Universality of Hofstadter Butterflies on Hyperbolic Lattices

Alexander Stegmaier, Lavi K. Upreti, Ronny Thomale, and Igor Boettcher
Phys. Rev. Lett. 128, 166402 – Published 22 April 2022
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Abstract

Motivated by recent realizations of hyperbolic lattices in superconducting waveguides and electric circuits, we compute the Hofstadter butterfly on regular hyperbolic tilings. Utilizing large hyperbolic lattices with periodic boundary conditions, we obtain the true bulk spectrum unaffected by boundary states. The butterfly spectrum with large extended gapped regions prevails, and its shape is universally determined by the fundamental tile, while the fractal structure is lost. We explain how these features originate from Landau levels in hyperbolic space and can be verified experimentally.

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  • Received 12 November 2021
  • Accepted 30 March 2022

DOI:https://doi.org/10.1103/PhysRevLett.128.166402

© 2022 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsAtomic, Molecular & Optical

Authors & Affiliations

Alexander Stegmaier1,*, Lavi K. Upreti1,*, Ronny Thomale1, and Igor Boettcher2,3

  • 1Institut für Theoretische Physik und Astrophysik, Universität Würzburg, 97074 Würzburg, Germany
  • 2Department of Physics, University of Alberta, Edmonton, Alberta T6G 2E1, Canada
  • 3Theoretical Physics Institute, University of Alberta, Edmonton, Alberta T6G 2E1, Canada

  • *These two authors contributed equally to this work.

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Vol. 128, Iss. 16 — 22 April 2022

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