The authors proposed a simple model for the lattice thermal conductivity of graphene in the framework of Klemens approximation. The Gruneisen parameters were introduced separately for the longitudinal and transverse phonon branches through averaging
over phonon modes obtained from the first-principles. The calculations show that Umklapp-limited thermal conductivity of graphene grows with the increasing linear dimensions of graphene flakes and can exceed that of the basal planes of bulk graphite when the flake size is on the order of few micrometers. The obtained results are in agreement with experimental data and reflect the two-dimensional nature of phonon transport in graphene.
We investigated theoretically the phonon thermal conductivity of single layer graphene. The phonon dispersion for all polarizations and crystallographic directions in graphene lattice was obtained using the valence-force field method. The three-phono
n Umklapp processes were treated exactly using an accurate phonon dispersion and Brillouin zone, and accouting for all phonon relaxation channels allowed by the momentum and energy conservation laws. The uniqueness of graphene was reflected in the two-dimensional phonon density of states and restrictions on the phonon Umklapp scattering phase-space. The phonon scattering on defects and graphene edges has been also included in the model. The calculations were performed for the Gruneisen parameter, which was determined from the ab initio theory as a function of the phonon wave vector and polarization branch, and for a range of values from experiments. It was found that the near room-temperature thermal conductivity of single layer graphene, calculated with a realistic Gruneisen parameter, is in the range ~ 2000 - 5000 W/mK depending on the defect concentration and roughness of the edges. Owing to the long phonon mean free path the graphene edges produce strong effect on thermal conductivity even at room temperature. The obtained results are in good agreement with the recent measurements of the thermal conductivity of suspended graphene.
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 slight
ly 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.
