Edge-localized phonons in nanographite ribbons

Based on the classical force constant model, we study numerically out-of-plane phonon dispersion relations for two types of nanographite ribbon confined by the armchair- and zigzag-shaped edges. We demonstrate how the edge-localized vibrational modes behave depending on edge environment by means of altering the effective mass of the edge sites. Special emphasis is placed on the qualitative difference in the behavior of the edge-localized phonon between the two edge shapes.