Transverse elastic waves in Fibonacci superlattices

We study the transverse elastic waves propagating in 6-mm class hexagonal crystals forming Fibonacci superlattices. These are formed by repetitions of CdS and ZnO slabs in A and B constituent blocks following the Fibonacci sequence. We study the periodic superlattices formed by the infinite repetition of a given Fibonacci generation together with the finite Fibonacci generations having stress-free surfaces, in order to compare the effects introduced by the different boundary conditions. We have also considered the effects of piezoelectricity when all the interfaces are metallized and kept at a fixed potential. We use the surface Green function matching method forNnonequivalent interfaces to obtain the dispersion relations and the density of states of these systems. We have studied the influence of the increasing order of the Fibonacci generations on the dispersion relation of the transverse elastic modes. The Fibonacci spectrum is clearly seen even for low-order Fibonacci generations and is almost not modified by the piezoelectric coupling when the interfaces are metallized.