Splitting rules for the electronic spectra of two-dimensional SML quasilattices

In the framework of single-electronic tight-binding nearest-interaction transfer model, after establishing the method of constructing a class of two-dimensional SML quasilattices, we have studied the spectral properties of two-dimensional SML quasilattices by means of a decomposition-decimation method based the renormalization-group technique. It is found that the spectra have a variety of multifurcating structures, the total spectra are symmetrical, and every spectral line splits into odd sub-bands in the higher hierarchy. The analytic results show that under the first approximation, there exist only six kinds of clusters and the bare energy splits into thirteen subbands, and under the second approximation, several kinds of new spitting manners occur, e.g., 1:33, 1:19. The analytical results are confirmed by numerical simulations. (C) 2004 Elsevier B.V. All rights reserved.