Abstract

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 a. At low temperature, it yields a power law sigma similar to T-beta, where the exponent beta varies with the ribbon width w from beta = 1 for a narrow ribbon (sigma similar to T, as a four-channel quantum wire) to beta = 3/2 (sigma similar to 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.