Advertisement

Unusual one-way edge state in acoustic gyroscopic continuum

  • XiaoMing ZhouEmail author
  • YuChen Zhao
Article
  • 90 Downloads

Abstract

Unusual one-way edge states have been observed in composite structures composed of periodic lattices loaded with gyroscopes. Here, we provide a continuum-mechanics understanding to the one-way edge state by formulating surface state equations of acoustic gyroscopic mediums with Hermite mass density tensor. We discover that the unidirectional edge effect arises from nontrivial off-diagonal components of Hermite densities, which causes the symmetric breaking of surface wave propagation towards forward and backward directions. Theoretical predictions on the velocity and decay length of surface waves coincide excellently with numerical simulations. The unidirectional edge state in a two-interface gyroscopic medium is also analyzed. Due to the rotational symmetry in geometry, the unidirectional edge state on one interface is able to prevent itself from the coupling to surface waves on the other interface regardless of the slab thickness. With these anomalous effects, surface waves residing on gyroscopic mediums can flow around the edge defects without back-scatterings, or can be split into two beams of equal energy magnitudes. Our findings may make a bridge that would help to reach the design of non-reciprocal composite materials via an effective medium approach.

Keywords

gyroscopic medium one-way edge state quantum Hall effect 

References

  1. 1.
    M. Z. Hasan, and C. L. Kane, Rev. Mod. Phys. 82, 3045 (2010), arXiv: 1002.3895.ADSCrossRefGoogle Scholar
  2. 2.
    F. D. M. Haldane, Phys. Rev. Lett. 61, 2015 (1988).ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljacic, Phys. Rev. Lett. 100, 013905 (2008), arXiv: 0712.1776.ADSCrossRefGoogle Scholar
  4. 4.
    Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacic, Nature 461, 772 (2009).ADSCrossRefGoogle Scholar
  5. 5.
    Y. Poo, R. X. Wu, Z. Lin, Y. Yang, and C. T. Chan, Phys. Rev. Lett. 106, 093903 (2011).ADSCrossRefGoogle Scholar
  6. 6.
    L. Zhang, J. Ren, J. S. Wang, and B. Li, Phys. Rev. Lett. 105, 225901 (2010), arXiv: 1008.0458.ADSCrossRefGoogle Scholar
  7. 7.
    M. Xiao, G. Ma, Z. Yang, P. Sheng, Z. Q. Zhang, and C. T. Chan, Nat. Phys. 11, 240 (2015).CrossRefGoogle Scholar
  8. 8.
    A. B. Khanikaev, R. Fleury, S. H. Mousavi, and A. Alù, Nat. Commun. 6, 8260 (2015).ADSCrossRefGoogle Scholar
  9. 9.
    Z. Yang, F. Gao, X. Shi, X. Lin, Z. Gao, Y. Chong, and B. Zhang, Phys. Rev. Lett. 114, 114301 (2015), arXiv: 1411.7100.ADSCrossRefGoogle Scholar
  10. 10.
    C. He, X. Ni, H. Ge, X. C. Sun, Y. B. Chen, M. H. Lu, X. P. Liu, and Y. F. Chen, Nat. Phys. 12, 1124 (2016), arXiv: 1512.03273.CrossRefGoogle Scholar
  11. 11.
    J. Lu, C. Qiu, L. Ye, X. Fan, M. Ke, F. Zhang, and Z. Liu, Nat. Phys. 13, 369 (2016), arXiv: 1709.05920.CrossRefGoogle Scholar
  12. 12.
    E. Prodan, and C. Prodan, Phys. Rev. Lett. 103, 248101 (2009), arXiv: 0909.3492.ADSCrossRefGoogle Scholar
  13. 13.
    R. Süsstrunk, and S. D. Huber, Science 349, 47 (2015), arXiv: 1503.06808.ADSCrossRefGoogle Scholar
  14. 14.
    L. M. Nash, D. Kleckner, A. Read, V. Vitelli, A. M. Turner, and W. T. M. Irvine, Proc. Natl. Acad. Sci. 112, 14495 (2015), arXiv: 1504.03362.ADSCrossRefGoogle Scholar
  15. 15.
    P. Wang, L. Lu, and K. Bertoldi, Phys. Rev. Lett. 115, 104302 (2015), arXiv: 1504.01374.ADSCrossRefGoogle Scholar
  16. 16.
    R. Fleury, D. L. Sounas, C. F. Sieck, M. R. Haberman, and A. Alù, Science 343, 516 (2014).ADSCrossRefGoogle Scholar
  17. 17.
    G. W. Milton, and J. R. Willis, Proc. R. Soc. A-Math. Phys. Eng. Sci. 463, 855 (2007).ADSCrossRefGoogle Scholar
  18. 18.
    M. Brun, I. S. Jones, and A. B. Movchan, Proc. R. Soc. A-Math. Phys. Eng. Sci. 468, 3027 (2012), arXiv: 1201.5855.ADSCrossRefGoogle Scholar
  19. 19.
    G. Carta, M. Brun, A. B. Movchan, N. V. Movchan, and I. S. Jones, Int. J. Solids Struct. 51, 2213 (2014).CrossRefGoogle Scholar
  20. 20.
    S. Yao, X. Zhou, and G. Hu, New J. Phys. 10, 043020 (2008).ADSCrossRefGoogle Scholar
  21. 21.
    Z. Wang, and X. Zhou, J. Acoust. Soc. Am. 140, 4276 (2016).ADSCrossRefGoogle Scholar
  22. 22.
    M. Ambati, N. Fang, C. Sun, and X. Zhang, Phys. Rev. B 75, 195447 (2007).ADSCrossRefGoogle Scholar
  23. 23.
    X. Zhou, M. B. Assouar, and M. Oudich, J. Appl. Phys. 116, 194501 (2014).CrossRefGoogle Scholar
  24. 24.
    X. Zhou, M. B. Assouar, and M. Oudich, Appl. Phys. Lett. 105, 233506 (2014).ADSCrossRefGoogle Scholar
  25. 25.
    N. Fang, D. Xi, J. Xu, M. Ambati, W. Srituravanich, C. Sun, and X. Zhang, Nat. Mater. 5, 452 (2006).ADSCrossRefGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Key Laboratory of Dynamics and Control of Flight Vehicle, Ministry of Education and School of Aerospace EngineeringBeijing Institute of TechnologyBeijingChina

Personalised recommendations