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Subwavelength topological valley-spin states in the space-coiling acoustic metamaterials

Zheng Sheng-Jie Xia Bai-Zhan Liu Ting-Ting Yu De-Jie

Subwavelength topological valley-spin states in the space-coiling acoustic metamaterials

Zheng Sheng-Jie, Xia Bai-Zhan, Liu Ting-Ting, Yu De-Jie
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  • Phononic crystals possess Dirac linear dispersion bands. In the vicinity of Dirac cones, phononic crystals exhibit topological properties which have good application prospects in control of acoustic waves. Up to now, the topological edge states of phononic crystals, based on the band structures arising from the Bragg scattering, cannot realize low-frequency sound waves by the topologically protected one-way edge transmission. In this paper, by introducing the space-coiling structure, a space-coiling phononic metamaterial with C3v symmetry is designed. At the K (K') points of the Brillouin zone, the bands linearly cross to a subwavelength Dirac degenerated cones. With a rotation of the acoustic metamaterials, the mirror symmetry will be broken and the Dirac degenerated cones will be reopened, leading to subwavelength topological phase transition and subwavelength topological valley-spin states. Lastly, along the topological interface between acoustic metamaterials with different topological valley-spin states, we successfully observe the phononic topologically valley-spin transmission. The subwavelength Dirac conical dispersion and the subwavelength topological valley-spin state breakthrough the limitation of the geometric dimension of the phononic topological insulator, and provide a theoretical basis for the application of the phononic topologically robust transmission in a subwavelength scale.
      Corresponding author: Xia Bai-Zhan, xiabz2013@hnu.edu.cn
    [1]

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    Bernevig B A, Hughes T L, Zhang S C 2006 Science 314 1757

    [3]

    Lu L, Joannopoulos J D, Soljaclc M 2014 Nat. Photon. 8 821

    [4]

    Wang Z, Chong Y D, Joannopoulos J D, Soljacic M 2009 Nature 461 772

    [5]

    Poo Y, Wu R X, Lin Z F, Yang Y, Chan C T 2011 Phys. Rev. Lett. 106 093903

    [6]

    Fang K J, Yu Z F, Fan S H 2012 Nat. Photon. 6 782

    [7]

    Hafezi M, Mittal S, Fan J, Migdall A, Taylor J M 2013 Nat. Photon. 7 1001

    [8]

    Khanikaev A B, Mousavi S H, Tse W K, Kargarian M, MacDonald A H, Shvets G 2013 Nat. Mater. 12 233

    [9]

    Wu L H, Hu X 2015 Phys. Rev. Lett. 114 223901

    [10]

    Fang K J, Fan S H 2013 Phys. Rev. Lett. 111 203901

    [11]

    Bandres M A, Rechtsman M C, Segev M 2016 Phys. Rev. X 6 011016

    [12]

    Cheng X, Jouvaud C, Ni X, Mousavi S H, Genack A Z, Khanikaev A B 2016 Nat. Mater. 15 542

    [13]

    Ma T, Khanikaev A B, Mousavi S H, Shvets G 2015 Phys. Rev. Lett. 114 127401

    [14]

    Wolfe J P 2005 Imaging Phonons: Acoustic Wave Propagation in Solids (New York: Cambridge University Press)

    [15]

    Johnson S G,Povinelli M L, Soljacic M, Karalis A, Jacobs S, Joannopoulos J D 2005 Appl. Phys. B: Lasers O. 81 283

    [16]

    Ssstrunk R, Huber S D 2016 Proc. Natl. Acad. Sci. USA 113 E4767

    [17]

    Nash L M, Kleckner D, Read A, Vitelli V, Turner A M, Irvine W T M 2015 Proc. Natl. Acad. Sci. USA 112 14495

    [18]

    Ong Z Y, Lee C H 2016 Phys. Rev. B 94 134203

    [19]

    Fleury R, Sounas D L, Sieck C F, Haberman M R, Alù A 2014 Science 343 516

    [20]

    Yang Z, Gao F, Shi X H, Lin X, Gao Z, Chong Y D, Zhang B 2015 Phys. Rev. Lett. 114 114301

    [21]

    Peng Y G, Qin C Z, Zhao D G, Shen Y X, Xu X Y, Bao M, Jia H, Zhu X F 2016 Nat. Commum. 7 13368

    [22]

    Chen Z G, Wu Y 2016 Phys. Rev. Appl. 5 054021

    [23]

    He C, Li Z, Ni X, Sun X C, Yu S Y, Lu M H, Liu X P, Chen Y F 2016 Appl. Phys. Lett. 108 031904

    [24]

    Fleury R, Khanikaev A B, Alù A 2016 Nat. Commun. 7 11744

    [25]

    Wei Q, Tian Y, Zuo S Y, Cheng Y, Liu X J 2017 Phys. Rev. B 95 094305

    [26]

    Lu J Y, Qiu C Y, Xu S J, Ye Y T, Ke M Z, Liu Z Y 2014 Phys. Rev. B 89 134302

    [27]

    Chen Z G, Ni X, Wu Y, He C, Sun X C, Zheng L Y, Lu M H, Chen Y F 2014 Sci. Rep. 4 4613

    [28]

    Li Y, Wu Y, Mei J 2014 Appl. Phys. Lett. 105 014107

    [29]

    Dai H Q, Liu T T, Jiao J R, Xia B Z, Yu D J 2017 J. Appl. Phys. 121 135105

    [30]

    Xiao M, Ma G C, Yang Z Y, Sheng P, Zhang Z Q, Chan C T 2015 Nat. Phys. 11 240

    [31]

    He C, Ni X, Ge H, Sun X C, Chen Y B, Lu M H, Liu X P, Chen Y F 2016 Nat. Phys. 12 1124

    [32]

    Lu J Y, Qiu C Y, Ye L P, Fan X Y, Ke M Z, Zhang F, Liu Z Y 2017 Nat. Phys. 13 369

    [33]

    Lu J Y, Qiu C Y, Ke M Z, Liu Z Y 2016 Phys. Rev. Lett. 116 093901

    [34]

    Ye L P, Qiu C Y, Lu J Y, Wen X H, Shen Y Y, Ke M Z, Zhang F, Liu Z Y 2017 Phys. Rev. B 95 174106

    [35]

    Zhang Z W, Wei Q, Cheng Y, Zhang T, Wu D J, Liu X J 2017 Phys. Rev. Lett. 118 084303

    [36]

    Xia B Z, Liu T T, Huang G L, Dai H Q, Jiao J R, Zang X G, Yu D J, Zheng S J, Liu J 2017 Phys. Rev. B 96 094106

    [37]

    Mei J, Chen Z G, Wu Y 2016 Sci. Rep. 6 32752

    [38]

    Skirlo S A, Lu L, Soljacic M 2014 Phys. Rev. Lett. 113 113904

    [39]

    He W Y, Chan C T 2015 Sci. Rep. 5 8186

    [40]

    Xia B Z, Zheng S J, Chen N, Liu T T, Jiao J R, Dai H Q, Yu D J, Liu J 2017 arXiv preprint arXiv:1706.08206

    [41]

    Simon Y, Fleury R, Lemoult F, Fink M, Lerosey G 2017 New J. Phys. 19 075003

    [42]

    Xia B Z, Li L P, Liu J, Yu D J 2017 J. Vib. Acoust. 140 011011

    [43]

    Liu J, Li L P, Xia B Z, Man X F 2017 Int. J. Solids. Struct. (Accept)

  • [1]

    Hasan M Z, Kane C L 2010 Rev. Mod. Phys. 82 3045

    [2]

    Bernevig B A, Hughes T L, Zhang S C 2006 Science 314 1757

    [3]

    Lu L, Joannopoulos J D, Soljaclc M 2014 Nat. Photon. 8 821

    [4]

    Wang Z, Chong Y D, Joannopoulos J D, Soljacic M 2009 Nature 461 772

    [5]

    Poo Y, Wu R X, Lin Z F, Yang Y, Chan C T 2011 Phys. Rev. Lett. 106 093903

    [6]

    Fang K J, Yu Z F, Fan S H 2012 Nat. Photon. 6 782

    [7]

    Hafezi M, Mittal S, Fan J, Migdall A, Taylor J M 2013 Nat. Photon. 7 1001

    [8]

    Khanikaev A B, Mousavi S H, Tse W K, Kargarian M, MacDonald A H, Shvets G 2013 Nat. Mater. 12 233

    [9]

    Wu L H, Hu X 2015 Phys. Rev. Lett. 114 223901

    [10]

    Fang K J, Fan S H 2013 Phys. Rev. Lett. 111 203901

    [11]

    Bandres M A, Rechtsman M C, Segev M 2016 Phys. Rev. X 6 011016

    [12]

    Cheng X, Jouvaud C, Ni X, Mousavi S H, Genack A Z, Khanikaev A B 2016 Nat. Mater. 15 542

    [13]

    Ma T, Khanikaev A B, Mousavi S H, Shvets G 2015 Phys. Rev. Lett. 114 127401

    [14]

    Wolfe J P 2005 Imaging Phonons: Acoustic Wave Propagation in Solids (New York: Cambridge University Press)

    [15]

    Johnson S G,Povinelli M L, Soljacic M, Karalis A, Jacobs S, Joannopoulos J D 2005 Appl. Phys. B: Lasers O. 81 283

    [16]

    Ssstrunk R, Huber S D 2016 Proc. Natl. Acad. Sci. USA 113 E4767

    [17]

    Nash L M, Kleckner D, Read A, Vitelli V, Turner A M, Irvine W T M 2015 Proc. Natl. Acad. Sci. USA 112 14495

    [18]

    Ong Z Y, Lee C H 2016 Phys. Rev. B 94 134203

    [19]

    Fleury R, Sounas D L, Sieck C F, Haberman M R, Alù A 2014 Science 343 516

    [20]

    Yang Z, Gao F, Shi X H, Lin X, Gao Z, Chong Y D, Zhang B 2015 Phys. Rev. Lett. 114 114301

    [21]

    Peng Y G, Qin C Z, Zhao D G, Shen Y X, Xu X Y, Bao M, Jia H, Zhu X F 2016 Nat. Commum. 7 13368

    [22]

    Chen Z G, Wu Y 2016 Phys. Rev. Appl. 5 054021

    [23]

    He C, Li Z, Ni X, Sun X C, Yu S Y, Lu M H, Liu X P, Chen Y F 2016 Appl. Phys. Lett. 108 031904

    [24]

    Fleury R, Khanikaev A B, Alù A 2016 Nat. Commun. 7 11744

    [25]

    Wei Q, Tian Y, Zuo S Y, Cheng Y, Liu X J 2017 Phys. Rev. B 95 094305

    [26]

    Lu J Y, Qiu C Y, Xu S J, Ye Y T, Ke M Z, Liu Z Y 2014 Phys. Rev. B 89 134302

    [27]

    Chen Z G, Ni X, Wu Y, He C, Sun X C, Zheng L Y, Lu M H, Chen Y F 2014 Sci. Rep. 4 4613

    [28]

    Li Y, Wu Y, Mei J 2014 Appl. Phys. Lett. 105 014107

    [29]

    Dai H Q, Liu T T, Jiao J R, Xia B Z, Yu D J 2017 J. Appl. Phys. 121 135105

    [30]

    Xiao M, Ma G C, Yang Z Y, Sheng P, Zhang Z Q, Chan C T 2015 Nat. Phys. 11 240

    [31]

    He C, Ni X, Ge H, Sun X C, Chen Y B, Lu M H, Liu X P, Chen Y F 2016 Nat. Phys. 12 1124

    [32]

    Lu J Y, Qiu C Y, Ye L P, Fan X Y, Ke M Z, Zhang F, Liu Z Y 2017 Nat. Phys. 13 369

    [33]

    Lu J Y, Qiu C Y, Ke M Z, Liu Z Y 2016 Phys. Rev. Lett. 116 093901

    [34]

    Ye L P, Qiu C Y, Lu J Y, Wen X H, Shen Y Y, Ke M Z, Zhang F, Liu Z Y 2017 Phys. Rev. B 95 174106

    [35]

    Zhang Z W, Wei Q, Cheng Y, Zhang T, Wu D J, Liu X J 2017 Phys. Rev. Lett. 118 084303

    [36]

    Xia B Z, Liu T T, Huang G L, Dai H Q, Jiao J R, Zang X G, Yu D J, Zheng S J, Liu J 2017 Phys. Rev. B 96 094106

    [37]

    Mei J, Chen Z G, Wu Y 2016 Sci. Rep. 6 32752

    [38]

    Skirlo S A, Lu L, Soljacic M 2014 Phys. Rev. Lett. 113 113904

    [39]

    He W Y, Chan C T 2015 Sci. Rep. 5 8186

    [40]

    Xia B Z, Zheng S J, Chen N, Liu T T, Jiao J R, Dai H Q, Yu D J, Liu J 2017 arXiv preprint arXiv:1706.08206

    [41]

    Simon Y, Fleury R, Lemoult F, Fink M, Lerosey G 2017 New J. Phys. 19 075003

    [42]

    Xia B Z, Li L P, Liu J, Yu D J 2017 J. Vib. Acoust. 140 011011

    [43]

    Liu J, Li L P, Xia B Z, Man X F 2017 Int. J. Solids. Struct. (Accept)

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  • Received Date:  29 September 2017
  • Accepted Date:  06 November 2017
  • Published Online:  05 November 2017

Subwavelength topological valley-spin states in the space-coiling acoustic metamaterials

    Corresponding author: Xia Bai-Zhan, xiabz2013@hnu.edu.cn
  • 1. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha 410082, China

Abstract: Phononic crystals possess Dirac linear dispersion bands. In the vicinity of Dirac cones, phononic crystals exhibit topological properties which have good application prospects in control of acoustic waves. Up to now, the topological edge states of phononic crystals, based on the band structures arising from the Bragg scattering, cannot realize low-frequency sound waves by the topologically protected one-way edge transmission. In this paper, by introducing the space-coiling structure, a space-coiling phononic metamaterial with C3v symmetry is designed. At the K (K') points of the Brillouin zone, the bands linearly cross to a subwavelength Dirac degenerated cones. With a rotation of the acoustic metamaterials, the mirror symmetry will be broken and the Dirac degenerated cones will be reopened, leading to subwavelength topological phase transition and subwavelength topological valley-spin states. Lastly, along the topological interface between acoustic metamaterials with different topological valley-spin states, we successfully observe the phononic topologically valley-spin transmission. The subwavelength Dirac conical dispersion and the subwavelength topological valley-spin state breakthrough the limitation of the geometric dimension of the phononic topological insulator, and provide a theoretical basis for the application of the phononic topologically robust transmission in a subwavelength scale.

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