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Acoustic higher-order topological insulator on a kagome lattice

Nature Materialsvolume 18pages108112 (2019) | Download Citation

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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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.

Author information

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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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.

Competing interests

The authors declare no competing interests.

Corresponding authors

Correspondence to Fei Gao or Yidong Chong or Baile Zhang.

Supplementary information

  1. Supplementary Information

    Supplementary Sections A–E, Supplementary Figures 1–5

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https://doi.org/10.1038/s41563-018-0251-x

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