SKM 2023 – wissenschaftliches Programm

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TT: Fachverband Tiefe Temperaturen

TT 17: Topology: Quantum Hall Systems

TT 17.5: Vortrag

Montag, 27. März 2023, 18:00–18:15, HSZ 304

Hofstadter butterflies in hyperbolic space — •Alexander Stegmaier¹, Lavi Upreti⁴, Ronny Thomale¹, and Igor Boettcher^2,3 — 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 — ⁴Department of Physics, University of Konstanz, 78464 Konstanz, Germany

Hofstadter's Butterfly is the spectrum of a charged particle moving in a tight binding lattice under a constant magnetic field. Beyond its well-known fractal-shaped spectrum, this model is also relevant as a prototypical topological Chern insulator.

In light of recent interest in the physics of lattices in hyperbolic space, we re-consider the problem of Hofstadter's butterfly in {p,q} lattices. They tile the hyperbolic plane, a 2D space with constant negative curvature, with regular p-gons, q of which meet at each vertex. We develop methods to calculate the bulk spectra of a hyperbolic tight-binding system and apply them to uncover the features of Hofstadter's Butterflies in hyperbolic space. We find that the move to negatively curved space destroys the spectra's fractality, but preserves features of the spectral gaps, depending on the type of tiling {p,q}.