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STUDIES ON THE PROPERTIES OF ELECTRONIC ENERGY SPECTRA FOR TWO DIMENSIONAL FIBONACCI-CLASS QUASICRYSTALS WITH ONE KIND OF ATOMS

In the framework of the single-electron tight-binding nearest interaction on-site model, we have studied the splitting rules of electronic energy spectra for two-dimensional Fibonacci-class quasicrystals FC(n) with one kind of atoms by means of the decomposition-decimation method based on the renormalization-group technique and have also calculated the electronic energy spectra numberically. It was found that there are-only three kinds of clusters,n×n, n×(n+1), and (n+1)×(n+1) for all of the two-dimensional quasilattices FC(n) and the electronic energy bands split as Y m-n-l . The general formula of the energy level numbers was obtained. We discovered that there was a kind of so called Fibonacci class number sets for the parameters used to describe the energy level number and got the first 11 determined integers of the sets. The experienced formula have been sought out. The analytic results are confirmed by numerical simulations.