Phonon Transport Simulations in Low-Dimensional Disordered Graphene Nanoribbons

In this paper, we investigate phonon transport in low-dimensional disordered armchair graphene nanoribbons (GNRs) in order to illuminate phonon transport effects in 1-D disordered systems. We use the nonequilibrium Green's function simulation technique for transport, coupled to the force constant method for obtaining the phonon bandstructure. We focus on how different parts of the phonon spectrum are influenced by geometrical confinement and line edge roughness. In the ballistic case, phonons throughout the entire phonon energy spectrum contribute to thermal transport. With the introduction of line-edge roughness, the phonon transmission is reduced, but quantitatively and qualitatively in different ways throughout the energy spectrum. We identify how each region of the spectrum reacts to low-dimensionality and disorder, and elaborate on how phonon transport is affected by that. We explain how and when phonons in different energies within the spectrum flow either ballistically, diffusively, or become localized depending on features of the channel geometry. Finally, we derive exponents related to the length and width dependence of the thermal transport in the GNRs under the influence of line-etch roughness. Our results could provide generic features of thermal transport in different classes of low-dimensional materials beyond GNRs, and could help to better understand the heat transport at the nanoscale.