One-Dimensional Quasicrystal as Being Obtained by Successive Application of Periodic Modulations to a Crystal —Structure of Fibonacci Sequence and the Electronic States

Abstract

The structure of one-dimensional quasicrystal is reconsidered so that we can intuitively understand its electronic properties. It is shown that the Fibonacci sequence is obtained from a regular crystal by successive application of periodic modulations, which have the periods increasing as n, n², n³, … (n=3) and are self-similar. Explanations are given for the peculiar spectra of electronic states on a one-dimensional quasiperiodic lattice as a result of the modulations applied to the crystal. Differences are also briefly discussed for the phonon and electronic band structure.