Abstract
In this work, the Kubo–Greenwood formula is used to investigate the electrical conduction in macroscopic Fibonacci lattices within a single-band tight-binding model. This investigation is carried out by means of a renormalization method, which allows the iterative evaluation of the products of the Green’s function in an exact way. The results of d.c. conductivity show an extremely fine band structure and a periodic oscillating pattern in the neighborhood of the transparent state. The a.c. conductivity of these transparent states as a function of the frequency shows a regular oscillating behavior, whose maximums decay following an inverse power law. Furthermore, the d.c. conduction in two-dimensional Fibonacci superlattices reveals a smooth dependence on the Fermi energy location and finally the transition from one- into two-dimensional conductivity is also analyzed.
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