Ballistic thermal conductance of graphene ribbons.

An elastic-shell-based theory for calculating the thermal conductance of graphene ribbons of arbitrary width w is presented. The analysis of vibrational modes of a continuum thin plate leads to a general equation for ballistic conductance sigma. At low temperature, it yields a power law sigma approximately T(beta), where the exponent beta varies with the ribbon width w from beta = 1 for a narrow ribbon (sigma approximately T, as a four-channel quantum wire) to beta = (3)/(2) (sigma approximately wT(3/2)) in the limit of wider graphene sheets. The ballistic results can be augmented by the phenomenological value of a phonon mean free path to account for scattering and agree well with the reported experimental observations.