Splitting rules for spectra of two-dimensional Fibonacci quasilattices

In the framework of the single-electron tight-binding on-site model, after establishing the method of constructing a class of two-dimensional Fibonacci quasilattices, we have studied the rules of energy spectra splitting for these quasilattices by means of a decomposition-decimation method based on the renormalization-group technique. Under the first approximation, the analytic results show that there exist only six kinds of clusters and the electronic energy bands split as type $Y$ and consist of nine subbands. Instead of the on-site model, the transfer model should be used for the higher hierarchy of the spectra, the electronic energy spectra split as type $F.$ The analytic results are confirmed by numerical simulations.