Splitting rules for the 2nd hierarchy structure of the electronic spectra of 2D FC(n) quasicrystals

Feng Li and Xiangbo Yang ()

The European Physical Journal B: Condensed Matter and Complex Systems, 2004, vol. 39, issue 4, 475-481

Abstract: On the basis of our former work and by means of the decomposition-decimation method, we study the splitting rules for the second hierarchy of the electronic energy spectra for two-dimensional Fibonacci-class quasicrystals with one kind of atom and two bond lengths. It is found that every line of the sub-spectra for n x n and (n + 1) x (n + 1) clusters of FC(n) $(n \geq 2)$ splits according to the type Y‘ (n-1)-2-1 and type Y n-2-1 respectively. The one for n x (n + 1) clusters of FC(n) consists of three sub-subbands when $n \le 2$ , and five sub-subbranches when $n \ge 3$ . The general formulae of the number of energy levels for the spectra of the second hierarchy are obtained. The analytical results are confirmed by numerical simulations. Copyright Springer-Verlag Berlin/Heidelberg 2004

Date: 2004
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DOI: 10.1140/epjb/e2004-00220-0

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