Hyperbolic matter in electrical circuits with tunable complex phases

Anffany Chen, Hauke Brand, Tobias Helbig, Tobias Hofmann, Stefan Imhof, Alexander Fritzsche, Tobias Kießling, Alexander Stegmaier, Lavi K. Upreti, Titus Neupert, Tomáš Bzdušek, Martin Greiter, Ronny Thomale and Igor Boettcher ()
Additional contact information
Anffany Chen: University of Alberta
Hauke Brand: Universität Würzburg
Tobias Helbig: Universität Würzburg
Tobias Hofmann: Universität Würzburg
Stefan Imhof: Universität Würzburg
Alexander Fritzsche: Universität Würzburg
Tobias Kießling: Universität Würzburg
Alexander Stegmaier: Universität Würzburg
Lavi K. Upreti: Universität Würzburg
Titus Neupert: University of Zurich
Tomáš Bzdušek: University of Zurich
Martin Greiter: Universität Würzburg
Ronny Thomale: Universität Würzburg
Igor Boettcher: University of Alberta

Nature Communications, 2023, vol. 14, issue 1, 1-8

Abstract: Abstract Curved spaces play a fundamental role in many areas of modern physics, from cosmological length scales to subatomic structures related to quantum information and quantum gravity. In tabletop experiments, negatively curved spaces can be simulated with hyperbolic lattices. Here we introduce and experimentally realize hyperbolic matter as a paradigm for topological states through topolectrical circuit networks relying on a complex-phase circuit element. The experiment is based on hyperbolic band theory that we confirm here in an unprecedented numerical survey of finite hyperbolic lattices. We implement hyperbolic graphene as an example of topologically nontrivial hyperbolic matter. Our work sets the stage to realize more complex forms of hyperbolic matter to challenge our established theories of physics in curved space, while the tunable complex-phase element developed here can be a key ingredient for future experimental simulation of various Hamiltonians with topological ground states.

Date: 2023
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Citations: View citations in EconPapers (4)

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DOI: 10.1038/s41467-023-36359-6

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