Ballistic to diffusive crossover of heat flow in graphene ribbons

Heat flow in nanomaterials is an important area of study, with both fundamental and technological implications. However, little is known about heat flow in two-dimensional (2D) devices or interconnects with dimensions comparable to the phonon mean free path (mfp). Here, we find that short, quarter-micron graphene samples reach ~35% of the ballistic heat conductance limit up to room temperature, enabled by the relatively large phonon mfp (~100 nm) in substrate-supported graphene. In contrast, patterning similar samples into nanoribbons (GNRs) leads to a diffusive heat flow regime that is controlled by ribbon width and edge disorder. In the edge-controlled regime, the GNR thermal conductivity scales with width approximately as ~W^{1.8+/-0.3}, being about 100 W/m/K in 65-nm-wide GNRs, at room temperature. Manipulation of device dimensions on the scale of the phonon mfp can be used to achieve full control of their heat-carrying properties, approaching fundamentally limited upper or lower bounds.