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

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) 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 , and five sub-subbranches when . 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.Received: 18 March 2004, Published online: 23 July 2004PACS: 71.23.Ft Quasicrystals - 63.90. + t Other topics in lattice dynamics (restricted to new topics in section 63) - 33.70.Jg Line and band widths, shapes, and shifts