Propagating and Localized Elementary Excitations in Decagonal Quasicrystals

We have studied the properties of elementary excitations in decagonal $(d)$ quasicrystals as an example of vibrational eigenstates in a model d-AlMn alloy. We show that the presence of a periodic direction leads to the following marked differences compared to icosahedral ( i) quasicrystals: distinctly higher eigenvalues, a much more structured density of states, and a stronger tendency towards the localization of certain eigenstates. These effects are related to the lower dimensionality of the quasiperiodicity, and to the coupling between longitudinal modes propagating along the periodic direction and transverse modes in the quasiperiodic plane, but polarized parallel to the periodic axis.