Prabith, K and Theocharis, G and Chaunsali, R (2024) Nonlinear corner states in a topologically nontrivial kagome lattice. In: Physical Review B, 110 (10).
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Abstract
We investigate a higher-order topological insulator (HOTI) under strong nonlinearity, focusing on the existence and stability of high-amplitude corner states, which can find applications in optics, acoustics, elastodynamics, and other wave-based systems. Our study centers on a breathing kagome lattice composed of point masses and springs, known to exhibit edge and corner states in its linear regime. By introducing on-site cubic nonlinearity, we analyze its impact on both edge and corner states. The nonlinear continuation of the corner state unveils stable high-amplitude corner states within the lattice, featuring nonzero displacements at even sites from the corner - a characteristic absent in the linear limit. Interestingly, the nonlinear continuation of the edge state reveals its transformation into distinct families of high-amplitude corner states via two pitchfork bifurcations. While some states maintain stability, others become unstable through real instability and Neimark-Sacker bifurcation. These unstable corner states dissipate their energy into the edges and the bulk over an extended period, as corroborated by long-time dynamical simulations. Consequently, our study provides insights into achieving significant energy localization at the corners of HOTIs through various classes of nonlinear states. © 2024 American Physical Society.
| Item Type: | Journal Article |
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| Publication: | Physical Review B |
| Publisher: | American Physical Society |
| Additional Information: | The copyright for this article belongs to authors. |
| Keywords: | Bifurcation (mathematics); Nonlinear optics, Elasto-dynamics; Existence and stability; High amplitudes; High-order; Higher-order; Kagome lattice; Linear regime; Point mass; Strong nonlinearity; Topological insulators, Topology |
| Department/Centre: | Division of Mechanical Sciences > Aerospace Engineering(Formerly Aeronautical Engineering) |
| Date Deposited: | 26 Oct 2024 09:55 |
| Last Modified: | 26 Oct 2024 09:55 |
| URI: | http://eprints.iisc.ac.in/id/eprint/86544 |
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