Abstract
We study the electronic properties of the generalized Fibonacci lattices generated by the inflation rule ( A, B) → ( AB n , A) with n > 1. A unified real-space renormalization-group scheme is presented for calculating the exact local Green's function at any given site. Analysis suggests that there are extended states in these lattices. Furthermore, the appearance of the extended states and the smoothness of the local density of states depends on the system parameters, implying that these exists a state transition phenomenon similar to that of the incommensurate Harper's model.
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