Realistic edge shape effects on the vibrational properties of graphene nanoribbons

Graphene nanoribbons (GNRs) are predicted to be essential components in future graphene nanoelectronics. Recent studies show that atomic scale edge structures of GNRs consist of armchair and zigzag edges with some other defects. Here we probe systematically the details of the phonon properties of GNRs with realistic edge structures consisting of armchair and zigzag edges along with some vacancies using the forced vibrational method. We have estimated the phonon density of states (PDOSs) and typical mode patterns of GNRs considering the effects of the mixture of various directional armchair edge and zigzag edge with some vacancies. We find that in-plane longitudinal and transverse optical (LO) and (TO) mode phonons of realistic edge shaped GNR are non-degenerate and moved down with the reduction of ribbon width. The PDOS at low frequency region changes significantly for the realistic edge structures. We observe a strongly localized eigenmodes of inplane transverse optical phonon (iTO) near the armchair edges and defect sites which are conceptually very good agreement with the Raman D peak comes from the armchair edges or the defects of GNRs activated by the iTO phonons.