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Quadratic solitons in higher-order topological insulators

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  • Kartashov, Yaroslav V.

Abstract

I consider higher-order topological insulator (HOTI) created in χ2 nonlinear medium and based on two-dimensional generalization of the Su-Schrieffer-Heeger waveguide array, where transition between trivial and topological phases is achieved by shift of the four waveguides in the unit cell towards its center or towards its periphery. Such HOTI can support linear topological corner states that give rise to rich families of quadratic topological solitons bifurcating from linear corner states. The presence of phase mismatch between parametrically interacting fundamental-frequency (FF) and second-harmonic (SH) waves drastically affects the bifurcation scenarios and domains of soliton existence, making the families of corner solitons much richer in comparison with those in HOTIs with cubic nonlinearity. For instance, the internal soliton structure strongly depends on the location of propagation constant in forbidden gaps in spectra of both FF and SH waves. Two different types of corner solitons are obtained, where either FF or SH wave dominates in the bifurcation point from linear corner state. Because the waveguides are two-mode for SH wave, its spectrum features two groups of forbidden gaps with corner states of different symmetry appearing in each of them. Such corner states give rise to different families of corner solitons. Stability analysis shows that corner solitons in quadratic HOTI may feature wide stability domains and therefore are observable experimentally. These results illustrate how parametric nonlinear interactions enrich the behavior of topological excitations and allow to control their shapes.

Suggested Citation

  • Kartashov, Yaroslav V., 2025. "Quadratic solitons in higher-order topological insulators," Chaos, Solitons & Fractals, Elsevier, vol. 194(C).
  • Handle: RePEc:eee:chsofr:v:194:y:2025:i:c:s0960077925002127
    DOI: 10.1016/j.chaos.2025.116199
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    References listed on IDEAS

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    1. Kartashov, Yaroslav V. & Konotop, Vladimir V., 2024. "Topological star junctions: Linear modes and solitons," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    2. Eric J. Meier & Fangzhao Alex An & Bryce Gadway, 2016. "Observation of the topological soliton state in the Su–Schrieffer–Heeger model," Nature Communications, Nature, vol. 7(1), pages 1-6, December.
    3. Christopher W. Peterson & Wladimir A. Benalcazar & Taylor L. Hughes & Gaurav Bahl, 2018. "A quantized microwave quadrupole insulator with topologically protected corner states," Nature, Nature, vol. 555(7696), pages 346-350, March.
    4. Yang Liu & Shuwai Leung & Fei-Fei Li & Zhi-Kang Lin & Xiufeng Tao & Yin Poo & Jian-Hua Jiang, 2021. "Bulk–disclination correspondence in topological crystalline insulators," Nature, Nature, vol. 589(7842), pages 381-385, January.
    5. Xiujuan Zhang & Farzad Zangeneh-Nejad & Ze-Guo Chen & Ming-Hui Lu & Johan Christensen, 2023. "A second wave of topological phenomena in photonics and acoustics," Nature, Nature, vol. 618(7966), pages 687-697, June.
    6. Christopher W. Peterson & Tianhe Li & Wentao Jiang & Taylor L. Hughes & Gaurav Bahl, 2021. "Trapped fractional charges at bulk defects in topological insulators," Nature, Nature, vol. 589(7842), pages 376-380, January.
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