Edge shape effect on vibrational modes in graphene nanoribbons: A numerical study

The phonon dispersion and the vibrational density of states (VDOS) of graphene nanoribbons (GNR) of various widths and edge shapes are calculated using the force constant model including the fifth-nearest neighbor atoms. Among typical graphene peaks like E2g (or G) and D peaks, several distinctive ribbon peaks are identified in the VDOS depending on the edge shape. According to our calculation, the edge nature of a GNR can be identified by several characteristic peaks in the VDOS: many out-of-plane edge localized modes are detected at about 630 cm−1 in armchair GNRs and many in-plane edge modes are detected at about 480 cm−1 in zigzag GNRs. In mixed-edge GNRs the intensity of these peaks is strongly correlated to the armchair-to-zigzag edge ratio.