Selective spatial localization of the atom displacements in one-dimensional hybrid quasi-regular (Thue–Morse and Rudin–Shapiro)/periodic structures

We have studied the vibrational frequencies and atom displacements of one-dimensional systems formed by combinations of Thue–Morse and Rudin–Shapiro quasi-regular stackings with periodic ones. The materials are described by nearest-neighbor force constants and the corresponding atom masses. These systems exhibit differences in the frequency spectrum as compared to the original simple quasi-regular generations and periodic structures. The most important feature is the presence of separate confinement of the atom displacements in one of the parts forming the total composite structure for different frequency ranges, thus acting as a kind of phononic cavity.