We have implemented a generic method, based on the 2n+1 theorem within density functional perturbation theory, to calculate the anharmonic scattering coefficients among three phonons with arbitrary wavevectors. The method is used to study the phonon
broadening in graphite and graphene mono- and bi-layer. The broadening of the high-energy optical branches is highly nonuniform and presents a series of sudden steps and spikes. At finite temperature, the two linearly dispersive acoustic branches TA and LA of graphene have nonzero broadening for small wavevectors. The broadening in graphite and bi-layer graphene is, overall, very similar to the graphene one, the most remarkable feature being the broadening of the quasi acoustical ZO branch. Finally, we study the intrinsic anharmonic contribution to the thermal conductivity of the three systems, within the single mode relaxation time approximation. We find the conductance to be in good agreement with experimental data for the out-of-plane direction but to underestimate it by a factor 2 in-plane.
We present a first-principles theoretical approach for evaluating the lattice thermal conductivity based on the exact solution of the Boltzmann transport equation. We use the variational principle and the conjugate gradient scheme, which provide us w
ith an algorithm faster than the one previously used in literature and able to always converge to the exact solution. Three-phonon normal and umklapp collision, isotope scattering and border effects are rigorously treated in the calculation. Good agreement with experimental data for diamond is found. Moreover we show that by growing more enriched diamond samples it is possible to achieve values of thermal conductivity up to three times larger than the commonly observed in isotopically enriched diamond samples with 99.93% C12 and 0.07 C13.
