Phonon properties of Fibonacci chains

摘要

This paper presents the phonon properties of Fibonacci chains in the harmonic approximation theoretically. Using the transfer matrix method, we investigate the influence of the atom masses on the phonon spectra of quasiperiodic chains. Our calculations show that the atom masses determine the widths and positions of gaps. Moreover, the phonon spectra of Fibonacci chains made by two atoms are self-similar in the high-frequency regions.