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

摘要

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)(ngreater than or equal to2) splits according to the type Y'((n-1)-2-1) and type Yn-2-1 respectively. The one for n x (n+1) clusters of FC(n) consists of three sub-subbands when nless than or equal to2, and five sub-subbranches when ngreater than or equal to3. 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.