Role of phason defects on the conductance of a one-dimensional 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.

Fermi surfaces and anomalous transport in quasicrystals

“…Within the one electron scheme, several theoretical approaches suggest an intermediate type of algebraic localization between purely extended states and exponentially localized states. [5,6,7,8] Different schemes were proposed to explain original transport properties, amongst which, nonballistic quantum diffusion for long relaxation times or hopping mechanisms induced by interband transitions at shorter ones. In this paper, we have shown how scaling analysis of the Kubo formula may lead to power-law temperature dependence of electronic conductivity in the low temperature regime.…”

“…[4] Theoretical works have been concerned with the relation between quasicrystalline order (short, mesoscopic and long-range) and electronic localization and diffusion modes. [5,6,7,8] The electronic structure of real quasicrystals can be deduced from ab-initio LMTO calculations, performed on realistic structural models of their approximants. [9,10] A pseudo-gap at Fermi level and a dense concentration of low dispersive bands in its close vicinity, constitute the main features of their electronic structure.…”

Electronic transport properties of quasicrystals

“…One of us, has investigated the effect of some particular phason defects in Fibonacci chains and quantum networks Landauer resistance 74,75 . These studies show how correlations of disorder induced by this kind of defects can lead to specific behavior of conductivity.…”

Fractal feature of localized electronic states in Fibonacci arrays of Aharonov-Bohm rings

“…There is a research study that investigated the behavior of conduc-tance in relation to the underlying chaotic map and its invariant. 8 Moulopoulos et al analytically provided that resonances occur at special points associated with the vanishing of invariant I of the underlying dynamical map.…”

“…8 In addition, Chakrabarti et al 18 presented that in the quasiperiodic system of AB rings based on tight-binding model, the value of the invariant should not necessarily correspond to zeros at the energy that the resonance occurs. Thus, the relationship between the resonance and the vanishing of the I-function could be presented by an idealized model ͑a full continuous model͒ of AB rings.…”