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We report a new topological phononic crystal in a ring-waveguide acoustic system. In the previous reports on topological phononic crystals, there are two types of topological phases:quantum Hall phase and quantum spin Hall phase. A key point in achieving quantum Hall insulator is to break the time-reversal (TR) symmetry, and for quantum spin Hall insulator, the construction of pseudo-spin is necessary. We build such pseudo-spin states under particular crystalline symmetry (C6v) and then break the degeneracy of the pseudo-spin states by introducing airflow to the ring. We study the topology evolution by changing both the geometric parameters of the unit cell and the strength of the applied airflow. We find that the system exhibits three phases:quantum spin Hall phase, conventional insulator phase and a new quantum anomalous Hall phase.The quantum anomalous Hall phase is first observed in phononics and cannot be simply classified by the Chern number or Z2 index since it results from TR-broken quantum spin Hall phase. We develop a tight-binding model to capture the essential physics of the topological phase transition. The analytical calculation based on the tight-binding model shows that the spin Chern number is a topological invariant to classify the bandgap. The quantum anomalous Hall insulator has a spin Chern number C±=(1,0) indicating the edge state is pseudo-spin orientation dependent and robust against TR-broken impurities.We also perform finite-element numerical simulations to verify the topological differences of the bandgaps. At the interface between a conventional insulator and a quantum anomalous Hall insulator, pseudo-spin dependent one-way propagation interface states are clearly observed, which are strikingly deferent from chiral edge states resulting from quantum Hall insulator and pairs of helical edge states resulting from quantum spin Hall insulator. Moreover, our pseudo-spin dependent edge state is robust against TR-broken impurities, which also sheds lights on spintronic devices.
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Keywords:
- phononic crystal /
- topology /
- quantum anomalous Hall effect
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[1] John S 1987 Phys. Rev. Lett. 58 2486
[2] Yablonovitch E 1987 Phys. Rev. Lett. 58 2059
[3] Klitzing K V, Dorda G, Pepper M 1980 Phys. Rev. Lett. 45 494
[4] Thouless D J, Kohmoto M, Nightingale M P, den Nijs M 1982 Phys. Rev. Lett. 49 405
[5] Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 226801
[6] Bernevig B A, Hughes T L, Zhang S C 2006 Science 314 1757
[7] König M, Wiedmann S, Brne C, Roth A, Buhmann H, Molenkamp L W, Qi X L, Zhang S C 2007 Science 318 766
[8] Qi X L, Wu Y S, Zhang S C 2006 Phys. Rev. B 74 085308
[9] Prodan E 2009 Phys. Rev. B 80 125327
[10] Kitagawa T, Berg E, Rudner M, Demler E 2010 Phys. Rev. B 82 235114
[11] Hasan M Z, Kane C L 2010 Rev. Mod. Phys. 82 3045
[12] Qi X L, Zhang S C 2011 Rev. Mod. Phys. 83 1057
[13] Moore J E 2010 Nature 464 194
[14] Haldane F D M, Raghu S 2008 Phys. Rev. Lett. 100 013904
[15] Wang Z, Chong Y D, Joannopoulos J D, Soljačić M 2008 Phys. Rev. Lett. 100 013905
[16] Khanikaev A B, Hossein Mousavi S, Tse W K, Kargarian M, MacDonald A H, Shvets G 2013 Nat. Mater. 12 233
[17] Rechtsman M C, Zeuner J M, Plotnik Y, Lumer Y,Podolsky D, Dreisow F, Nolte S, Segev M, Szameit A 2013 Nature 496 196
[18] Lu L, Joannopoulos J D, Soljacic M 2014 Nat. Photon. 8 821
[19] Yang Z, Gao F, Shi X, Lin X, Gao Z, Chong Y, Zhang B 2015 Phys. Rev. Lett. 114 114301
[20] Xiao M, Ma G, Yang Z, Sheng P, Zhang Z Q, Chan C T 2015 Nat. Phys. 11 240
[21] Lu J, Qiu C, Ke M, Liu Z 2016 Phys. Rev. Lett. 116 093901
[22] Fleury R, Sounas D L, Sieck C F, Haberman M R, Alù A 2014 Science 343 516
[23] Wu L H, Hu X 2015 Phys. Rev. Lett. 114 223901
[24] He C, Sun X C, Liu X P, Lu M H, Chen Y, Feng L, Chen Y F 2016 Proc. Natl. Acad. Sci. USA 113 4924
[25] Zhang Z, Wei Q, Cheng Y, Zhang T, Wu D, Liu X 2017 Phys. Rev. Lett. 118 084303
[26] Xu L, Wang H X, Xu Y D, Chen H Y, Jiang J H 2016 Opt. Express 24 18059
[27] 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
[28] Ni X, He C, Sun X C, Liu X P, Lu M H, Feng L, Chen Y F 2015 New J. Phys. 17 053016
[29] Chen Z G, Wu Y 2016 Phys. Rev. Appl. 5 054021
[30] Haldane F D M 1988 Phys. Rev. Lett. 61 2015
[31] Liu C X, Qi X L, Dai X, Fang Z, Zhang S C 2008 Phys. Rev. Lett. 101 146802
[32] Li H, Sheng L, Shen R, Shao L B, Wang B, Sheng D N, Xing D Y 2013 Phys. Rev. Lett. 110 266802
[33] 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
[34] Alexandradinata A, Fang C, Gilbert M J, Bernevig B A 2014 Phys. Rev. Lett. 113 116403
[35] Liu C X, Zhang R X, van Leeuwen B K 2014 Phys. Rev. B 90 085304
[36] Sakoda K 2012 Opt. Express 20 3898
[37] Liu C X, Qi X L, Zhang H, Dai X, Fang Z, Zhang S C 2010 Phys. Rev. B 82 045122
[38] Chen Z G, Mei J, Sun X C, Zhang X, Zhao J, Wu Y 2017 Phys. Rev. A 95 043827
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