Universality of Hofstadter butterflies on hyperbolic lattices

Motivated by recent experimental breakthroughs in realizing hyperbolic lattices in superconducting waveguides and electric circuits, we compute the Hofstadter butterfly on regular hyperbolic tilings. By utilizing large hyperbolic lattices with periodic boundary conditions, we obtain the true hyperbo...

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Bibliographic Details
Published in:arXiv.org 2022-02
Main Authors: Stegmaier, Alexander, Upreti, Lavi K, Thomale, Ronny, Boettcher, Igor
Format: Article
Language:English
Subjects:
Boundary conditions
Circuits
Hyperbolic coordinates
Lattices
Waveguides
Online Access:Get full text
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Summary:Motivated by recent experimental breakthroughs in realizing hyperbolic lattices in superconducting waveguides and electric circuits, we compute the Hofstadter butterfly on regular hyperbolic tilings. By utilizing large hyperbolic lattices with periodic boundary conditions, we obtain the true hyperbolic bulk spectrum that is unaffected by contributions from boundary states. Our results reveal that the butterfly spectrum with large extended gapped regions prevails and that its shape is universally determined by the number of edges of the fundamental tile, while the fractal structure is lost in such a non-Euclidean case. We explain how these intriguing features are related to the nature of Landau levels in hyperbolic space, and how they could be verified experimentally.
ISSN:2331-8422
DOI:10.48550/arxiv.2111.05779