PROPAGATING AND CONFINED VIBRATIONAL EXCITATIONS IN QUASI-CRYSTALS

We present detailed investigations of vibrational modes in a hierarchy of rational (or commensurate) approximants to icosahedral quasicrystals, based on exact diagonalization of the dynamical matrix and recursion calculations of the vibrational spectrum. Our results demonstrate the existence of well defined longitudinal and transverse acoustic modes with isotropic dispersion relations in the vicinity of quasiperiodically distributed special points in wavenumber space, the 'GAMMA points' of the reciprocal quasilattice. Stationary eigenmodes are found around other high-symmetry points in reciprocal space corresponding to quasi-Brillouin zone boundaries. We show that strictly localized ('confined') modes exist and that their origin is a local topological frustration, i.e. in a local deviation from ideal icosahedral packing.