六边形声子晶体的拓扑边缘态分析

张凯; 洪放; 罗杰; 邓子辰

doi:10.1007/s10409-021-09030-x

Topological edge state analysis of hexagonal phononic crystals

doi: 10.1007/s10409-021-09030-x

Zhang Kai^{1, 2,*
, ,},
Hong Fang^{1, 2},
Luo Jie^{1, 2},
Deng Zichen^{1, 2}

1.
School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi’an 710072, China;
2.
MIIT Key Laboratory of Dynamics and Control of Complex Systems, Northwestern Polytechnical University, Xi’an 710072, China

Funds:

the National Natural Science Foundation of China Grant

More Information

Corresponding author: Zhang Kai, E-mail addresses: kzhang@nwpu.edu.cn (Kai Zhang)

摘要

摘要: 在本研究中, 我们提出了由六边形铝板和六根手性排列直杆组成的谷声子晶体. 将谷声子晶体引入拓扑绝缘体(TI)系统, 通过在频带上实现支持拓扑保护边缘波(TPEWs)的拓扑边缘态, 可以在具有界面路径的系统上引导拓扑保护边缘波的传播. 本文的手性拓扑边缘态实现机理与镜面对称系统的拓扑边缘态实现机理不完全相同. 与传统的打破镜像对称不同, 本文通过调节手性单胞中直杆的长度差异而非打破镜面对称, 从而在狄拉克点打开了具有拓扑边缘模式间隙的新的完全带隙. 我们研究了手性系统中的色散特性, 并将色散特性应用于界面上的波导, 以获得可设计的路径系统. 此外, 我们模拟了TPEWs在不同路径下的鲁棒传播, 并证明了其对缺陷后向散射的免疫力. 最后, 证明了手性体系中谷霍尔效应的存在. 这一研究结果将为手性材料拓扑状态的进一步研究奠定基础.
Abstract: In this study, we propose valley phononic crystals that consist of a hexagonal aluminum plate with six chiral arrangements of ligaments. Valley phononic crystals were introduced into a topological insulator (TI) system to produce topologically protected edge waves (TPEWs) along the topological interfaces. The implementation of chiral topological edge states is different from the implementation of topological edge states of systems with symmetry. Unlike the conventional breaking of mirror symmetry, a new complete band with topological edge modes gap was opened up at the Dirac point by tuning the difference in lengths of the ligaments in the chiral unit cells. We investigated the dispersion properties in chiral systems and applied the dispersion properties to waveguides on the interfaces to achieve designable route systems. Furthermore, we simulated the robust propagation of TPEWs in different routes and demonstrated their immunity to backscattering at defects. Finally, the existence of the valley Hall effect in chiral systems was demonstrated. The study findings may lead to the further study of the topological states of chiral materials.
- Phononic crystals /
- Topologically protected edge waves /
- Chiral unit cells /
- Topological insulator

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1. a Designed chiral unit cell composed of a hexagonal plate and six rectangular ligaments. b Brillouin zone. c-d Two types of disturbed unit cells with alternate distributions of ligaments of lengths 12 and 20 mm, respectively.

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2. a Dispersion curves for chiral valley PCs where the length of the ligaments is b = 20 mm. b Dispersion curve for disturbed chiral valley PCs, with two types of ligaments of lengths b₁ = 20 mm, b₂ = 12 mm, respectively. c Two separated modes at the K and K′ points in the band structure shown in b, respectively. d Frequency variations in the bandgap with respect to the difference in length ∆b between the two types of ligaments. The blue area indicates the frequency range of the bandgap.

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3. a Supercell with 8 unit cells of different types (Type I and Type II) along the e₁ direction. Periodic boundary conditions are applied in the e₁ direction. b Dispersion curves for the supercell composed of two types of unit cells, b₁ = 12 mm, b₂ = 20 mm and b₁ = 20 mm, b₂ = 12 mm. c Frequency range curves of interface mode under different ∆b values. d Acoustic pressure field on the interface of the supercell in a.

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4. a Interface configuration of valley topological PCs. b-d Simulation of a displacement field at 2.5 kHz along a straight interface route, Z-shaped route, and U-shaped route, respectively. e-g Simulation of the transmission spectra of the TPEWs in b-d. h Simulation of a displacement field at 2.5 kHz along cross routes. i Acoustic zigzag transmission of robustness against cavities in the valley topological PCs.

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5. Time domain simulation shows the propagation of plane acoustic excitation along routes with corners. a-d Wave propagation along the sharp shape route at 2, 4, 6, and 8 ms, respectively. e-h Wave propagation along the U-shaped route at 4, 6, 8, and 10 ms, respectively. The frequency of the plane acoustic excitation field is 2.5 kHz..

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