Phonons in aperiodically ordered layer systems

We have studied the phonons in multilayer structures following different aperiodic sequences (Fibonacci, Thue-Morse, Period-Doubling) along the growth direction. We have employed a nearest-neighbor force constant model giving a reasonably realistic description of metal systems. We have seen that the phonon dispersion relation at symmetry points does not present in a clear way the spectrum fragmentation seen in one dimension models. It has been found that for low frequencies at Brillouin zone center the vibration pattern is similar to that seen in one dimension models. On the other hand for higher frequencies at that point and at other symmetry points regular vibration patterns appear.