Wave packet simulations of phonon boundary scattering at graphene edges

Abstract

Wave packet dynamics is used to investigate the scattering of longitudinal (LA), transverse (TA), and bending-mode (ZA) phonons at the zigzag and armchair edges of suspended graphene. The interatomic forces are calculated using a linearized Tersoff potential. The strength of a boundary scattering event at impeding energy flow is described by a forward scattering coefficient, similar in spirit to a specularity parameter. For armchair boundaries, this scattering coefficient is found to depend strongly on the magnitude, direction, and polarization of the incident wavevector, while for zigzag boundaries, the forward scattering coefficient is found to always be unity regardless of wavevector and polarization. Wave packet splitting is observed for ZA phonons incident on armchair boundaries, while both splitting and mode conversion are observed for LA and TA phonons incident on both zigzag and armchair boundaries. These simulation results show that armchair boundaries impede the forward propagation of acoustic phonon energy much more strongly than zigzag boundaries do, suggesting that graphene nanoribbons will have substantially lower thermal conductivity in armchair rather than zigzag orientation.