Critical eigenstates and their properties in one- and two-dimensional quasicrystals

Nicolas Macé, Anuradha Jagannathan, Pavel Kalugin, Rémy Mosseri, and Frédéric Piéchon
Phys. Rev. B 96, 045138 – Published 26 July 2017

Abstract

We present exact solutions for some eigenstates of hopping models on one- and two-dimensional quasiperiodic tilings and show that they are “critical” states, by explicitly computing their multifractal spectra. These eigenstates are shown to be generically present in 1D quasiperiodic chains, of which the Fibonacci chain is a special case. We then describe properties of the ground states for a class of tight-binding Hamiltonians on the 2D Penrose and Ammann-Beenker tilings. Exact and numerical solutions are seen to be in good agreement.

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  • Received 17 June 2017

DOI:https://doi.org/10.1103/PhysRevB.96.045138

©2017 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Nicolas Macé1,*, Anuradha Jagannathan1, Pavel Kalugin1, Rémy Mosseri2, and Frédéric Piéchon1

  • 1Laboratoire de Physique des Solides, Université Paris-Saclay, 91400 Orsay, France
  • 2Laboratoire de Physique Théorique de la Matière Condensée, Université Pierre et Marie Curie, 75005 Paris, France

  • *Corresponding author: nicolas.mace@u-psud.fr

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Issue

Vol. 96, Iss. 4 — 15 July 2017

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