Valley-Locked Edge States and Corner States in Dendritic Phonon Crystals#br#

doi:10.13438/j.cnki.jdzk.2025.06.005

Abstract

Abstract: To study the acoustic wave propagation characteristics of two-dimensional higher-order topological insulators,a third-order dendritic valley phononic crystal structure with C3v symmetry was designed.By rotating the scatterers to break spatial symmetry,the valley Hall edge states were successfully realized.On this basis,a Zigzag interface topological waveguide and a triangular corner structure were constructed,and their acoustic wave transmission behaviors were analyzed.The results show that in the topological waveguide,the acoustic waves are effectively localized at the Zigzag interface;in the triangular corner structure,corner states with valley switchability and selectivity appear.

Key words: phonon crystal, edge state, topological transport, corner state

LIU Shuqi, LIU Yuanli, KONG Peng, ZHAO Heping. Valley-Locked Edge States and Corner States in Dendritic Phonon Crystals#br#[J]. Journal of Jishou University(Natural Sciences Edition), 2025, 46(6): 35-41.

References

[1] TAO Liyun,LIU Yahong,DU Lianlian,et al.Evolution of the Edge States and Corner States in a Multilayer Honeycomb Valley-Hall Topological Metamaterial[J].Physical Review B,2023,107(3):035431.DOI:10.1103/PhysRevB.107.035431.
[2] LIU Zhengrong,HUA Chunbo,TAN Peng,et al.Higher-Order Topological Insulators in Hyperbolic Lattices[J].Physical Review B,2023,107(12):125302.DOI:10.1103/PhysRevB.107.125302.
[3] ZHANG Xiaopeng,LI Yan,WANG Yaguang,et al.Narrow-Band Filter Design of Phononic Crystals with Periodic Point Defects via Topology Optimization[J].International Journal of Mechanical Sciences,2021,212:106829.DOI:10.1016/j.ijmecsci.2021.106829.
[4] MA Tianxue,FAN Quanshui,ZHANG Chuanzeng,et al.Flexural Wave Energy Harvesting by the Topological Interface State of a Phononic Crystal Beam[J].Extreme Mechanics Letters,2022,50:101578.DOI:10.1016/j.eml.2021.101578.
[5] TSUI D C,STORMER H L,GOSSARD A C.Two-Dimensional Magnetotransport in the Extreme Quantum Limit[J].Physical Review Letters,1982,48(22):1559-1562.
[6] CHEN Yafeng,MENG Fei,SUN Guangyong,et al.Topological Design of Phononic Crystals for Unidirectional Acoustic Transmission[J].Journal of Sound and Vibration,2017,410:103-123.
[7] FLEURY ROMAIN,SOUNAS DIMITRIOS L,SIECK CALEB F,et al.Sound Isolation and Giant Linear Nonreciprocity in a Compact Acoustic Circulator[J].Science,2014,343:516-519.
[8] XUE Haoran,YANG Yihao,ZHANG Baile.Topological Acoustics[J].Nature Reviews Materials,2022,7(12):974-990.
[9] LU Jiuyang,QIU Chunyin,KE Manzhu,et al.Valley Vortex States in Sonic Crystals[J].Physical Review Letters,2016,116(9):093901.DOI:10.1103/PhysRevLett.116.093901.
[10] LU Jiuyang,QIU Chunyin,YE Liping,et al.Observation of Topological Valley Transport of Sound in Sonic Crystals[J].Nature Physics,2017,13(4):369-374.
[11] 李荫铭,孔鹏,毕仁贵,等.二维蜂窝弹性材料拓扑态的研究[J].吉首大学学报(自然科学版),2022,43(4):47-50.
[12] GAO Nan,QU Sichao,SI Liang,et al.Broadband Topological Valley Transport of Elastic Wave in Reconfigurable Phononic Crystal Plate[J].Applied Physics Letters,2021,118(6):063502.DOI:10.1063/5.0036840.
[13] ZHANG Quan,CHEN Yi,ZHANG Kai,et al.Dirac Degeneracy and Elastic Topological Valley Modes Induced by Local Resonant States[J].Physical Review B,2020,101(1):014101.DOI:org/10.1103/PhysRevB.101.014101.
[14] XIA Baizhan,ZHANG Jie,TONG Liang,et al.Topologically Valley-Polarized Edge States in Elastic Phononic Plates Yielded by Lattice Defects[J].International Journal of Solids and Structures,2022,239/240:111413.DOI:10.1016/j.ijsolstr.2021.111413.
[15] 蒋婧,孔鹏,邓科.二维谷声子晶体拓扑绝缘体的高阶拓扑角态[J].吉首大学学报(自然科学版),2025,46(1):39-44.
[16] WEI Runhang,YAN Zhimiao,TAN Ting.Defect-Reconfigurable Topological Valley Transport for Information Processing and Acoustic Communication[J].Applied Materials Today,2025,44:102759.DOI:10.1016/j.apmt.2025.102759.
[17] CAI Chengxin,HE Guangchen,ZHENG Zhoufu,et al.Ultra-Wideb and Valley Transmission on Elastic Topological Phononic Crystals[J].Results in Physics,2023,50:106570.DOI:10.1016/j.rinp.2023.106570.
[18] MA Ze,LIU Yang,XIE Yuxin,et al.A Simple Elastic Phononic Crystal Plate with Adjustable Topological Valley Transmission Paths[J].Extreme Mechanics Letters,2022,57:101910.DOI:10.1016/j.eml.2022.101910.
[19] ZHANG Qiankun,XING Xiaohua,ZOU Die,et al.Robust Topological Valley-Locked Waveguide Transport in Photonic Heterostructures[J].Results in Physics,2023,54:107066.DOI:10.1016/j.rinp.2023.107066.
[20] LIU Shan,DENG Weiyin,HUANG Xueqin,et al.Robust Acoustic Waveguide Transport in Heterostructures Based on Acoustic Topological Insulators[J].Physical Review Applied,2022,18(3):034066.DOI:10.1103/PhysRevApplied.18.034066.