Hyperbolic matter in electrical circuits with tunable complex phases

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 experi...

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Bibliographic Details
Published in:Nature communications 2023-02, Vol.14 (1), p.622-622, Article 622
Main Authors: Chen, Anffany, Brand, Hauke, Helbig, Tobias, Hofmann, Tobias, Imhof, Stefan, Fritzsche, Alexander, Kießling, Tobias, Stegmaier, Alexander, Upreti, Lavi K., Neupert, Titus, Bzdušek, Tomáš, Greiter, Martin, Thomale, Ronny, Boettcher, Igor
Format: Article
Language:English
Subjects:
639/766/119/2792
639/766/119/995
Band theory
Circuits
Graphene
Humanities and Social Sciences
multidisciplinary
Physics
Quantum gravity
Quantum phenomena
Relativity
Science
Science (multidisciplinary)
Simulation
Topology
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Summary: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. Hyperbolic lattices emulate particle dynamics equivalent to those in negatively curved space, with connections to general relativity. Here, the authors use electric circuits with a novel complex-phase circuit element to simulate hyperbolic graphene with negligible boundary contributions.
ISSN:2041-1723
2041-1723
DOI:10.1038/s41467-023-36359-6