Electronic properties of the tight-binding Fibonacci Hamiltonian

Abstract

The analysis of the electronic properties of the tight-binding Fibonacci Hamiltonian is carried out using dynamical systems techniques. Two classes of Fibonacci sequences are considered, corresponding to the cases when there are two types of building blocks and also when there are three types of building blocks. The recursion relations for the traces of the transfer matrices are determined and studied for various extensions of the Fibonacci case with the golden mean. Some differences are obtained between the various types of second-order Fibonacci sequences and are most likely due to long-range order. Applications of this work to the transmission of light through a multilayered medium and the electrical resistance of a one-dimensional quasicrystal, as determined by the Landauer formula, are presented.