In a recent preprint Kong et al, arXiv:0902.0642v1 (2009) claimed to calculate the lattice thermal conductivity of single and bi-layer graphene from first principles. The main findings were that the Umklapp-limited thermal conductivity is only slightly higher than that of high-quality bulk graphite along the basal plane, and that it does not strongly depend on the number of atomic layers. Here we explain that the calculation of Kong et al used a truncation procedure with a hidden parameter, a cut-off frequency for the long-wavelength acoustic phonons, which essentially determined the final result. Unlike in bulk graphite, there is no physical justification for introducing the cut-off frequency for the long wavelength phonons in graphene. It leads to substantial underestimation of graphenes lattice thermal conductivity and a wrong conclusion about the dependence on the number of atomic layers. We outline the proper way for calculating the lattice thermal conductivity of graphene, which requires an introduction of other scattering mechanisms to avoid a logarithmic divergence of the thermal conductivity integral.
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