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二维声子晶体中简单旋转操作导致的拓扑相变

王健 吴世巧 梅军

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二维声子晶体中简单旋转操作导致的拓扑相变

王健, 吴世巧, 梅军

Topological phase transitions caused by a simple rotational operation in two-dimensional acoustic crystals

Wang Jian, Wu Shi-Qiao, Mei Jun
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  • 构建了一种简单的二维声子晶体:由两个横截面为三角形的钢柱所组成的复式元胞按三角点阵的形式排列在空气中,等效地形成了一个蜂巢点阵结构.当三角形钢柱的取向与三角点阵的高对称方向一致时,整个体系具有C6v对称性.研究发现:在保持钢柱填充率不变的条件下,只需要将所有三角柱绕着自己的中心旋转180,就可实现二重简并的p态和d态在布里渊区中心点处的频率反转,且该能带反转过程实质上是一个拓扑相变过程.通过利用点的p态和d态的空间旋转对称性,构造了一个赝时反演对称性,并在声学系统中实现了类似于电子系统中量子自旋霍尔效应的赝自旋态.随后通过kp微扰法导出了点附近的有效哈密顿量,并分别计算了拓扑平庸和非平庸系统的自旋陈数,揭示了能带反转和拓扑相变的内在联系.最后通过数值模拟演示了受到拓扑不变量保护的声波边界态的单向传输行为和对缺陷的背向散射抑制.文中所研究的声波体系,尽管材料普通常见,但其拓扑带隙的相对宽度超过21%,比已报道的类似体系的带隙都要宽,且工作原理涵盖从次声波到超声波的很大频率范围,从而在实际应用上具有较大的优势和潜力.
    We design a two-dimensional acoustic crystal (AC) to obtain topologically protected edge states for sound waves. The AC is composed of a triangular array of a complex unit cell consisting of two identical triangle-shaped steel rods arranged in air. The steel rods are placed on the vertices of the hexagonal unit cell so that the whole lattice possesses the C6v symmetry. We show that by simply rotating all triangular rods around their respective centers by 180 degrees, a topological phase transition can be achieved, and more importantly, such a transition is accomplished with no need of changing the fill ratios or changing the positions of the rods. Interestingly, the achieved topologically nontrivial band gap has a very large frequency width, which is really beneficial to future applications. The topological properties of the AC are rooted in the spatial symmetries of the eigenstates. It is well known that there are two doubly-degenerate eigenstates at the point for a C6v point group, and they are usually called the p and d states in electronic system. By utilizing the spatial symmetries of the p and d states in the AC, we can construct the pseudo-time reversal symmetry which renders the Kramers doubling in this classical system. We find pseudospin states in the interface between topologically trivial and nontrivial ACs, where anticlockwise (clockwise) rotational behaviors of time-averaged Poynting vectors correspond to the pseudospin-up (pseudospin-down) orientations of the edge states, respectively. These phenomena are very similar to the real spin states of quantum spin Hall effect in electronic systems. We also develop an effective Hamiltonian for the associated bands to characterize the topological properties of the AC around the Brillouin zone center by the kp perturbation method. We calculate the spin Chern numbers of the ACs, and reveal the inherent link between the band inversion and the topological phase transition. With full-wave simulations, we demonstrate the one-way propagation of sound waves along the interface between topologically distinct ACs, and demonstrate the robustness of the edge states against different types of defects including bends, cavity and disorder. Our design provides a new way to realize acoustic topological effects in a wide frequency range spanning from infrasound to ultrasound. Potential applications and acoustic devices based on our design are expected, so that people can manipulate and transport sound waves in a more efficient way.
      通信作者: 梅军, phjunmei@scut.edu.cn
    • 基金项目: 国家自然科学基金(批准号:11274120,11574087)资助的课题.
      Corresponding author: Mei Jun, phjunmei@scut.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11274120, 11574087).
    [1]

    Klitzing K V, Dorda G, Pepper M 1980 Phys. Rev. Lett. 45 494

    [2]

    Thouless D J, Kohmoto M, Nightingale M P, den Nijs M 1982 Phys. Rev. Lett. 49 405

    [3]

    Laughlin R B 1983 Phys. Rev. Lett. 50 1395

    [4]

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

    [5]

    Bernevig B A, Zhang S C 2006 Phys. Rev. Lett. 96 106802

    [6]

    Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 226801

    [7]

    Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 146802

    [8]

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

    [9]

    Qi X L, Zhang S C 2011 Rev. Mod. Phys. 83 1057

    [10]

    Wang Z, Chong Y D, Joannopoulos J D, Soljačić M 2008 Phys. Rev. Lett. 100 013905

    [11]

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

    [12]

    Fang Y T, He H Q, Hu J X, Chen L K, Wen Z 2015 Phys. Rev. A 91 033827

    [13]

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

    [14]

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

    [15]

    Ni X, He C, Sun X C, Liu X P, Lu M H, Feng L, Chen Y F 2015 New J. Phys. 17 053016

    [16]

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

    [17]

    Khanikaev A B, Fleury R, Mousavi S H, Al A 2015 Nat. Commun. 6 8260

    [18]

    Fleury R, Sounas D L, Al A 2015 Phys. Rev. B 91 174306

    [19]

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

    [20]

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

    [21]

    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

    [22]

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

    [23]

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

    [24]

    Wang H X, Xu L, Chen H Y, Jiang J H 2016 Phys. Rev. B 93 235155

    [25]

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

    [26]

    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

    [27]

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

    [28]

    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

    [29]

    Li Y, Mei J 2015 Opt. Express 23 12089

    [30]

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

    [31]

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

    [32]

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

    [33]

    Ma T, Shvets G 2016 New J. Phys. 18 025012

    [34]

    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

    [35]

    Mei J, Wu Y, Chan C T, Zhang Z Q 2012 Phys. Rev. B 86 035141

    [36]

    Wu Y 2014 Opt. Express 22 1906

    [37]

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

    [38]

    Shen S Q, Shan W Y, Lu H Z 2011 Spin 1 33

  • [1]

    Klitzing K V, Dorda G, Pepper M 1980 Phys. Rev. Lett. 45 494

    [2]

    Thouless D J, Kohmoto M, Nightingale M P, den Nijs M 1982 Phys. Rev. Lett. 49 405

    [3]

    Laughlin R B 1983 Phys. Rev. Lett. 50 1395

    [4]

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

    [5]

    Bernevig B A, Zhang S C 2006 Phys. Rev. Lett. 96 106802

    [6]

    Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 226801

    [7]

    Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 146802

    [8]

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

    [9]

    Qi X L, Zhang S C 2011 Rev. Mod. Phys. 83 1057

    [10]

    Wang Z, Chong Y D, Joannopoulos J D, Soljačić M 2008 Phys. Rev. Lett. 100 013905

    [11]

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

    [12]

    Fang Y T, He H Q, Hu J X, Chen L K, Wen Z 2015 Phys. Rev. A 91 033827

    [13]

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

    [14]

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

    [15]

    Ni X, He C, Sun X C, Liu X P, Lu M H, Feng L, Chen Y F 2015 New J. Phys. 17 053016

    [16]

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

    [17]

    Khanikaev A B, Fleury R, Mousavi S H, Al A 2015 Nat. Commun. 6 8260

    [18]

    Fleury R, Sounas D L, Al A 2015 Phys. Rev. B 91 174306

    [19]

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

    [20]

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

    [21]

    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

    [22]

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

    [23]

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

    [24]

    Wang H X, Xu L, Chen H Y, Jiang J H 2016 Phys. Rev. B 93 235155

    [25]

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

    [26]

    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

    [27]

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

    [28]

    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

    [29]

    Li Y, Mei J 2015 Opt. Express 23 12089

    [30]

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

    [31]

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

    [32]

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

    [33]

    Ma T, Shvets G 2016 New J. Phys. 18 025012

    [34]

    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

    [35]

    Mei J, Wu Y, Chan C T, Zhang Z Q 2012 Phys. Rev. B 86 035141

    [36]

    Wu Y 2014 Opt. Express 22 1906

    [37]

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

    [38]

    Shen S Q, Shan W Y, Lu H Z 2011 Spin 1 33

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出版历程
  • 收稿日期:  2017-07-24
  • 修回日期:  2017-09-19
  • 刊出日期:  2017-11-05

二维声子晶体中简单旋转操作导致的拓扑相变

  • 1. 华南理工大学物理与光电学院, 广州 510641
  • 通信作者: 梅军, phjunmei@scut.edu.cn
    基金项目: 国家自然科学基金(批准号:11274120,11574087)资助的课题.

摘要: 构建了一种简单的二维声子晶体:由两个横截面为三角形的钢柱所组成的复式元胞按三角点阵的形式排列在空气中,等效地形成了一个蜂巢点阵结构.当三角形钢柱的取向与三角点阵的高对称方向一致时,整个体系具有C6v对称性.研究发现:在保持钢柱填充率不变的条件下,只需要将所有三角柱绕着自己的中心旋转180,就可实现二重简并的p态和d态在布里渊区中心点处的频率反转,且该能带反转过程实质上是一个拓扑相变过程.通过利用点的p态和d态的空间旋转对称性,构造了一个赝时反演对称性,并在声学系统中实现了类似于电子系统中量子自旋霍尔效应的赝自旋态.随后通过kp微扰法导出了点附近的有效哈密顿量,并分别计算了拓扑平庸和非平庸系统的自旋陈数,揭示了能带反转和拓扑相变的内在联系.最后通过数值模拟演示了受到拓扑不变量保护的声波边界态的单向传输行为和对缺陷的背向散射抑制.文中所研究的声波体系,尽管材料普通常见,但其拓扑带隙的相对宽度超过21%,比已报道的类似体系的带隙都要宽,且工作原理涵盖从次声波到超声波的很大频率范围,从而在实际应用上具有较大的优势和潜力.

English Abstract

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