Local heat current flow in ballistic phonon transport of graphene nanoribbons

Utilizing the nonequilibrium Green's function method, we study the local heat current flow of phonons in nanoscale ballistic graphene nanoribbon, where boundary scattering leads to the formation of atomic-scale current vortices. We further map out the atomic temperature distribution in the ribbon with B & uuml;ttiker's probe approach. From the heat current and temperature distribution, we observe inverted temperature response in the ribbon, where the heat current direction goes from the colder to the hotter region. Moreover, we show that atomic scale defect can generate heat vortex at certain frequency, but it is averaged out when including contributions from all the phonon modes. Meanwhile, our results have recovered residual-resistivity dipole features manifested at the vicinity of local defects. These results extend the study of local heat vortex and negative temperature response in the bulk hydrodynamic regime to the atomic-scale ballistic regime, further confirming boundary scattering is crucial to generate backflow of heat current.