Sone Kazuki, Ezawa Motohiko, Gong Zongping, Sawada Taro, Yoshioka Nobuyuki, Sagawa Takahiro
Department of Physics, University of Tsukuba, Tsukuba, Ibaraki, 305-8571, Japan.
Department of Applied Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan.
Nat Commun. 2025 Jan 29;16(1):422. doi: 10.1038/s41467-024-55237-3.
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.
近期关于拓扑材料的研究正在拓展到非线性领域，然而其核心原理，即体边对应关系，在强非线性领域仍有待阐明。在此，我们揭示出非线性拓扑边缘模式可通过增加非线性度而表现出向空间混沌的转变，这可能是体边对应关系失效的一种普遍机制。具体而言，我们揭示了描述零模空间分布的潜在动力学系统，并展示了混沌的出现。我们还提出了在足够弱的非线性条件下拓扑不变量的绝对值与稳定流形维度之间的对应关系。我们的结果为研究非线性体边对应关系提供了一个通用的指导原则，该原则有可能扩展到任意维度。
