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Since the topological insulator concept was expanded from the field of quantum waves to the field of elastic waves, the research related to the elastic system valley Hall insulator has been developed rapidly because of its novel physical properties, rich design ability for wave modulation and simple implementation conditions. To address the limitations of small energy and inflexible structure of the edge-state transmission of valley Hall insulators in traditional structure, a topological waveguide heterostructure is designed based on the valley locking principle. The original configuration of this structure features a honeycomb lattice connected by rectangular veins. The energy band structure and transmission characteristics of the model are calculated using the equivalent structural parameter method. It is found that there are three Dirac points at the corner point K of the Brillouin zone, and the spatial inversion symmetry of the system can be broken by changing the structural parameters, so as to realize the topological phase transition of the out-of-plane body elastic mode in three frequency bands. The topological heterogeneous structure is formed by superimposing Dirac point phonon crystals between two topological insulators, and the topological waveguide state possesses advantages, such as multiband, tunability, and robustness. The structure can be used to design energy splitters and energy convergers to achieve flexible manipulation of elastic waves. This study enriches topological acoustics, and the designed multi-band elastic topological insulator has potential applications in multi-band communication and information processing.
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Keywords:
- phononic crystals /
- elastic waves /
- topological waveguide states /
- multiband
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图 1 声子晶体模型示意图
Figure 1. Schematic diagram of the phonon crystal model.
图 2 面外弹性波模式的能带结构图 (a) 当$ {a_1} > {a_2} $时, 几何模型及能带图, 阴影部分表示带隙; (b) 当$ {a_1}={a_2} $时, 几何模型及能带结构; (c) 当$ {a_1} < {a_2} $时, 几何模型及能带结构
Figure 2. Energy band structure diagrams of the out-of-plane body elastic wave mode: (a) When $ {a_1} > {a_2} $, geometric model energy band diagram and its band gap (shaded); (b) when $ {a_1}={a_2} $, geometric model and energy band structure; (c) when $ {a_1} < {a_2} $, geometric model and energy band structure.
图 3 拓扑相变图 (a) 3组$K^+ $和$K^- $特征态频率随着r的变化; (b)第1频段的谷态本征位移场图; (c)第2频段的谷态本征位移场图; (d)第3频段的谷态本征位移场图
Figure 3. Topological phase transition diagrams: (a) Variation of 3 sets of $ K^+ $ and $K^- $ eigenstate frequencies with r ; (b) valley eigenshift field map for the first frequency band; (c) valley eigenshift field map for the second frequency band; (d) valley eigenshift field map for the third frequency band.
图 4 拓扑异质结构示意图
Figure 4. Schematic diagram of topological heterogeneous structure.
图 5 (a) U1U2U3型超胞投影能带; (b) kx = 0.6时91.4 kHz, 300.9 kHz, 435.2 kHz三个频段内U1U2U3型超胞的谷波导态; (c) U3U2U1型超胞投影能带; (d) kx = 0.6时82.9 kHz, 306.9 kHz, 436.7 kHz三个频段内U3U2U1型超胞的谷波导态
Figure 5. (a) Projected energy bands of U1U2U3-type supercells; (b) the valley waveguide states of U1U2U3-type supercells at 91.4 kHz, 300.9 kHz, and 435.2 kHz bands for kx = 0.6; (c) the projected energy bands of U3U2U1-type supercells; (d) the valley waveguide states of U3U2U1-type supercells at 82.9 kHz, 306.9 kHz, and 436.7 kHz bands for kx = 0.6.
图 6 面外弹性波模式的波导输运 (a) A_{15}|B_5 |C_{15}型波导, 在左侧施加激励的${u_z}$绝对值场图; (b) A_{15}|B_15 |C_{15}型波导, 在左侧施加激励的${u_z}$绝对值场图; (c) A_{15}|B_n|C_{15}型波导, 波导频宽随着B域层数n的变化; (d) A_{15}|C_15 |A_{15}型波导, 在左侧施加激励的${u_z}$绝对值场图
Figure 6. Waveguide transmission in the out-of-plane elastic wave mode: (a) ${u_z}$ absolute value field plot for waveguide type A_{15}|B_5 |C_{15} with excitation applied on the left side. (b) ${u_z}$ absolute value field plot for waveguide type A_{15}|B_15 |C_{15} with excitation applied on the left side. (c) Variation of waveguide frequency band of A_{15}|B_n|C_{15} waveguide with the number of B-domain layers n. The waveguide frequency band is the same as the number of II-domain layers. (d) ${u_z}$ absolute value field plot for waveguide type A_{15}|C_15 |A_{15} with excitation applied on the left side.
图 7 (a)引入缺陷的结构示意图; (b)线元激发的带缺陷的面外偏振弹性波模式输运
Figure 7. (a) Schematic of the structure with introduced defects; (b) elastic wave mode transmission of an out-of-plane polarizer with defects excited by a line element.
图 8 (a) 能量汇聚器示意图; (b) ABC型能量汇聚器的${u_z}$绝对值场线结果图; (c) ABC型2个线元能量测量结果
Figure 8. (a) Schematic diagram of the energy aggregator; (b) plot of ${u_z}$ absolute value field line results for ABC-type energy aggregator; (c) energy measurement results of ABC-type 2 line element.
图 9 能量分束器的${u_z}$绝对值场图 (a) 分束结构示意图; (b) ABC型能量分束器的${u_z}$绝对值场图
Figure 9. ${u_z}$ absolute value field diagram of the energy beam splitter: (a) Schematic diagram of the beam splitting structure; (b) ${u_z}$ absolute value field diagram of the ABC-type energy beam splitter.
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[1] Bernevig B A, Hughes T L, Zhang S C 2006 Science 314 1757
Google Scholar
[2] Moore J E 2010 Nature 464 194
Google Scholar
[3] 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
Google Scholar
[4] Miniaci M, Pal R, Morvan B, Ruzzene M 2018 Phys. Rev. X 8 031074
Google Scholar
[5] Zhou W J, Wu B, Su Y, Liu D Y, Chen W Q, Bao R H 2021 Mech. Adv. Mater. Struct. 28 221
Google Scholar
[6] Zeng Y, Zhang S Y, Zhou H T, et al. 2021 Mater. Des. 208 109906
Google Scholar
[7] Wang K, Zhou J X, Chang Y P, Ouyang H J, Xu D L, Yang Y 2020 Nonlinear Dyn. 101 755
Google Scholar
[8] Ding Y J, Peng Y G, Zhu Y F, et al. 2019 Phys. Rev. Lett. 122 014302
Google Scholar
[9] Yang Z J, Gao F, Shi X H, Lin X, Gao Z, Chong Y D, Zhang B L 2015 Phys. Rev. Lett. 114 114301
Google Scholar
[10] Wang P, Lu L, Bertoldi K 2015 Phys. Rev. Lett. 115 104302
Google Scholar
[11] Gao N, Qu S C, Si L, Wang J, Chen W Q 2021 Appl. Phys. Lett. 118 063502
Google Scholar
[12] Chen Y F, Meng F, Huang X D 2021 Mech. Syst. Signal Process. 146 107054
Google Scholar
[13] Huo S Y, Chen J J, Huang H B, Wei Y J, Tan Z H, Feng L Y, Xie X P 2021 Mech. Syst. Signal Process. 154 107543
Google Scholar
[14] 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
Google Scholar
[15] Brendel C, Peano V, Painter O, Marquardt F 2018 Phys. Rev. B 97 020102
Google Scholar
[16] Lin J H, Qi Y J, He Z J, Bi R G, Dong K 2024 Appl. Phys. Lett. 124 082202
Google Scholar
[17] 王一鹤, 张志旺, 程营, 刘晓峻 2019 68 227805
Google Scholar
Wang Y H, Zhang Z W, Cheng Y, Liu X J 2019 Acta Phys. Sin. 68 227805
Google Scholar
[18] 贾鼎, 葛勇, 袁寿其, 孙宏祥 2019 68 224301
Google Scholar
Jia D, Ge Y, Yuan S Q, Sun H X 2019 Acta Phys. Sin. 68 224301
Google Scholar
[19] 郑周甫, 尹剑飞, 温激鸿, 郁殿龙 2020 69 156201
Google Scholar
Zheng Z F, Yin J F, Wen J H, Yu D L 2020 Acta Phys. Sin. 69 156201
Google Scholar
[20] Jiang Z, Zhou Y Y, Zheng S J, Liu J T, Xia B Z 2023 Int. J. Mech. Sci. 255 108464
Google Scholar
[21] Huo S, Chen J, Huang H, 2017 Sci. Rep. 7 10335
Google Scholar
[22] Yang Z Z, Li X, Peng Y Y, 2020 Phys. Rev. Lett. 125 255502.
Google Scholar
[23] Xu G G, Sun X W, Wen X D 2023 J Appl Phys. 133 095110
Google Scholar
[24] Wang M D, Zhou W Y, Bi L, Qiu C Y, Ke M Z, Liu Z Y 2020 Nat. Commun. 11 3000
Google Scholar
[25] Huo S Y, Xie G H, Qiu S J, Gong X C, Fan S Z, Fu C M, Li Z Y 2022 Mech. Adv. Mater. Struct. 29 7772
Google Scholar
[26] Wang J Q, Zhang Z D, Yu S Y, Ge H, Liu K F, Wu T, Sun X C, Liu L, Chen H Y, He C 2022 Nat. Commun. 13 1324
Google Scholar
[27] Liu S, Deng W Y, Huang X Q, Lu J Y, Ke M Z, Liu Z Y 2022 Phys. Rev. Appl. 18 034066
Google Scholar
[28] Chen Y, Guo Z, Liu Y 2024 J. Phys. D: Appl. Phys. 57 465306.
Google Scholar
[29] 王艳锋 2015 博士学位论文 (北京: 北京交通大学)
Wang Y F 2015 Ph. D. Dissertation (Beijin: Beijinjiaotong University
[30] Lai Y, Zhang Z Q 2003 Appl. Phys. Lett. 83 3900-
Google Scholar
[31] Mei J, Liu Z Y, Shi J, et al. 2003 Phys. Rev. B. 67 245107
Google Scholar
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