The influence of phason disorder on the electronic spectrum and eigenstates of Fibonacci lattices

Abstract

The electronic properties of a Fibonacci lattice with one mistake (phason flip) is studied. The phason is treated as a perturbation of the perfect chain, and we show that it is equivalent to the presence of two substitutional impurities. The effects of the phason on the electronic spectrum are that localized and resonant eigenstates are observed all over the whole spectrum and the distribution of energy level-spacing is modified by reducing the tendency of lever-clustering. On the contrary, it is also shown that phasons applied at certain sites of the chain left the spectrum unaffected.