Transmission and frequency spectra of acoustic phonons in Thue-Morse superlattices

We study the transmission and frequency spectra of phonons in aperiodic Thue-Morse superlattices. Calculations based on the transfer-matrix method predict rich structures of the transmission dips and frequency gaps, and their basic properties are well described by the superlattice-structure factors that we derive. The angular dependence of the phonon transmission is also calculated and the existence of the intermode reflection of phonons is confirmed. Our results indicate that in the single-layer superlattice the spectral structures of phonons associated with the nonperiodicity of the Thue-Morse sequence dominate those arising from the underlying periodicity. This suggests that, for an experimental verification of the phonon spectra unique to the aperiodic nature of the sequence, the single-layer superlattice is more appropriate than the double-layer one. The latter exhibits a significant correlation with a corresponding periodic superlattice in the spectral dips and gaps