Higher-order topological states in photonic kagome crystals with long-range interactions


Photonic topological insulators enable topological boundary modes that are resilient to defects and disorder, irrespective of manufacturing precision. This property is known as topological protection. Although originally limited to dimensionality of modes one lower than that of topological insulators, the recently discovered higher-order topological insulators (HOTIs) offer topological protection over an extended range of dimensionalities. Here, we introduce a photonic HOTI with kagome lattice that exhibits topological bulk polarization, leading to the emergence of one-dimensional edge states, as well as higher-order zero-dimensional states confined to the corners of the structure. Interestingly, in addition to the corner states due to nearest-neighbour interactions, we discover a new class of topological corner states induced by long-range interactions and specific to photonic systems. Our findings demonstrate that photonic HOTIs possess richer physics than their condensed-matter counterparts, offering opportunities for engineering novel designer electromagnetic states with unique topological robustness.

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Fig. 1: Kagome lattice and corresponding bulk and edge band spectra.
Fig. 2: Simulation results of topological edge states and type I and type II corner states.
Fig. 3: Localization mechanism of type II corner states.
Fig. 4: Experimental observation of HOT type I and type II corner and edge states.

Data availability

Data that are not already included in the paper and/or in the Supplementary Information are available on request from the authors.


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This work was supported by the Defense Advanced Research Projects Agency under the Nascent programme with grant no. HR00111820040 and by the National Science Foundation with grant nos EFRI-1641069 and DMR-1809915. Experimental investigation of corner states was partially supported by the Russian Science Foundation (grant no. 16-19-10538). Theoretical analysis of type II corner states was partially supported by the Russian Foundation for Basic Research (grant no. 18-32-20065).

Author information

A.B.K. initiated the research. M.L., X.N. and M.G. derived the theoretical results. M.L. and D.Z. performed numerical simulations and designed the structure. D.Z., D.F. and A.S. designed and carried out the experiment. M.L. and D.Z. performed the data analysis. A.B.K. and A.A. supervised the research and wrote the main text. All authors discussed the results and contributed to the final version of the manuscript.

Correspondence to Alexander B. Khanikaev.

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Supplementary Information

Supplementary Figs. 1–8 and refs. 1–4.

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Li, M., Zhirihin, D., Gorlach, M. et al. Higher-order topological states in photonic kagome crystals with long-range interactions. Nat. Photonics 14, 89–94 (2020). https://doi.org/10.1038/s41566-019-0561-9

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