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Observation of novel topological states in hyperbolic lattices

Author

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  • Weixuan Zhang

    (Key Laboratory of advanced optoelectronic quantum architecture and measurements of Ministry of Education, Beijing Key Laboratory of Nanophotonics & Ultrafine Optoelectronic Systems, School of Physics, Beijing Institute of Technology)

  • Hao Yuan

    (Key Laboratory of advanced optoelectronic quantum architecture and measurements of Ministry of Education, Beijing Key Laboratory of Nanophotonics & Ultrafine Optoelectronic Systems, School of Physics, Beijing Institute of Technology)

  • Na Sun

    (Key Laboratory of advanced optoelectronic quantum architecture and measurements of Ministry of Education, Beijing Key Laboratory of Nanophotonics & Ultrafine Optoelectronic Systems, School of Physics, Beijing Institute of Technology)

  • Houjun Sun

    (Beijing Key Laboratory of Millimeter wave and Terahertz Techniques, School of Information and Electronics, Beijing Institute of Technology)

  • Xiangdong Zhang

    (Key Laboratory of advanced optoelectronic quantum architecture and measurements of Ministry of Education, Beijing Key Laboratory of Nanophotonics & Ultrafine Optoelectronic Systems, School of Physics, Beijing Institute of Technology)

Abstract

The discovery of novel topological states has served as a major branch in physics and material sciences. To date, most of the established topological states have been employed in Euclidean systems. Recently, the experimental realization of the hyperbolic lattice, which is the regular tessellation in non-Euclidean space with a constant negative curvature, has attracted much attention. Here, we demonstrate both in theory and experiment that exotic topological states can exist in engineered hyperbolic lattices with unique properties compared to their Euclidean counterparts. Based on the extended Haldane model, the boundary-dominated first-order Chern edge state with a nontrivial real-space Chern number is achieved. Furthermore, we show that the fractal-like midgap higher-order zero modes appear in deformed hyperbolic lattices, and the number of zero modes increases exponentially with the lattice size. These novel topological states are observed in designed hyperbolic circuit networks by measuring site-resolved impedance responses and dynamics of voltage packets. Our findings suggest a useful platform to study topological phases beyond Euclidean space, and may have potential applications in the field of high-efficient topological devices, such as topological lasers, with enhanced edge responses.

Suggested Citation

  • Weixuan Zhang & Hao Yuan & Na Sun & Houjun Sun & Xiangdong Zhang, 2022. "Observation of novel topological states in hyperbolic lattices," Nature Communications, Nature, vol. 13(1), pages 1-10, December.
  • Handle: RePEc:nat:natcom:v:13:y:2022:i:1:d:10.1038_s41467-022-30631-x
    DOI: 10.1038/s41467-022-30631-x
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    Cited by:

    1. Qiaolu Chen & Zhe Zhang & Haoye Qin & Aleksi Bossart & Yihao Yang & Hongsheng Chen & Romain Fleury, 2024. "Anomalous and Chern topological waves in hyperbolic networks," Nature Communications, Nature, vol. 15(1), pages 1-7, December.
    2. Anffany Chen & Hauke Brand & Tobias Helbig & Tobias Hofmann & Stefan Imhof & Alexander Fritzsche & Tobias Kießling & Alexander Stegmaier & Lavi K. Upreti & Titus Neupert & Tomáš Bzdušek & Martin Greit, 2023. "Hyperbolic matter in electrical circuits with tunable complex phases," Nature Communications, Nature, vol. 14(1), pages 1-8, December.
    3. Lei Huang & Lu He & Weixuan Zhang & Huizhen Zhang & Dongning Liu & Xue Feng & Fang Liu & Kaiyu Cui & Yidong Huang & Wei Zhang & Xiangdong Zhang, 2024. "Hyperbolic photonic topological insulators," Nature Communications, Nature, vol. 15(1), pages 1-9, December.
    4. Weixuan Zhang & Fengxiao Di & Xingen Zheng & Houjun Sun & Xiangdong Zhang, 2023. "Hyperbolic band topology with non-trivial second Chern numbers," Nature Communications, Nature, vol. 14(1), pages 1-9, December.

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