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

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 , n 2 , n 3 , ··· ( 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.