Phonon thermal conductivities of multi-layered graphene

Using an exact numerical solution of the phonon Boltzmann equation, we show that the intrinsic lattice thermal conductivities, $\kappa $, of $N$-layer graphene ($N$=1-5) are dominated by contributions from out-of-plane, flexural (ZA) phonon modes contrary to previous theories based on the relaxation time approximation, which assumed this contribution to be negligible [1, 2]. We find a reduction of $\kappa $ with increasing $N$ due to interlayer coupling, which: 1) lifts the degeneracy of the flexural acoustic mode frequencies, 2) makes the ZA phonon branch become linear near the zone-center, and 3) breaks a selection rule for anharmonic phonon-phonon scattering in two-dimensional systems. \\[4pt] [1] P. G. Klemens and D. F. Pedraza, Carbon vol. 32, pp. 735-741 (1994). \\[0pt] [2] B. D. Kong, S. Paul, M. B. Nardelli and K. W. Kim, Phys. Rev. B 80, 033406 (2009).