Vibrational density of states, dynamical structure factor and eigenstates of icosahedral models

Abstract

Extending our previous studies on icosahedral models, we numerically calculate the integrated density of states (IDOS), the dynamical structure factor, and special eigenstates of the ABCK tiling decorated by Danzer and Talis. We find a broadening of the structure factor at frequencies where the IDOS exhibits kinks. These kinks arise from a strong increase of the imaginary part of the Green's function (strong damping of plane-wave modes) and indicate localization. The centers of the localized vibrations mainly form icosahedra. The occurrence of distinct regimes in the IDOS may be related to the hierarchical structure of the tiling. The flatness of the optical branches in the dynamical structure factor implies strong localization of optical modes.