Abstract
The electronic transport in the Fibonacci array of ideal one-dimensional T stubs is studied by utilizing the scaling analysis for the Fibonacci invariant, which is derived from the Kohmoto-Kadanoff-Tang (KKT) renormalization-group theory [Phys. Rev. Lett. 50, 1870 (1983)] and Landauer resistance (LR). The orbit of the KKT map is confined to a two-dimensional manifold (i.e., the invariant is independent of the generation number $j$). However, in our model, the invariant is not independent of $j$ in the transmission rift (i.e., fine transmission gap), and it is characterized by a scaling law as in the case of the Aharonov-Bohm ring model by Nomata and Horie in a previous work [Phys. Rev. B 75, 115130 (2007)]. The relationship between the local maximum value and the width of the transmission rift on the LR for the two-terminal case is characterized by a scaling law as in the case of the $I$ function, which is a $j$-dependent invariant. In addition, self-similarity for the LR appears in the entire region of $k$ when the scaling index is in good agreement with that at another $j$. It is found that self-similarity appears in the LR when the transmission probability exhibits self-similarity.
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