Oscillatory behavior of the specific heat at low temperature in quasiperiodic structures

We investigate the thermodynamical properties of plasmon–polaritons that propagate in multiple semiconductor layers arranged in a quasi-periodical fashion of Fibonacci and Thue–Morse types. We have chosen these two types of quasi-periodic structures for the following reasons: (i) both were realized experimentally, so they are not mere academic examples of a quasi-crystal; (ii) it is believed that the Thue–Morse chain is more disordered than the Fibonacci one, i.e., it has a degree of aperiodicity intermediate between the Fibonacci chain and the random systems. More precisely, the Fourier amplitude spectrum of the Thue–Morse sequence is singular continuous, while for the Fibonacci case we found δ-function peaks not arranged periodically. Both analytical and numerical studies on the temperature dependence of the excitationʹs specific heat associated with the generation number n=1,2,3,… for their multiscale fractal energy spectra are presented. We show that when T tends to zero, the specific heat displays oscillations and when T tends to infinity, the specific heat goes to zero as T−2, because the energy spectrum considered is bounded.