Thermal conductance of graphene and dimerite

We investigate the phonon thermal conductance of graphene regarding the graphene sheet as the large-width limit of graphene strips in the ballistic limit. We find that the thermal conductance depends weakly on the direction angle θ of the thermal flux periodically with period π/3. It is further shown that the nature of this directional dependence is the directional dependence of group velocities of the phonon modes in the graphene, originating from the D₆ₕ symmetry in the honeycomb structure. By breaking the D₆ₕ symmetry in graphene, we see more obvious anisotropic effect in the thermal conductance as demonstrated by dimerite.