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.

arXiv comment9+14 pages, 5+7 figures

References in corpus (43)

• Topological Insulators
• Topological insulators and superconductors
• Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Photonic Analogue of Two-dimensional Topological Insulators and Helical One-Way Edge Transport in Bi-Anisotropic Metamaterials
• Periodic table for topological insulators and superconductors
• Topological Acoustics
• Direct Measurement of the Zak phase in Topological Bloch Bands
• Topological Boundary Modes in Isostatic Lattices
• Nonlinear topological photonics
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• Edge Solitons in Nonlinear Photonic Topological Insulators
• Nonlinear conduction via solitons in a topological mechanical insulator
• Active topological photonics
• Nonlinearity-induced photonic topological insulator
• Self-induced topological transitions and edge states supported by nonlinear staggered potentials
• Non-linear second-order topological insulators
• Quantized Nonlinear Thouless Pumping
• Topological characterization of chiral models through their long time dynamics
• Observation of Edge Solitons in Photonic Graphene
• Topologically Enhanced Harmonic Generation in a Nonlinear Transmission Line Metamaterial
• Nontrivial coupling of light into a defect: the interplay of nonlinearity and topology
• Anomalous single-mode lasing induced by nonlinearity and the non-Hermitian skin effect
• Nonlinear Thouless pumping: solitons and transport breakdown
• Active topolectrical circuits
• Topological edge states and gap solitons in the nonlinear Dirac model
• Nonlinearity induced topological physics in momentum space and real space
• A two-leg Su-Schrieffer-Heeger chain with glide reflection symmetry
• Stability of topological edge states under strong nonlinear effects
• Edge Solitons in Lieb Topological Floquet Insulators
• Topological Anderson insulating phases in the long-range Su-Schrieffer-Heeger model
• Topological Invariant and Anomalous Edge Modes of Strongly Nonlinear Systems
• Dynamical nonlinear higher-order non-Hermitian skin effects and topological trap-skin phase
• Nonlinear non-Hermitian skin effect
• Topological synchronization of quantum van der Pol oscillators
• Topological synchronization of coupled nonlinear oscillators
• Nonlinear Dirac Cones
• Topologically-enforced bifurcations in superconducting circuits
• Topological edge solitons and their stability in a nonlinear Su-Schrieffer-Heeger model
• Nonlinear Topological Mechanics in Elliptically Geared Isostatic Metamaterials
• Bulk-edge correspondence for nonlinear eigenvalue problems
• Topological bulk solitons in a nonlinear photonic Chern insulator

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• 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