Thermal conductance attributed to phonon and electron in graphene nanoribbon

Abstract

In this work, the energy transport of phonon and electron in graphene nanoribbons (GNRs) are investigated by the nonequilibrium Green's function method without considering the interaction of phonon and electron. The heat current of phonon contribution comes from the gradient of temperature. While for the electron contribution, it stems from the gradient of both temperature and electrochemical potential. The corresponding intermediate functions satisfy the Onsager relationship. Thermal conductances are calculated in GNR and compared to those in square lattice ribbon model respectively. It is found that both the phonon and electron thermal conductances in square lattice ribbon are smaller than those in GNRs at low temperature and surpass those in armchair and zigzag GNRs respectively, as the temperature increases. Meanwhile, the heat transport is related to the edges of GNRs. These phenomena depend on their dispersion relations and energy band structures.