Abstract
The geometric-phase concept has far-reaching implications in many branches of physics1,2,3,4,5,6,7,8,9,10,11,12,13,14. The geometric phase that specifically characterizes the topological property of bulk bands in one-dimensional periodic systems is known as the Zak phase15,16. Recently, it has been found that topological notions can also characterize the topological phase of mechanical isostatic lattices13. Here, we present a theoretical framework and two experimental methods to determine the Zak phase in a periodic acoustic system. We constructed a phononic crystal with a topological transition point in the acoustic band structure where the band inverts and the Zak phase in the bulk band changes following a shift in system parameters. As a consequence, the topological characteristics of the bandgap change and interface states form at the boundary separating two phononic crystals having different bandgap topological characteristics. Such acoustic interface states with large sound intensity enhancement are observed at the phononic crystal interfaces.
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Acknowledgements
G.M. thanks Ke Sun for his technical support with measurements and signal processing. M.X. thanks Mengyuan He for his help with the numerical calculation of the Zak phase. This work was supported by the Hong Kong Research Grants Council (Grant No. AoE/P-02/12).
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M.X., Z.Q.Z. and C.T.C. provided the theoretical framework. M.X. carried out the numerical simulations. G.M. fabricated the samples and carried out experimental measurements. M.X., G.M., Z.Q.Z. and C.T.C. wrote the manuscript. All authors were involved in the analysis and discussion of the results.
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Xiao, M., Ma, G., Yang, Z. et al. Geometric phase and band inversion in periodic acoustic systems. Nature Phys 11, 240–244 (2015). https://doi.org/10.1038/nphys3228
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DOI: https://doi.org/10.1038/nphys3228
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