Ballistic and Diffusive Thermal Conductivity of Graphene

This paper is a contribution to the Physical Review Applied collection in memory of Mildred S. Dresselhaus.Phonon-related thermal conductivity of graphene is calculated as a function of the temperature and sample size of graphene in which the crossover of ballistic and diffusive thermal conductivity occurs at around 100 K. The diffusive thermal conductivity of graphene is evaluated by calculating the phonon mean free path for each phonon mode in which the anharmonicity of a phonon and the phonon scattering by a C13 isotope are taken into account. We show that phonon-phonon scattering of out-of-plane acoustic phonon by the anharmonic potential is essential for the largest thermal conductivity. Using the calculated results, we can design the optimum sample size, which gives the largest thermal conductivity at a given temperature for applying thermal conducting devices.