmonic properties from a generalized third order ab~initio approach: theory and applications to graphite and graphene