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Electronic properties of the generalized Thue-Morse lattices: a dynamical-map approach

As an extension of the Thue-Morse lattice, the authors consider the generalized Thue-Morse lattices associated with the sequences Sx given by the recursion relation Sl+1=(Sln,Slm)> for l>or=0 with S0=(AB), in which m and n are positive integers and Sl is the complement of Sl obtained by interchanging A and B in Sl. 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.