The thermal conductivities of graphene and graphite are computed within the framework of Callaway's effective relaxation time theory. Analytical expressions derived by Nihira and Iwata for phonon dispersion relations and vibrational density of states are employed, based on the semicontinuum model proposed by Komatsu and Nagamiya. The conductivity of graphene is predicted to be higher than the in-plane conductivity of graphite for all temperatures. Incorporation of the ${}^{13}$C isotope can be expected to produce significant reduction in the conductivity of graphene in the temperature range 50–300 K. In the presence of tensile strain on graphene, the specific heat increases, but the conductivity can decrease or increase depending on the level of the purity and temperature of the sample.

• Received 18 January 2013

DOI:https://doi.org/10.1103/PhysRevB.87.115421