▎ 摘　　要

We investigated the vibrational properties of graphene nanoribbons by means of first-principles calculations on the basis of density-functional theory. We confirm that the phonon modes of graphene nanoribbons with armchair- and zigzag-type edges can be interpreted as fundamental oscillations and their overtones. These show a characteristic dependence on the nanoribbon width. Furthermore, we demonstrate that a mapping of the calculated Gamma-point phonon frequencies of nanoribbons onto the phonon dispersion of graphene corresponds to an "unfolding" of nanoribbons' Brillouin zone onto that of graphene. We consider the influence of spin states with respect to the phonon spectra of zigzag nanoribbons and provide comparisons of our results with past studies.