Role of phason-defects on the conductance of a 1-d quasicrystal

Abstract

We have studied the influence of a particular kind of phason-defect on the Landauer resistance of a Fibonacci chain. Depending on parameters, we sometimes find the resistance to decrease upon introduction of defect or temperature, a behavior that also appears in real quasicrystalline materials. We demonstrate essential differences between a standard tight-binding model and a full continuous model. In the continuous case, we study the conductance in relation to the underlying chaotic map and its invariant. Close to conducting points, where the invariant vanishes, and in the majority of cases studied, the resistance is found to decrease upon introduction of a defect. Subtle interference effects between a sudden phason-change in the structure and the phase of the wavefunction are also found, and these give rise to resistive behaviors that produce exceedingly simple and regular patterns.