Lattice vibrations in graphene nanoribbons from density functional theory

This work shows results of our investigation of the lattice vibrations in graphene nanoribbons with zigzag and armchair type edges, which we performed by the use of density functional theory. The boundary conditions induced by the nanoribbon edges allow for an interpretation of the phonons as fundamental modes and their respective overtones. The calculated phonons show a characteristic dependence on the nanoribbon width. In this context, we considered a possible influence of the antiferromagnetic ground state of zigzag nanoribbons with respect to the phonons. 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 the nanoribbons' Brillouin zone onto that of graphene and yields good agreement. We further show symmetry properties of armchair and zigzag nanoribbons and full phonon dispersions for small-width nanoribbons. (C) 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim