Transition from topological to chaos in the nonlinear Su-Schrieffer-Heeger model

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.

9+14 pages, 5+7 figures

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• Topological Acoustics
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• Active topological photonics
• Quantized Nonlinear Thouless Pumping
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Cited by in corpus (11)

• Hopf Bifurcation of Nonlinear Non-Hermitian Skin Effect
• Protected chaos in a topological lattice
• Versatile Control of Nonlinear Topological States in Non-Hermitian Systems
• Nonlinear quadrupole topological insulators
• Quantum theory of fractional topological pumping of lattice solitons
• Defect engineering spin centers in interacting many-body Su-Schrieffer-Heeger chains
• Nonlinearity-induced transition in heat conduction through a topological metamaterial of rotors
• Non-self-averaging topological Anderson insulator
• Theory of anomalous Landau-Zener tunneling induced by nonlinear coupling
• Soliton Pumping in the Rice-Mele Model with On-Cell Kerr Nonlinearity
• Dark solitons in nonlinear Su-Schrieffer-Heeger lattices