Clustering properties of energy spectra for one-dimensional generalized Fibonacci lattices

Abstract

Clustering properties of energy spectra for one-dimensional (1D) generalized Fibonacci (GF) lattices are studied. Branching rules (BR) of the energy spectra for the silver-mean (SM) and the copper-mean (CM) lattices are established by means of the idea of an approximated renormalization-group (RG) scheme and confirmed by diagonalizing the Hamiltonian matrices. The SM and CM lattices have six and five global subband structures, respectively. There coexist trifurcation and pentafurcation in the splittings of subbands which are not shown in the ordinary Fibonacci lattice. This study gives a rather intuitive picture in understanding the electronic properties of the GF lattices.