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Acoustic higher-order topological insulator on a kagome lattice

Nature Materials volume 18, pages 108–112 (2019)Cite this article

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Abstract

Higher-order topological insulators1,2,3,4,5 are a family of recently predicted topological phases of matter that obey an extended topological bulk–boundary correspondence principle. For example, a two-dimensional (2D) second-order topological insulator does not exhibit gapless one-dimensional (1D) topological edge states, like a standard 2D topological insulator, but instead has topologically protected zero-dimensional (0D) corner states. The first prediction of a second-order topological insulator1, based on quantized quadrupole polarization, was demonstrated in classical mechanical6 and electromagnetic7,8 metamaterials. Here we experimentally realize a second-order topological insulator in an acoustic metamaterial, based on a ‘breathing’ kagome lattice9 that has zero quadrupole polarization but a non-trivial bulk topology characterized by quantized Wannier centres2,9,10. Unlike previous higher-order topological insulator realizations, the corner states depend not only on the bulk topology but also on the corner shape; we show experimentally that they exist at acute-angled corners of the kagome lattice, but not at obtuse-angled corners. This shape dependence allows corner states to act as topologically protected but reconfigurable local resonances.

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Fig. 1: Kagome lattice and its acoustic implementation.
Fig. 2: Eigenmode simulations of a triangular acoustic structure.
Fig. 3: Observation of topological corner states in a triangle-shaped finite acoustic structure.
Fig. 4: Observation of topological corner states in a parallelogram-shaped finite acoustic structure.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

This work was sponsored by the Singapore Ministry of Education under grant nos MOE2015-T2-1-070, MOE2015-T2-2-008, MOE2016-T3-1-006 and Tier 1 RG174/16 (S), and the Young Thousand Talent Plan, China, National Natural Science Foundation of China under grant no. 61801426.

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Authors and Affiliations

  1. Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore

    Haoran Xue, Yahui Yang, Yidong Chong & Baile Zhang

  2. State Key Laboratory of Modern Optical Instrumentation, and College of Information Science and Electronic Engineering, Zhejiang University, Hangzhou, China

    Fei Gao

  3. Centre for Disruptive Photonic Technologies, Nanyang Technological University, Singapore, Singapore

    Yidong Chong & Baile Zhang

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  1. Haoran Xue
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  2. Yahui Yang
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Contributions

All the authors contributed extensively to this work. H.X. and Y.Y. fabricated the structures and performed measurements. H.X., Y.Y. and F. G. performed the simulations. Y.C. and B.Z. supervised the project.

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Correspondence to Fei Gao, Yidong Chong or Baile Zhang.

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Supplementary Sections A–E, Supplementary Figures 1–5

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Xue, H., Yang, Y., Gao, F. et al. Acoustic higher-order topological insulator on a kagome lattice. Nature Mater 18, 108–112 (2019). https://doi.org/10.1038/s41563-018-0251-x

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