材料期刊网

As an extension of the Thue-Morse lattice, we consider the generalized Thue-Morse lattices associated with the sequences S(x) given by the recursion relation S(l+1) = {S(l)n, SBAR(l)m} for l greater-than-or-equal-to 0 with S0 = (AB}, in which m and n are positive integers and SBAR(l) is the complement of S(l) obtained by interchanging A and B in S(l). A unified trace map is derived to study the electronic energy spectra for the diagonal tight-binding model. The results show that the spectra exhibit a new kind of self-similarity.