ELECTRONIC STATES OF QUASIPERIODIC SYSTEMS: FIBONACCI AND PENROSE LATTICES

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Abstract
Since the experiment of Shechtman et al. which suggests the crystal with the pentagonal symmetry (quasicrystal), there has been a lot of interest in the quasiperiodic systems. These can be regarded as being intermediate between ordered and disordered systems, and novel physical properties are expected. In fact, the quasicrystal in one-dimension is known to have exotic electronic properties: Cantor set energy spectrum, existence of self-similar and fractal wavefunctions and so on. These properties have intrinsically related to the renormalization-group theory and the nonlinear dynamical systems which could lead to chaos. The electronic properties of the Fibonacci lattice (1-D quasicrystal) and the Penrose lattice (2-D quasicrystal) are discussed.

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