Vibrational properties of quasiregular systems with mirror symmetry

We have studied the vibrational frequencies and atom displacements of one-dimensional systems formed by combinations of quasiregular stackings having mirror symmetry. The materials are described by nearest-neighbor force constants and the corresponding atom masses. Fibonacci, Thue–Morse and Rudin–Shapiro sequences are considered. These systems exhibit differences in the frequency spectrum as compared to the original systems with no mirror symmetry. Localized modes are found in the wide primary gaps and near the band edges of the Fibonacci structures. In the Rudin–Shapiro structures localized modes near the band edges are also found whereas in the Thue–Morse structures no such features are found. Besides this a selective confinement of the atom displacements in one of the sequences forming the total system is found for different frequency ranges in all the systems studied.