Observation of nonlinear fractal higher order topological insulator

Hua Zhong; Victor O. Kompanets; Yiqi Zhang; Yaroslav V. Kartashov; Meng Cao; Yongdong Li; Sergei A. Zhuravitskii; Nikolay N. Skryabin; Ivan V. Dyakonov; Alexander A. Kalinkin; Sergei P. Kulik; Sergey V. Chekalin; Victor N. Zadkov

doi:10.1038/s41377-024-01611-1

Your Location：

Home >

Browse articles >

Observation of nonlinear fractal higher order topological insulator

Original Articles

- Observation of nonlinear fractal higher order topological insulator
- Light: Science & Applications Vol. 13, Issue 11, Pages: 2699-2714(2024)
- Affiliations：
  
  1.Key Laboratory for Physical Electronics and Devices, Ministry of Education, School of Electronic Science and Engineering, Xi'an Jiaotong University, 710049 Xi'an, China
  2.Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow 108840, Russia
  3.Quantum Technology Centre, Faculty of Physics, M. V. Lomonosov Moscow State University, Moscow 119991, Russia
  4.Faculty of Physics, Higher School of Economics, Moscow 105066, Russia
- Author bio：
  
  Yiqi Zhang (zhangyiqi@xjtu.edu.cn)
  Yaroslav V. Kartashov (kartashov@isan.troitsk.ru)
- Funds：
- DOI：10.1038/s41377-024-01611-1
  CLC：
- Received：11 April 2024，
  
  Revised：27 August 2024，
  
  Accepted：2024-08-27，
  
  Published Online：20 September 2024，
  
  Published：30 November 2024
- Accepted：
Scan QR Code
Zhong, H. et al. Observation of nonlinear fractal higher order topological insulator. Light: Science & Applications, 13, 2699-2714 (2024).
DOI：

Zhong, H. et al. Observation of nonlinear fractal higher order topological insulator. Light: Science & Applications, 13, 2699-2714 (2024). DOI： 10.1038/s41377-024-01611-1.

摘要

Abstract

Higher-order topological insulators (HOTIs) are unique materials hosting topologically protected states

whose dimensionality is at least by 2 lower than that of the bulk. Topological states in such insulators may be strongly confined in their corners which leads to considerable enhancement of nonlinear processes involving such states. However

all nonlinear HOTIs demonstrated so far were built on periodic bulk lattice materials. Here

we demonstrate the first

nonlinear photonic

HOTI with the fractal origin. Despite their fractional effective dimensionality

the HOTIs constructed here on two different types of the Sierpiński gasket waveguide arrays

may support topological corner states for unexpectedly wide range of coupling strengths

even in parameter regions where conventional HOTIs b

ecome trivial. We demonstrate thresholdless spatial solitons bifurcating from corner states in nonlinear fractal HOTIs and show that their localization can be efficiently controlled by the input beam power. We observe sharp differences in nonlinear light localization on outer and multiple inner corners and edges representative for these fractal materials. Our findings not only represent a new paradigm for nonlinear topological insulators

but also open new avenues for potential applications of fractal materials to control the light flow.

关键词

Keywords

references

Bunde, A. & Havlin, S. Fractals in Science (Springer, 1994).

Song, Z. G., Zhang, Y. Y. & Li, S. S. The topological insulator in a fractal space. Appl. Phys. Lett. 104 , 233106 (2014)..

He, J., Liang, Y. & Kou, S. P. Topological hierarchy insulators and topological fractal insulators. Europhys. Lett. 112 , 17010 (2015)..

Kempkes, S. N. et al. Design and characterization of electrons in a fractal geometry. Nat. Phys. 15 , 127–131 (2019)..

Pai, S. & Prem, A. Topological states on fractal lattices. Phys. Rev. B 100 , 155135 (2019)..

Iliasov, A. A., Katsnelson, M. I. & Yuan, S. J. Hall conductivity of a Sierpiński carpet. Phys. Rev. B 101 , 045413 (2020)..

Fremling, M. et al. Existence of robust edge currents in Sierpiński fractals. Phys. Rev. Res. 2 , 013044 (2020)..

Xu, X. Y. et al. Quantum transport in fracta l networks. Nat. Photonics 15 , 703–710 (2021)..

Liu, C. et al. Sierpiński structure and electronic topology in Bi thin films on InSb(111)B surfaces. Phys. Rev. Lett. 126 , 176102 (2021)..

Ivaki, M. N. et al. Topological random fractals. Commun. Phys. 5 , 327 (2022)..

Manna, S. et al. Anyon braiding on a fractal lattice with a local Hamiltonian. Phys. Rev. A 105 , L021302 (2022)..

Yang, Z. J. et al. Photonic Floquet topological insulators in a fractal lattice. Light Sci. Appl. 9 , 128 (2020)..

Biesenthal, T. et al. Fractal photonic topological insulators. Science 376 , 1114–1119 (2022)..

Zheng, S. J. et al. Observation of fractal higher-order topological states in acoustic metamaterials. Sci. Bull. 67 , 2069–2075 (2022)..

Li, J. K. et al. Higher-order topological phase in an acoustic fractal lattice. Sci. Bull. 67 , 2040–2044 (2022)..

Ren, B. Q. et al. Theory of nonlinear corner states in photonic fractal lattices. Nanophotonics 12 , 3829–3838 (2023)..

Li, M. et al. Fractal photonic anomalous Floquet topological insulators to generate multiple quantum chiral edge states. Light Sci. Appl. 12 , 262 (2023)..

Manna, S. & Roy, B. Inner skin effects on non-Hermitian topological fractals. Commun. Phys. 6 , 10 (2023)..

He, J. J. et al. Mode engineering in reconfigurable fractal topological circuits. Phys. Rev. B 109 , 235406 (2024)..

Xie, Y. Q. et al. Fractal-like photonic lattices and localized states arising from singular and nonsingular flatbands. APL Photonics 6 , 116104 (2021)..

Song, L. M. et al. Topological flatband loop states in fractal-like photonic lattices. Laser Photonics Rev. 17 , 2200315 (2023)..

Lu, L., Joannopoulos, J. D. & Soljačić, M. Topological photonics. Nat. Photonics 8 , 821–829 (2014)..

Ozawa, T. et al. Topological photonics. Rev. Mod. Phys. 91 , 015006 (2019)..

Zhang, X. J. et al. A second wave of topological phenomena in photonics and acoustics. Nature 618 , 687–697 (2023)..

Wang, Z. et al. Observation of unidirectional backscattering-immune topological electromagnetic states. Nature 461 , 772–775 (2009)..

Rechtsman, M. C. et al. Photonic Floquet topological insulators. Nature 496 , 196–200 (2013)..

Noh, J., Huang, S., Chen, K. P. & Rechtsman, M. C. Observation of photonic topological valley Hall edge states. Phys. Rev. Lett. 120 , 063902 (2018)..

Peterson, C. W. et al. A quantized microwave quadrupole insulator with topologically protected corner states. Nature 555 , 346–350 (2018)..

Noh, J. et al. Topological protection of photonic mid-gap defect modes. Nat. Photonics 12 , 408–415 (2018)..

Mittal, S. et al. Photonic quadrupole topological phases. Nat. Photonics 13 , 692–696 (2019)..

El Hassan, A. et al. Corner states of light in photonic waveguides. Nat. Photonics 13 , 697–700 (2019)..

Xie, B. Y. et al. Higher-order band topology. Nat. Rev. Phys. 3 , 520–532 (2021)..

Lin, Z. K. et al. Topological phenomena at defects in acoustic, photonic and solid-state lattices. Nat. Rev. Phys. 5 , 483–495 (2023)..

Li, J. K. et al. Fractality-induced topological phase squeezing and devil's staircase. Phys. Rev. Res. 5 , 023189 (2023)..

Hatsugai, Y. Chern number and edge states in the integer quantum Hall effect. Phys. Rev. Lett. 71 , 3697–3700 (1993)..

Manna, S., Nandy, S. & Roy, B. Higher-order topological phases on fractal lattices. Phys. Rev. B 105 , L201301 (2022)..

Brzezińska, M., Cook, A. M. & Neupert, T. Topology in the Sierpiński-Hofstadter problem. Phys. Rev. B 98 , 205116 (2018)..

Smirnova, D. et al. Nonlinear topological photonics. Appl. Phys. Rev. 7 , 021306 (2020)..

Lumer, Y. et al. Self-localized states in photonic topological insulators. Phys. Rev. Lett. 111 , 243905 (2013)..

Ablowitz, M. J., Curtis, C. W. & Ma, Y. P. Linear and nonlinear traveling edge waves in optical honeycomb lattices. Phys. Rev. A 90 , 023813 (2014)..

Leykam, D. & Chong, Y. D. Edge solitons in nonlinear-photonic topological insulators. Phys. Rev. Lett. 117 , 143901 (2016)..

Kartashov, Y. V. & Skryabin, D. V. Modulational instability and solitary waves in polariton topological insulators. Optica 3 , 1228–1236 (2016)..

Ablowitz, M. J. & Cole, J. T. Tight-binding methods for general longitudinally driven photonic lattices: edge stat es and solitons. Phys. Rev. A 96 , 043868 (2017)..

Ivanov, S. K. et al. Vector topological edge solitons in Floquet insulators. ACS Photonics 7 , 735–745 (2020)..

Zhong, H. et al. Nonlinear topological valley Hall edge states arising from type-Ⅱ Dirac cones. Adv. Photonics 3 , 056001 (2021)..

Mukherjee, S. & Rechtsman, M. C. Observation of Floquet solitons in a topological bandgap. Science 368 , 856–859 (2020)..

Mukherjee, S. & Rechtsman, M. C. Observation of unidirectional solitonlike edge states in nonlinear Floquet topological insulators. Phys. Rev. X 11 , 041057 (2021)..

Xia, S. Q. et al. Nontrivial coupling of light into a defect: the interplay of nonlinearity and topology. Light Sci. Appl. 9 , 147 (2020)..

Guo, M. et al. Weakly nonlinear topological gap solitons in Su-Schrieffer-Heeger photonic lattices. Opt. Lett. 45 , 6466–6469 (2020)..

Kartashov, Y. V. et al. Observation of edge solitons in topological trimer arrays. Phys. Rev. Lett. 128 , 093901 (2022)..

Hadad, Y., Soric, J. C., Khanikaev, A. B. & Alù, A. Self-induced topological protection in nonlinear circuit arrays. Nat. Electron. 1 , 178–182 (2018)..

Zangeneh-Nejad, F. & Fleury, R. Nonlinear second-order topological insulators. Phys. Rev. Lett. 123 , 053902 (2019)..

Maczewsky, L. J. et al. Nonlinearity-induced photonic topological insulator. Science 370 , 701–704 (2020)..

Kirsch, M. S. et al. Nonlinear second-order photonic topological insulators. Nat. Phys. 17 , 995–1000 (2021)..

Hu, Z. C. et al. Nonlinear control of photonic higher-order topological bound states in the continuum. Light Sci. Appl. 10 , 164 (2021)..

Arkhipova, A. A. et al. Observation of π solitons in oscillating waveguide arrays. Sci. Bull. 68 , 2017–2024 (2023)..

Arévalo, E. & Mejía-Cortés, C. Extended in-band and band-gap solutions of the nonlinear honeycomb lattice. Phys. Rev. A 90 , 023835 (2014)..

Arévalo, E. & Morales-Molina, L. Geometrical frustration in nonlinear photonic lattices. Phys. Rev. A 98 , 023864 (2018)..

Ren, B. Q. et al. Observation of nonlinear disclination states. Light Sci. Appl. 12 , 194 (2023)..

Wang, Y. Y. et al. Precise mode control of laser-written waveguides for broadband, low-dispersion 3D integrated optics. Light Sci. Appl. 13 , 130 (2024)..

Li, L. Q., Kong, W. J. & Chen, F. Femtosecond laser-inscribed optical waveguides in dielectric crystals: a concise review and recent advances. Adv. Photonics 4 , 024002 (2022)..

Wheeler, W. A., Wagner, L. K. & Hughes, T. L. Many-body electric multipole operators in extended systems. Phys. Rev. B 100 , 245135 (2019)..

Kang, B., Shiozaki, K. & Cho, G. Y. Many-body order parameters for multipoles in solids. Phys. Rev. B 100 , 245134 (2019)..

Malomed, B. A. Basic fractional nonlinear-wave models and solitons. Chaos 34 , 022102 (2024)..

Xu, C. et al. Quasicrystal metasurface for dual functionality of holography and diffraction generation. eLight 4 , 9 (2024)..

Van Miert, G. & Ortix, C. On the topological immunity of corner states in two-dimensional crystalline insulators. npj Quantum Mater. 5 , 63 (2020)..

Herrera, M. A. J. et al. Corner modes of the breathing kagome lattice: origin and robustness. Phys. Rev. B 105 , 085411 (2022)..

Ezawa, M. Higher-order topological insulators and semimetals on the breathing kagome and pyrochlore lattices. Phys. Rev. Lett. 120 , 026801 (2018)..

Kempkes, S. N. et al. Robust zero-energy modes in an electronic higher-order topological insulator. Nat. Mater. 18 , 1292–1297 (2019)..

Zhang, Y. H. et al. Realizatio n of photonic p -orbital higher-order topological insulators. eLight 3 , 5 (2023)..

Yatsugi, K., Pandarakone, S. E. & Iizuka, H. Higher-order topological corner state in a reconfigurable breathing kagome lattice consisting of magnetically coupled LC resonators. Sci. Rep. 13 , 8301 (2023)..

Tao, L. Y. et al. Multi-type topological states in higher-order photonic insulators based on kagome metal lattices. Adv. Opt. Mater. 11 , 2300986 (2023)..

Song, L. M. et al. Observation of topologically distinct corner states in "bearded" photonic kagome lattices. Adv. Opt. Mater. 12 , 2301614 (2024)..

Fu, L. Topological crystalline insulators. Phys. Rev. Lett. 106 , 106802 (2011)..

Benalcazar, W. A., Li, T. H. & Hughes, T. L. Quantization of fractional corner charge in C n -symmetric higher-order topological crystalline insulators. Phys. Rev. B 99 , 245151 (2019)..

Fang, C. & Fu, L. New classes of topological crystalline insulators having surface rotation anomaly. Sci. Adv. 5 , eaat2374 (2019)..

Peterson, C. W. et al. Trapped fractional charges at bulk defects in topological insulators. Nature 589 , 376–380 (2021)..

Liu, Y. et al. Bulk-disclination correspondence in topological crystalline insulators. Nature 589 , 381–385 (2021)..

Zhou, Z. et al. Prospects and applications of on-chip lasers. eLight 3 , 1 (2023)..

Yin, S., Galiffi, E. & Alù, A. Floquet metamaterials. eLight 2 , 8 (2022)..

Liu, T. et al. Thermal photonics with broken symmetries. eLight 2 , 25 (2022)..

Agrawal, G. P. Nonlinear Fiber Optics 4th edn. (Academic Press, 2006).

Nair, P. N. S. et al. Fabrication of opaque and transparent 3D structures using a single material via two-photon polymerisation lithography. Light: Adv. Manuf. 4 , 243 (2023)..

Views

Downloads

CSCD

Alert me when the article has been cited

Submit

Tools

Publicity Resources

No data

Related Author

No data

Related Institution

No data

⁰