INFLUENCES OF SPRING CONSTANTS AND GENERATIONS ON THE PHONON SPECTRA OF FIBONACCI CHAIN

Abstract

In the frame work of the nearest-neighbor harmonic spring model, we calculate the phonon spectra by means of the transfer matrix method and investigate the influences of the spring constants, the periodicity, the degree of defect for a periodic chain and the length of a chain on the phonon spectra of Fibonacci chain. It is found that for a certain generation chain the range of the phonon spectra enlarges from the low- to high-frequency zone with the increment of the parameter λ, and when the structure of a chain is certain, the spectra range decreases and more and more phonon states with higher frequencies disappear with the increment of generation. Consequently, when the chain tends to be infinite, there only exist very few phonon states with low-frequency. On the other hand, for a certain Fibonacci chain, phonon states with high-frequency can be formed only when λ is larger than the corresponding critical value.