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Transition from the topological to the chaotic in the nonlinear Su–Schrieffer–Heeger model

Author

Listed:
  • Kazuki Sone

    (University of Tsukuba
    The University of Tokyo)

  • Motohiko Ezawa

    (The University of Tokyo)

  • Zongping Gong

    (The University of Tokyo)

  • Taro Sawada

    (The University of Tokyo)

  • Nobuyuki Yoshioka

    (The University of Tokyo
    RIKEN Cluster for Pioneering Research (CPR)
    Japan Science and Technology Agency (JST), PRESTO)

  • Takahiro Sagawa

    (The University of Tokyo
    The University of Tokyo)

Abstract

Recent studies on topological materials are expanding into the nonlinear regime, while the central principle, namely the bulk–edge correspondence, is yet to be elucidated in the strongly nonlinear regime. Here, we reveal that nonlinear topological edge modes can exhibit the transition to spatial chaos by increasing nonlinearity, which can be a universal mechanism of the breakdown of the bulk–edge correspondence. Specifically, we unveil the underlying dynamical system describing the spatial distribution of zero modes and show the emergence of chaos. We also propose the correspondence between the absolute value of the topological invariant and the dimension of the stable manifold under sufficiently weak nonlinearity. Our results provide a general guiding principle to investigate the nonlinear bulk–edge correspondence that can potentially be extended to arbitrary dimensions.

Suggested Citation

  • Kazuki Sone & Motohiko Ezawa & Zongping Gong & Taro Sawada & Nobuyuki Yoshioka & Takahiro Sagawa, 2025. "Transition from the topological to the chaotic in the nonlinear Su–Schrieffer–Heeger model," Nature Communications, Nature, vol. 16(1), pages 1-10, December.
    • Handle: RePEc:nat:natcom:v:16:y:2025:i:1:d:10.1038_s41467-024-55237-3
    DOI: 10.1038/s41467-024-55237-3
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    References listed on IDEAS

    as
    1. Marius Jürgensen & Sebabrata Mukherjee & Mikael C. Rechtsman, 2021. "Quantized nonlinear Thouless pumping," Nature, Nature, vol. 596(7870), pages 63-67, August.
    2. Nader Mostaan & Fabian Grusdt & Nathan Goldman, 2022. "Quantized topological pumping of solitons in nonlinear photonics and ultracold atomic mixtures," Nature Communications, Nature, vol. 13(1), pages 1-10, December.
    3. Di Zhou & D. Zeb Rocklin & Michael Leamy & Yugui Yao, 2022. "Topological invariant and anomalous edge modes of strongly nonlinear systems," Nature Communications, Nature, vol. 13(1), pages 1-9, December.
    4. You Wang & Li-Jun Lang & Ching Hua Lee & Baile Zhang & Y. D. Chong, 2019. "Topologically enhanced harmonic generation in a nonlinear transmission line metamaterial," Nature Communications, Nature, vol. 10(1), pages 1-7, December.
    5. Nader Mostaan & Fabian Grusdt & Nathan Goldman, 2022. "Publisher Correction: Quantized topological pumping of solitons in nonlinear photonics and ultracold atomic mixtures," Nature Communications, Nature, vol. 13(1), pages 1-1, December.
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