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SCIENCE CHINA Physics, Mechanics & Astronomy, Volume 63 , Issue 2 : 224611(2020) https://doi.org/10.1007/s11433-019-9601-6

Tailoring edge and interface states in topological metastructures exhibiting the acoustic valley Hall effect

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  • ReceivedJun 12, 2019
  • AcceptedJul 29, 2019
  • PublishedSep 19, 2019
PACS numbers

Abstract

In this study, we investigate the acoustic topological insulator or topological metastructure, where an acoustic wave can exist only in an edge or interface state instead of propagating in bulk. Breaking the structural symmetry enables the opening of the Dirac cone in the band structure and the generation of a new band gap, wherein a topological edge or interface state emerges. Further, we systematically analyze two types of topological states that stem from the acoustic valley Hall effect mechanism; one type is confined to the boundary, whereas the other type can be observed at the interface between two topologically different structures. Results denote that the selection of different boundaries along with appropriately designed interfaces provides the acoustic waves in the band gap range with abilities of one-way propagation, dual-channel propagation, immunity from back-scattering at sharp corners, and/or transition between propagation at interfaces and boundaries. Furthermore, we show that the acoustic wave propagation paths can be tailored in diverse and arbitrary ways by combing the two aforementioned types of topological states.


Funded by

the National Natural Science Foundation of China(Grant,Nos.,11532001,11621062,11872329)

the Fundamental Research Funds for the Central Universities(Grant,No.,2016XZZX001-05)

and the Shenzhen Scientific and Technological Fund for R & D(Gran,No.,JCYJ20170816172316775)


Acknowledgment

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11532001, 11621062, and 11872329), the Fundamental Research Funds for the Central Universities (Grant No. 2016XZZX001-05), and the Shenzhen Scientific and Technological Fund for R & D (Grant No. JCYJ20170816172316775).


References

[1] Hasan M. Z., Kane C. L.. Rev. Mod. Phys., 2010, 82: 3045 CrossRef ADS arXiv Google Scholar

[2] Yin J., Ruzzene M., Wen J., Yu D., Cai L., Yue L.. Sci. Rep., 2018, 8: 6806 CrossRef PubMed ADS Google Scholar

[3] Süsstrunk R., Huber S. D.. Science, 2015, 349: 47 CrossRef PubMed ADS arXiv Google Scholar

[4] Xia B. Z., Wang G. B., Zheng S. J.. J. Mech. Phys. Solids, 2019, 124: 471 CrossRef ADS Google Scholar

[5] Khanikaev A. B., H. Mousavi S., Tse W. K., Kargarian M., MacDonald A. H., Shvets G.. Nat. Mater., 2013, 12: 233 CrossRef PubMed ADS arXiv Google Scholar

[6] Skirlo S. A., Lu L., Soljačić M.. Phys. Rev. Lett., 2014, 113: 113904 CrossRef PubMed ADS Google Scholar

[7] Nanthakumar S. S., Zhuang X., Park H. S., Nguyen C., Chen Y., Rabczuk T.. J. Mech. Phys. Solids, 2019, 125: 550 CrossRef ADS Google Scholar

[8] Zhou X. M., Zhao Y. C.. Sci. China-Phys. Mech. Astron., 2019, 62: 014612 CrossRef ADS Google Scholar

[9] Guo H. M.. Sci. China-Phys. Mech. Astron., 2016, 59: 637401 CrossRef ADS Google Scholar

[10] Khanikaev A. B., Fleury R., Mousavi S. H., Alù A.. Nat. Commun., 2015, 6: 8260 CrossRef PubMed ADS Google Scholar

[11] Wang P., Lu L., Bertoldi K.. Phys. Rev. Lett., 2015, 115: 104302 CrossRef PubMed ADS arXiv Google Scholar

[12] Chen Z. G., Wu Y.. Phys. Rev. Appl., 2016, 5: 054021 CrossRef ADS arXiv Google Scholar

[13] Chen Y., Liu X. N., Hu G. K.. J. Mech. Phys. Solids, 2019, 122: 54 CrossRef ADS Google Scholar

[14] Wang P., Zheng Y., Fernandes M. C., Sun Y., Xu K., Sun S., Kang S. H., Tournat V., Bertoldi K.. Phys. Rev. Lett., 2017, 118: 084302 CrossRef PubMed ADS arXiv Google Scholar

[15] Huang X., Lai Y., Hang Z. H., Zheng H., Chan C. T.. Nat. Mater., 2011, 10: 582 CrossRef PubMed ADS Google Scholar

[16] Liu T. W., Semperlotti F.. Phys. Rev. Appl., 2018, 9: 14001 CrossRef ADS arXiv Google Scholar

[17] Yang Z. J., Gao F., Shi X. H., Lin X., Gao Z., Chong Y. D., Zhang B. L.. Phys. Rev. Lett., 2015, 114: 114301 CrossRef PubMed ADS arXiv Google Scholar

[18] Ou Y. X., Singh M., Wang J.. Sci. China-Phys. Mech. Astron., 2012, 55: 2226 CrossRef ADS arXiv Google Scholar

[19] Vila J., Pal R. K., Ruzzene M.. Phys. Rev. B, 2017, 96: 134307 CrossRef ADS arXiv Google Scholar

[20] Ye L. P., Qiu C. Y., Lu J. Y., Wen X. H., Shen Y. Y., Ke M. Z., Zhang F., Liu Z. Y.. Phys. Rev. B, 2017, 95: 174106 CrossRef ADS arXiv Google Scholar

[21] Nguyen B. H., Zhuang X., Park H. S., Rabczuk T.. J. Appl. Phys., 2019, 125: 095106 CrossRef ADS Google Scholar

[22] Lu J. Y., Qiu C. Y., Ke M. Z., Liu Z. Y.. Phys. Rev. Lett., 2016, 116: 093901 CrossRef PubMed ADS arXiv Google Scholar

[23] Lu J. Y., Qiu C. Y., Ye L. P., Fan X. Y., Ke M. Z., Zhang F., Liu Z. Y.. Nat. Phys., 2017, 13: 369 CrossRef ADS arXiv Google Scholar

[24] Liu T. W., Semperlotti F.. Phys. Rev. Appl., 2019, 11: 014040 CrossRef ADS Google Scholar

[25] Mei J., Wu Y., Chan C. T., Zhang Z. Q.. Phys. Rev. B, 2012, 86: 035141 CrossRef ADS arXiv Google Scholar

[26] Liu F., Huang X., Chan C. T.. Appl. Phys. Lett., 2012, 100: 071911 CrossRef ADS Google Scholar

[27] Wen X. H., Qiu C. Y., Qi Y. J., Ye L. P., Ke M. Z., Zhang F., Liu Z. Y.. Nat. Phys., 2019, 15: 352 CrossRef ADS arXiv Google Scholar

[28] Mousavi S. H., Khanikaev A. B., Wang Z.. Nat. Commun., 2015, 6: 8682 CrossRef PubMed ADS arXiv Google Scholar

[29] Guo Y., Dekorsy T., Hettich M.. Sci. Rep., 2017, 7: 18043 CrossRef PubMed ADS Google Scholar

[30] Dai H. Q., Liu T. T., Jiao J. R., Xia B. Z., Yu D. J.. J. Appl. Phys., 2017, 121: 135105 CrossRef ADS Google Scholar

[31] Wang Z., Chong Y. D., Joannopoulos J. D., Soljacić M.. Phys. Rev. Lett., 2008, 100: 013905 CrossRef PubMed ADS arXiv Google Scholar

[32] Torrent D., Sánchez-Dehesa J.. Phys. Rev. Lett., 2012, 108: 174301 CrossRef PubMed ADS Google Scholar

[33] Raghu S., Haldane F. D. M.. Phys. Rev. A, 2008, 78: 033834 CrossRef ADS Google Scholar

[34] Chen X. D., Zhao F. L., Chen M., Dong J. W.. Phys. Rev. B, 2017, 96: 020202 CrossRef ADS arXiv Google Scholar

[35] Lu J. Y., Qiu C. Y., Xu S. J., Ye Y. T., Ke M. Z., Liu Z. Y.. Phys. Rev. B, 2014, 89: 134302 CrossRef ADS Google Scholar

[36] He C., Ni X., Ge H., Sun X. C., Chen Y. B., Lu M. H., Liu X. P., Chen Y. F.. Nat. Phys., 2016, 12: 1124 CrossRef ADS arXiv Google Scholar

  • Figure 1

    (a) Schematics of a hexagonal sonic crystal. Bottom panel: the parameters of the sonic crystal. (b) Schematics of a unit cell modelled in COMSOL Multiphysics. Bottom panel: the corresponding first Brillouin zone.

  • Figure 2

    The band structures of the sonic crystal with r=0 (a) and r=0.1/−0.1 (b), respectively.

  • Figure 3

    (Color online) (a) The dispersion curves of the structures with r=0.1 and r=−0.1. (b) The valley states at K1 and K2 when r=0.1. (c) The valley states at K1 and K2 when r=−0.1. The arrows in (b) or (c) indicate the direction of the energy flow.

  • Figure 4

    (Color online) (a) The initial shape of the supercell and magnification of the top edge. (b) The corresponding dispersion relation and edge modes at points Q1 and Q2 (1.43 kHz).

  • Figure 5

    (a) The division of the edge; (b) the typical edge or boundary types in different regions.

  • Figure 6

    (a)-(h) Dispersion curves corresponding to different edges shown in Figure5(b): Type 1-Type 8.

  • Figure 7

    The divisions of Region I (a) and Region III (b) in detail.

  • Figure 8

    (Color online) The dispersion relations of the supercell with different types of edges and the corresponding pressure profiles of the edge modes at the frequency 1.43 kHz. (a) Top edge is Type 2 and bottom edge is Type 4; (b) top edge is Type 8 and bottom edge is Type 4; (c) top edge is Type 2 and bottom edge is Type 3; (d) top edge is Type 8 and bottom edge is Type 3.

  • Figure 9

    (Color online) Simulations of acoustic wave propagation. The red star is a point harmonic source with the frequency 1.43 kHz. (a), (b) Top boundary: Type 8, bottom boundary: Type 4; (c) top boundary: Type 2, bottom boundary: Type 3; (d) top boundary: Type 8, bottom boundary: Type 3.

  • Figure 10

    (Color online) Simulations of acoustic wave propagation in a triangular structure (r=0.1) with different boundaries as indicated in (a)-(d).

  • Figure 11

    (Color online) The combination of structures with r=0.1 and r=−0.1 with different edges (a), (c), (e) and (g), and the corresponding dispersion spectra and the acoustic pressure profiles of the edge modes at the frequency 1.43 kHz (b), (d), (f) and (h).

  • Figure 12

    (Color online) (a)-(h) Simulation of acoustic wave propagation along several designed paths at the frequency 1.43 kHz.

  • Table 1   Existence of edge state in the supercell with =0.1

    Top edge (exist or not)

    Bottom edge (exist or not)

    Type 2/Type 3 (×)

    Type 3 (√)

    Type 4/Type 8 (√)

    Type 4 (×)

  • Table 2   Existence of edge state in the supercell with =−0.1

    Top edge (exist or not)

    Bottom edge (exist or not)

    Type 3 (√)

    Type 2/Type 3 (×)

    Type 4 (×)

    Type 4/Type 8 (√)

  • Table 3   Existence of the edge and interface states in the composite supercell with different edges as shown in Figure

    Figure

    Top edge(exist or not)

    Bottom edge(exist or not)

    Interface state (exist or not)

    11(a)

    Type 2 (×)

    Type 2 (×)

    Any type (√)

    11(c)

    Type 8 (√)

    Type 2 (×)

    Any type (√)

    11(e)

    Type 2 (×)

    Type 8 (√)

    Any type (√)

    11(g)

    Type 8 (√)

    Type 8 (√)

    Any type (√)

  • Table 4   The types of the top boundary in Figure (c)-(e) and the existence of the edge state

    Figure

    Left part of top boundary (exist or not)

    Right part of top boundary (exist or not)

    12(c)

    Type 4 (×)

    Type 4 (√)

    12(d)

    Type 3 (√)

    Type 3 (×)

    12(e)

    Type 3 (√)

    Type 4 (√)

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