Transition from topological to chaos in the nonlinear Su-Schrieffer-Heeger model
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866918013722165248 |
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| author | Sone, Kazuki Ezawa, Motohiko Gong, Zongping Sawada, Taro Yoshioka, Nobuyuki Sagawa, Takahiro |
| author_facet | Sone, Kazuki Ezawa, Motohiko Gong, Zongping Sawada, Taro Yoshioka, Nobuyuki Sagawa, Takahiro |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_03038 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Transition from topological to chaos in the nonlinear Su-Schrieffer-Heeger model Sone, Kazuki Ezawa, Motohiko Gong, Zongping Sawada, Taro Yoshioka, Nobuyuki Sagawa, Takahiro Mesoscale and Nanoscale Physics Statistical Mechanics Chaotic Dynamics 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. |
| title | Transition from topological to chaos in the nonlinear Su-Schrieffer-Heeger model |
| topic | Mesoscale and Nanoscale Physics Statistical Mechanics Chaotic Dynamics |
| url | https://arxiv.org/abs/2403.03038 |