Nonmonotonic crossover and scaling behaviors in a disordered 1D quasicrystal

Abstract

We consider a noninteracting disordered 1D quasicrystal in the weak disorder regime. We show that the critical states of the pure model approach strong localization in strikingly different ways, depending on their renormalization properties. A finite size scaling analysis of the inverse participation ratios of states (IPR) of the quasicrystal shows that they are described by several kinds of scaling functions. While most states show a progressively increasing IPR as a function of the scaling variable, other states exhibit a nonmonotonic `re-entrant' behavior wherein the IPR first decreases, and passes through a minimum, before increasing. This surprising behavior is explained in the framework of perturbation renormalization group treatment, where wavefunctions can be computed analytically as a function of the hopping amplitude ratio and the disorder, however it is not specific to this model. Our results should help to clarify results of recent studies of localization due to random and quasiperiodic potentials.

arXiv commentRevised and expanded text (10 pages, 9 figs) as accepted for publication in Phys Rev B

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• Topological critical states and anomalous electronic transmittance in one dimensional quasicrystals
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• Bulk topological signatures of a quasicrystal
• Properties of the Ammann-Beenker tiling and its square approximants
• Closing of gaps and gap labeling and passage from molecular states to critical states in a 2D quasicrystal
• Effects of Disorder in the Fibonacci Quasicrystal
• The Fibonacci quasicrystal: case study of hidden dimensions and multifractality
• Missing link between the 2D Quantum Hall problem and 1D quasicrystals