Using the linearized Boltzmann transport equation and perturbation theory, we analyze the reduction in the intrinsic thermal conductivity of few-layer graphene sheets accounting for all possible three-phonon scattering events. Even with weak coupling between layers, a significant reduction in the thermal conductivity of the out-of-plane acoustic modes is apparent. The main effect of this weak coupling is to open many new three-phonon scattering channels that are otherwise absent in graphene. The highly restrictive selection rule that leads to a high thermal conductivity of ZA phonons in single-layer graphene is only weakly broken with the addition of multiple layers, and ZA phonons still dominate thermal conductivity. We also find that the decrease in thermal conductivity is mainly caused by decreased contributions of the higher-order overtones of the fundamental out-of-plane acoustic mode. Moreover, the extent of reduction is largest when going from single to bilayer graphene and saturates for four layers. The results compare remarkably well over the entire temperature range with measurements of of graphene and graphite.

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