2000 character limit reached
Nonlinear Corner States in Topologically Nontrivial Kagome Lattice
Published 3 Apr 2024 in cond-mat.mes-hall and nlin.PS | (2404.02504v1)
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 onsite 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 non-zero 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.
- W. A. Benalcazar, B. A. Bernevig, and T. L. Hughes, Quantized electric multipole insulators, Science 357, 61 (2017a).
- W. A. Benalcazar, T. Li, and T. L. Hughes, Quantization of fractional corner charge in Cnsubscript𝐶𝑛{C}_{n}italic_C start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT-symmetric higher-order topological crystalline insulators, Physical Review B 99, 245151 (2019).
- J. A. Medina-Vázquez, Influence of asymmetric long-range interactions on corner states in photonic higher-order topological insulators, Physical Review A 107, 043503 (2023).
- J. A. Medina-Vázquez, E. Y. González-Ramírez, and J. G. Murillo-Ramírez, Corner states in photonic higher-order dirac semimetals, Physical Review A 107, 053511 (2023).
- L. Zhou and W. Yu, Visualization of rainbow trapping effect in higher-order topological insulators, Physical Review B 107, 174105 (2023).
- J.-X. Yin, B. Lian, and M. Z. Hasan, Topological Kagome magnets and superconductors, Nature 612, 647 (2022).
- E. Tang, J. Agudo-Canalejo, and R. Golestanian, Topology protects chiral edge currents in stochastic systems, Physical Review X 11, 031015 (2021).
- M. Ezawa, Non-Hermitian higher-order topological states in nonreciprocal and reciprocal systems with their electric-circuit realization, Physical Review B 99, 201411 (2019).
- M. J. Ablowitz, C. W. Curtis, and Y.-P. Ma, Linear and nonlinear traveling edge waves in optical honeycomb lattices, Physical Review A 90, 023813 (2014).
- D. Leykam and Y. D. Chong, Edge solitons in nonlinear-photonic topological insulators, Physical Review Letters 117, 143901 (2016).
- Y. V. Kartashov and D. V. Skryabin, Modulational instability and solitary waves in polariton topological insulators, Optica 3, 1228 (2016).
- J. Vila, G. H. Paulino, and M. Ruzzene, Role of nonlinearities in topological protection: Testing magnetically coupled fidget spinners, Physical Review B 99, 125116 (2019).
- D. D. Snee and Y.-P. Ma, Edge solitons in a nonlinear mechanical topological insulator, Extreme Mechanics Letters 30, 100487 (2019).
- A. Darabi and M. J. Leamy, Tunable nonlinear topological insulator for acoustic waves, Physical Review Applied 12, 044030 (2019).
- S. Mukherjee and M. C. Rechtsman, Observation of unidirectional solitonlike edge states in nonlinear floquet topological insulators, Physical Review X 11, 041057 (2021).
- Y.-P. Ma and H. Susanto, Topological edge solitons and their stability in a nonlinear Su-Schrieffer-Heeger model, Physical Review E 104, 054206 (2021).
- J. R. Tempelman, K. H. Matlack, and A. F. Vakakis, Topological protection in a strongly nonlinear interface lattice, Physical Review B 104, 174306 (2021).
- L. Jezequel and P. Delplace, Nonlinear edge modes from topological one-dimensional lattices, Physical Review B 105, 035410 (2022).
- C. Li and Y. V. Kartashov, Topological gap solitons in Rabi Su-Schrieffer-Heeger lattices, Physical Review B 108, 184301 (2023).
- B. Michen and J. C. Budich, Nonlinear interference challenging topological protection of chiral edge states, Physical Review A 108, L021501 (2023).
- M. I. Rosa, M. J. Leamy, and M. Ruzzene, Amplitude-dependent edge states and discrete breathers in nonlinear modulated phononic lattices, New Journal of Physics 25, 103053 (2023).
- S. Mukherjee and M. C. Rechtsman, Observation of Floquet solitons in a topological bandgap, Science 368, 856 (2020).
- Y. Hadad, A. B. Khanikaev, and A. Alu, Self-induced topological transitions and edge states supported by nonlinear staggered potentials, Physical Review B 93, 155112 (2016).
- R. S. Savelev, M. A. Gorlach, and A. N. Poddubny, Topological interface states mediated by spontaneous symmetry breaking, Physical Review B 98, 045415 (2018).
- R. Chaunsali and G. Theocharis, Self-induced topological transition in phononic crystals by nonlinearity management, Physical Review B 100, 014302 (2019).
- B. G.-g. Chen, N. Upadhyaya, and V. Vitelli, Nonlinear conduction via solitons in a topological mechanical insulator, Proceedings of the National Academy of Sciences 111, 13004 (2014).
- Y. Hadad, V. Vitelli, and A. Alu, Solitons and propagating domain walls in topological resonator arrays, ACS Photonics 4, 1974 (2017).
- A. N. Poddubny and D. A. Smirnova, Ring Dirac solitons in nonlinear topological systems, Physical Review A 98, 013827 (2018).
- F. Zangeneh-Nejad and R. Fleury, Nonlinear second-order topological insulators, Physical Review Letters 123, 053902 (2019).
- A. L. Vanel, O. Schnitzer, and R. V. Craster, Asymptotic network models of subwavelength metamaterials formed by closely packed photonic and phononic crystals, Europhysics Letters 119, 64002 (2017).
- N. Lazarides and G. Tsironis, Superconducting metamaterials, Physics Reports 752, 1 (2018).
- M. Remoissenet, Waves called solitons: concepts and experiments (Springer Science & Business Media, 2013).
- X. Zhu, H. Wang, and L.-X. Zheng, Defect solitons in Kagome optical lattices, Optics Express 18, 20786 (2010).
- R. A. Vicencio and M. Johansson, Discrete flat-band solitons in the Kagome lattice, Physical Review A 87, 061803 (2013).
- M. I. Molina, Localized modes in nonlinear photonic Kagome nanoribbons, Physics Letters A 376, 3458 (2012).
- M. Ezawa, Higher-order topological insulators and semimetals on the breathing Kagome and pyrochlore lattices, Physical review letters 120, 026801 (2018).
- Z. Wang and Q. Wei, An elastic higher-order topological insulator based on Kagome phononic crystals, Journal of Applied Physics 129 (2021).
- L. Fang and M. J. Leamy, Dispersion morphing in stretchable rotator lattices, Physical Review Applied 20, 034057 (2023).
- J. Marín and S. Aubry, Finite size effects on instabilities of discrete breathers, Physica D: Nonlinear Phenomena 119, 163 (1998).
- S. Aubry, Discrete breathers: localization and transfer of energy in discrete hamiltonian nonlinear systems, Physica D: Nonlinear Phenomena 216, 1 (2006).
- S. Flach and A. V. Gorbach, Discrete breathers—advances in theory and applications, Physics Reports 467, 1 (2008).
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.