搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

双表面周期性弹性声子晶体板中的谷拓扑态

李荫铭 孔鹏 毕仁贵 何兆剑 邓科

引用本文:
Citation:

双表面周期性弹性声子晶体板中的谷拓扑态

李荫铭, 孔鹏, 毕仁贵, 何兆剑, 邓科

Valley topological states in double-surface periodic elastic phonon crystal plates

Li Yin-Ming, Kong Peng, Bi Ren-Gui, He Zhao-Jian, Deng Ke
PDF
HTML
导出引用
  • 随着拓扑理论的概念被引入到人工结构的研究中, 由于其具有传输保护、能量无损耗、缺陷免疫等新奇的物理性质, 引起了广泛的关注. 本文基于弹性材料设计了一种双表面周期性结构声子晶体, 其上、下表面由周期性排列的三角棱柱散射体组成, 在只关注面外模式的Lamb波的情况下, 构建了弹性声子晶体的谷拓扑态. 只需简单旋转散射体, 体系就会出现能带的反转, 研究发现通过调节散射体的高度, 可以实现谷拓扑边缘态频率的调控, 由不同的谷霍尔材料组成的边缘界面处可以实现较宽频率的激发, 进一步证实了边缘态频率可调控的思想可以在弹性材料中实现, 并利用两种不同相组成的声子晶体板研究了拓扑输运情况, 表现出优异的输运性能. 这为谷拓扑保护弹性波激发中实现新的自由度.
    The topological insulator, as its novel physical properties, such as transmission protection, energy loss free and defect immunity, has aroused much interest recently. It is necessary to introduce the concept of topology into elastic materials to enrich the research contents of elastic waves. The concept of valley state provides a simplest solution to realize topological states. In this work, we design a double surface periodic phononic crystal based on elastic material, the upper and lower surfaces are composed of periodically arranged triangular prismatic scatterers. Valley topological states of elastic phononic crystals are observed only when focusing on Lamb waves in out-of-plane mode by numerical simulation. We also analyze theoretically the valley Chern number. As the angle between the triangular prism and the positive direction of the X axis is greater than 0, the Chern number of K is 1/2; when the angle is less than 0, the Chern number is –1/2 . The K has the number opposite to the Chern number. By simply tuning the geometry of the scatterer, the inversion of the energy band will occur and the topological phase transition will be realized. We find that the frequency of edge state in valley topology can be regulated by adjusting the heights of scatterers. Moreover, wide frequency excitation is achieved at the edge interface composed of different valley Hall materials, which proves that the idea of adjustable edge state frequency can be implemented in elastic materials. According to the two different valley phase phononic crystals, we study the topological transport, exhibiting excellent transmission performance, even the Z-shaped interface. We find that the designed double surface structure has a stronger immune effect to defects than single surface, achieving a new degree of freedom in the valley topology protection of elastic wave excitation.
      通信作者: 孔鹏, kongpeng@jsu.edu.cn ; 何兆剑, hzj@whu.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 11964011, 11764016)、湖南省教育厅科研基金(批准号: 20C1530)和吉首大学基金(批准号: Jdy20027)资助的课题.
      Corresponding author: Kong Peng, kongpeng@jsu.edu.cn ; He Zhao-Jian, hzj@whu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11964011, 11764016), the Research Foundation of Education Bureau of Hunan Province, China (Grant No. 20C1530), and the Jishou University Foundation, China (Grant No. Jdy20027).
    [1]

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

    [2]

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

    [3]

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

    [4]

    Xiao D, Yao W, Niu Q 2007 Phys. Rev. Lett. 99 236809Google Scholar

    [5]

    Vila J, Pal R K, Ruzzene M 2017 Phys. Rev. B 96 134307Google Scholar

    [6]

    Chen Y, Liu X, Hu G 2019 J Mech Phys Solids 122 54Google Scholar

    [7]

    Gao N, Qu S, Si L, Wang J, Chen W 2021 Appl. Phys. Lett. 118 063502Google Scholar

    [8]

    Zhang Q, Chen Y, Zhang K, Hu G 2020 Phys. Rev. B 101 014101Google Scholar

    [9]

    Machon T, Alexander G P, Goldstein R E, Pesci A I 2016 Phys. Rev. Lett. 117 017801Google Scholar

    [10]

    Schaibley J R, Yu H Y, Clark G, Rivera P, Ross J S, Seyler K L, Yao W, Xu X 2016 Nat. Rev. Mater. 1 16055Google Scholar

    [11]

    Gorbachev R, Song J, Yu G, Kretinin A, Withers F, Cao Y, Mishchenko A, Grigorieva I, Novoselov K S, Levitov L 2014 Science 346 448Google Scholar

    [12]

    Wang Y T, Luan P G, Zhang S 2015 New J. Phys. 17 073031Google Scholar

    [13]

    Yan M, Lu J, Li F, Deng W, Huang X, Ma J, Liu Z 2018 Nat. Mater. 17 993Google Scholar

    [14]

    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 1124Google Scholar

    [15]

    Noh J, Huang S, Chen K P, Rechtsman M C 2018 Phys. Rev. Lett. 120 063902Google Scholar

    [16]

    Collins M J, Zhang F, Bojko R, Chrostowski L, Rechtsman M C 2016 Phys. Rev. A 94 063827Google Scholar

    [17]

    Mak K F, McGill K L, Park J, McEuen P L 2014 Science 344 1489Google Scholar

    [18]

    Martin I, Blanter Y M, Morpurgo A 2008 Phys. Rev. Lett. 100 036804Google Scholar

    [19]

    Jung J, Zhang F, Qiao Z, MacDonald A H 2011 Phys. Rev. B 84 075418Google Scholar

    [20]

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

    [21]

    Yantchev V, Katardjiev I 2013 J. Micromech. Microeng. 23 043001Google Scholar

    [22]

    Tian Z H, Shen C, Li J F, et al. 2020 Nat. Commun. 11 762Google Scholar

  • 图 1  (a)声子晶体单胞结构; (b)单胞俯视图

    Fig. 1.  (a) Unit cell of the phononic crystal; (b) top view of the unit cell.

    图 2  (a) 散射体高度$h = 0.28{\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\text{mm}}$时声子晶体的能带结构; (b)${K_1}$, ${K_2}$能谷频率随散射体角度的变化, 红色箭头和绿色箭头分别表示散射体顺时针和逆时针手征性回转; (c)$\theta = 20^\circ $${K_1}$, ${K_2}$谷每一帧图形经过三分之一周期的位移场, 黑色虚线是中轴线, 红色箭头表示每一帧散射体位移的最大位置

    Fig. 2.  (a) Band structure of the phonon crystal with the height of scatter $h = 0.28{\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\text{mm}}$; (b) variation of valley frequencies of ${K_1}$ and ${K_2}$ with the change of scatterer angle, red arrows and green arrows indicate clockwise and counterclockwise scatterer hand sign slewing respectively; (c) the displacement fields of ${K_1}$ and ${K_2}$ at $\theta = 20^\circ $ for each frame of the graph after one-third of the period, the black dashed line is the central axis, and the red arrow indicates the maximum position of the scatterer displacement for each frame.

    图 3  (a)由A和B相声子晶体组成的条形超胞, 红色虚线表示两相界面; (b) 超胞沿$\varGamma {\text{-}}K$方向的投影能带结构, 浅灰色区域为体态结构, 浅红色区域为边缘态区域, 红色实线为连接上、下体态的边缘态; (c)条形超胞在边缘态频率的位移场

    Fig. 3.  (a) Bar-shaped supercell composed of phonon crystals of A phase and B phase. The red dashed line indicates the interface; (b) the projected band structure of the supercell along the $\varGamma {\text{-}}K$ direction, the light grey region is the bulk structure, the light red region is the edge state region, and the red solid line is the edge state; (c) displacement field of the strip supercell at the edge state frequency.

    图 4  (a)狄拉克点及上、下能谷的频率随着散射体高度的变化; (b)各散射体高度下对应的边缘态, 其中相同颜色虚线则对应的是该散射体高度下的边缘态区域; (c)散射体连续变化示意图

    Fig. 4.  (a) Frequency of the Dirac point and the upper and lower valleys with different scatterer height; (b) the edge state at each scatterer height, where the same color dashed line corresponds to the edge state region at that scatterer height; (c) schematic diagram of continuous change of scatterer.

    图 5  (a)由B, A相声子晶体组成的矩形超胞, 红色虚线表示两相界面, 红色五角星为点源; (b) 激励频率为0.33 MHz时的边缘态位移场; (c)当散射体高度h = 0.20, 0.24 , 0.32, 0.36 mm时, 对应的中心带隙频率激发边缘态的位移场

    Fig. 5.  (a) A rectangular supercell composed of crystal B and A, the red dotted line represents the interface between the two phases, and the red pentagram is the point source; (b) displacement field of edge state when excitation frequency is 0.33 MHz; (c) when the scatterer height h = 0.20, 0.24 , 0.32, 0.36 mm, the displacement field of the edge state excited by the frequency of the corresponding central band gap.

    图 6  (a) B-A相声子晶体组成的“Z”字形界面超胞, 红色虚线为两相界面, 红色五角星为点源; (b)频率为0.33 MHz的点源激励的边缘态位移场; (c), (d)引入空腔和无序后边缘态的位移场分布, 插图部分为界面结构放大图

    Fig. 6.  (a) The Z shaped interface supercell was composed by B-A crystal, the red dotted line is the two-phase interface, and the red pentacle is the point source; (b) edge state displacement field of point source excitation with frequency of 0.33 MHz; (c), (d) the distribution of edge state displacement field after the introduction of cavity and disordered respectively; the part in the illustration is an enlarged view of interface structure.

  • [1]

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

    [2]

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

    [3]

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

    [4]

    Xiao D, Yao W, Niu Q 2007 Phys. Rev. Lett. 99 236809Google Scholar

    [5]

    Vila J, Pal R K, Ruzzene M 2017 Phys. Rev. B 96 134307Google Scholar

    [6]

    Chen Y, Liu X, Hu G 2019 J Mech Phys Solids 122 54Google Scholar

    [7]

    Gao N, Qu S, Si L, Wang J, Chen W 2021 Appl. Phys. Lett. 118 063502Google Scholar

    [8]

    Zhang Q, Chen Y, Zhang K, Hu G 2020 Phys. Rev. B 101 014101Google Scholar

    [9]

    Machon T, Alexander G P, Goldstein R E, Pesci A I 2016 Phys. Rev. Lett. 117 017801Google Scholar

    [10]

    Schaibley J R, Yu H Y, Clark G, Rivera P, Ross J S, Seyler K L, Yao W, Xu X 2016 Nat. Rev. Mater. 1 16055Google Scholar

    [11]

    Gorbachev R, Song J, Yu G, Kretinin A, Withers F, Cao Y, Mishchenko A, Grigorieva I, Novoselov K S, Levitov L 2014 Science 346 448Google Scholar

    [12]

    Wang Y T, Luan P G, Zhang S 2015 New J. Phys. 17 073031Google Scholar

    [13]

    Yan M, Lu J, Li F, Deng W, Huang X, Ma J, Liu Z 2018 Nat. Mater. 17 993Google Scholar

    [14]

    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 1124Google Scholar

    [15]

    Noh J, Huang S, Chen K P, Rechtsman M C 2018 Phys. Rev. Lett. 120 063902Google Scholar

    [16]

    Collins M J, Zhang F, Bojko R, Chrostowski L, Rechtsman M C 2016 Phys. Rev. A 94 063827Google Scholar

    [17]

    Mak K F, McGill K L, Park J, McEuen P L 2014 Science 344 1489Google Scholar

    [18]

    Martin I, Blanter Y M, Morpurgo A 2008 Phys. Rev. Lett. 100 036804Google Scholar

    [19]

    Jung J, Zhang F, Qiao Z, MacDonald A H 2011 Phys. Rev. B 84 075418Google Scholar

    [20]

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

    [21]

    Yantchev V, Katardjiev I 2013 J. Micromech. Microeng. 23 043001Google Scholar

    [22]

    Tian Z H, Shen C, Li J F, et al. 2020 Nat. Commun. 11 762Google Scholar

  • [1] 杨艳丽, 段志磊, 薛海斌. 非厄米Su-Schrieffer-Heeger链边缘态和趋肤效应依赖的电子输运特性. 物理学报, 2023, 72(24): 247301. doi: 10.7498/aps.72.20231286
    [2] 高慧芬, 周小芳, 黄学勤. 二维声子晶体中Zak相位诱导的界面态. 物理学报, 2022, 71(4): 044301. doi: 10.7498/aps.71.20211642
    [3] 谭自豪, 孙小伟, 宋婷, 温晓东, 刘禧萱, 刘子江. 球形复合柱表面波声子晶体的带隙特性仿真. 物理学报, 2021, 70(14): 144301. doi: 10.7498/aps.70.20210165
    [4] 高慧芬, 周小芳, 黄学勤. 二维声子晶体中Zak相位诱导的界面态. 物理学报, 2021, (): . doi: 10.7498/aps.70.20211642
    [5] 骆全斌, 黄学勤, 邓伟胤, 吴迎, 陆久阳, 刘正猷. 声子晶体板中的第二类狄拉克点和边缘传输. 物理学报, 2021, 70(18): 184302. doi: 10.7498/aps.70.20210712
    [6] 郑周甫, 尹剑飞, 温激鸿, 郁殿龙. 基于声子晶体板的弹性波拓扑保护边界态. 物理学报, 2020, 69(15): 156201. doi: 10.7498/aps.69.20200542
    [7] 耿治国, 彭玉桂, 沈亚西, 赵德刚, 祝雪丰. 手性声子晶体中拓扑声传输. 物理学报, 2019, 68(22): 227802. doi: 10.7498/aps.68.20191007
    [8] 贾鼎, 葛勇, 袁寿其, 孙宏祥. 基于蜂窝晶格声子晶体的双频带声拓扑绝缘体. 物理学报, 2019, 68(22): 224301. doi: 10.7498/aps.68.20190951
    [9] 卢曼昕, 邓文基. 一维二元复式晶格的拓扑不变量与边缘态. 物理学报, 2019, 68(12): 120301. doi: 10.7498/aps.68.20190214
    [10] 许楠, 张岩. 三聚化非厄密晶格中具有趋肤效应的拓扑边缘态. 物理学报, 2019, 68(10): 104206. doi: 10.7498/aps.68.20190112
    [11] 王健, 吴世巧, 梅军. 二维声子晶体中简单旋转操作导致的拓扑相变. 物理学报, 2017, 66(22): 224301. doi: 10.7498/aps.66.224301
    [12] 陈泽国, 吴莹. 声子晶体中的多重拓扑相. 物理学报, 2017, 66(22): 227804. doi: 10.7498/aps.66.227804
    [13] 王青, 盛利. 磁场中的拓扑绝缘体边缘态性质. 物理学报, 2015, 64(9): 097302. doi: 10.7498/aps.64.097302
    [14] 侯丽娜, 侯志林, 傅秀军. 局域共振型声子晶体中的缺陷态研究. 物理学报, 2014, 63(3): 034305. doi: 10.7498/aps.63.034305
    [15] 刘启能, 刘沁. 固-固无限周期声子晶体中SH波全反射隧穿的谐振理论. 物理学报, 2013, 62(4): 044301. doi: 10.7498/aps.62.044301
    [16] 刘启能. 一维固-固结构圆柱声子晶体中弹性波的传输特性. 物理学报, 2011, 60(3): 034301. doi: 10.7498/aps.60.034301
    [17] 蔡 力, 韩小云, 温熙森. 长波条件下二维声子晶体中的弹性波传播及各向异性. 物理学报, 2008, 57(3): 1746-1752. doi: 10.7498/aps.57.1746
    [18] 李晓春, 易秀英, 肖清武, 梁宏宇. 三组元声子晶体中的缺陷态. 物理学报, 2006, 55(5): 2300-2305. doi: 10.7498/aps.55.2300
    [19] 温激鸿, 王 刚, 刘耀宗, 郁殿龙. 基于集中质量法的一维声子晶体弹性波带隙计算. 物理学报, 2004, 53(10): 3384-3388. doi: 10.7498/aps.53.3384
    [20] 齐共金, 杨盛良, 白书欣, 赵 恂. 基于平面波算法的二维声子晶体带结构的研究. 物理学报, 2003, 52(3): 668-671. doi: 10.7498/aps.52.668
计量
  • 文章访问数:  2843
  • PDF下载量:  96
  • 被引次数: 0
出版历程
  • 收稿日期:  2022-06-30
  • 修回日期:  2022-08-26
  • 上网日期:  2022-12-08
  • 刊出日期:  2022-12-24

/

返回文章
返回