Splitting rules for the electronic energy spectra of 2D FC(n) with three kinds of atoms and one bond length

In this paper we study the splitting rules of energy spectra for two-dimensional Fibonacci-class quasilattices (FC(n)) with three kinds of atoms (A, B, and C) and one bond length by means of a decomposition-decimation method, and find that the sublattices of B atoms and C atoms are different from those of normal two-dimensional FC(n) and the corresponding splitting manners are new and interesting. B atom forms a kind of two-dimensional so-called FC(n)’, which structure is some different from that of normal FC(n-1) (n≥2), but the spectra lines are as the same as that of the latter. C atom forms two kinds of interesting one-dimensional periodic chains: n-atom chain and (n-1)-atom chain, which spectra will both tend to become continuous, respectively. The analytical results are confirmed by numerical simulations.