Electronic specific heat properties in one-dimensional quasicrystals

In this paper we investigate the thermodynamical properties of electrons in one-dimensional quasiperiodic potentials, arranged in accordance with the pure and generalized Fibonacci sequences. The sequences are described in terms of a series of generations that obey peculiar recursion relations, and have controlled disorder, i.e., they are neither random nor periodic. Their electronic energy spectra are calculated using the one-dimensional Schrödinger equation in a tight-binding approximation. We present both analytical and numerical studies on the temperature dependence of the electronʹs specific heat associated with their multiscale fractal energy spectra. We show that when T→0, the specific heat displays oscillations, and when T→∞, the specific heat goes to zero with T−2.