双层声子晶体：搭建一阶拓扑到高阶拓扑的桥梁
论文
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速递
Acoustic higher-order topology derived from first-order with built-in Zeeman-like fields
Xueqin Huang, Jiuyang Lu, Zhongbo Yan, Mou Yan, Weiyin Deng, Gang Chen, Zhengyou Liu
Science Bulletin, 2022, 67(5): 488–494
doi: 10.1016/j.scib.2021.11.020
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简介
具有拓扑角态或铰链态的高阶拓扑绝缘体已成为当前拓扑物理研究的热门方向. 然而, 关于一阶拓扑绝缘体与高阶拓扑绝缘体之间联系的研究工作却寥寥无几. 最近, 高阶拓扑绝缘体与Z2拓扑绝缘体之间的联系被建立起来. 在面内Zeeman场的作用下, Z2拓扑绝缘体会转变成高阶拓扑绝缘体, 体系存在零维的角态. 这种面内Zeeman场可以通过铁磁近邻效应或磁性原子掺杂来实现, 但是这样的实现方式大大增加了实验的复杂性. 本研究利用耦合共振腔设计了双层声子晶体. 该体系可以等效成具有内禀面内Zeeman场的Kane-Mele模型. 在锯齿形边界上, 存在具有带隙的螺旋性边界态, 而在边界态的带隙中出现了零维角态，从而表明了高阶拓扑态的存在. 文章还进一步研究了六边形环形样品中具有互补几何结构的内外角角态, 发现其声压场分别具有奇和偶对称. 该工作搭建了一阶拓扑到高阶拓扑之间的桥梁. 利用声子晶体的这种人造类Zeeman场, 有望为研究新型拓扑态提供良好的平台.
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图文速览
Fig. 1 Corner states in the lattice model. (a) Schematic of the hexagonal sample of a bilayer hexagonal lattice. (b) Unit cell with bilayer structure with sites A (red) and B (blue), the intralayer couplings t0 (gray), and interlayer couplings tc (cyan). (c) Bulk state dispersion along the high-symmetry lines. Inset: the first Brillouin zone. (d) Phase diagram obtained by varying the interlayer chiral coupling and on-site energy. The orange region corresponds to the nontrivial second-order topological phase and the red star denotes the phase chosen for demonstrating the corner states. (e) Projected dispersion of a ribbon in the presence of the zigzag boundaries indicated by the dashed box in (a). (f) Eigenvalues for the hexagon-shaped sample. The red spheres represent the corner states. Inset: Local density of states of the corner states for the upper and lower layers. The plot parameters for (c), (e) and (f) are chosen as t0=−1, tc= t0/4, and m0=0.
Fig. 2 Bulk and boundary state dispersions of the PC sample. (a) Schematic of the unit cell. (b) Bulk state dispersion along the high symmetry lines. (c) Simulated and measured boundary state dispersions. The color maps represent the measured data, while the gray and red lines denote the projected bulk and the boundary state dispersions, respectively. (d) Pressure field distributions of the eigenmodes at
Fig. 3 Corner states in a hexagon-shaped PC. (a) Schematic of a hexagonal PC. Inset: Partial view of the PC sample. The green star represents the position of the exciting source. (b) Simulated eigenfrequencies with the side length of 14 unit cells. The red, blue, and black spheres represent the corner, edge, and bulk states, respectively. Inset: Simulated pressure field distribution of the corner mode at the frequency marked by the red arrow.(c) Measured (left panel) and simulated (right panel) pressure field distributions of the corner marked by the dashed rectangle in (a) at 3.6 kHz. (d) Measured acoustic response spectrum as a function of the frequency. The structural parameters are the same as those in Fig. 2. The color bars in (b) and (c), and the spectrum in (d) are normalized by their maxima.
Fig. 4 Corner states at the outer and inner boundaries of a hexagonal ring-shaped PC. (a) Schematic of the PC sample. A pair of inner and outer corners is denoted by Cin and Cout. (b) Simulated eigenfrequencies of the PC sample. There are twelve corner modes (red) in the gap of edge states (blue). (c) Simulated (left panel) and measured (right panel) pressure field distributions in the Cout corner boxed by the dashed rectangle in (a) at 3.6 kHz. (d) Corresponding results for the Cin corner. The width of the ring is 13 unit cells. (e), (f) Measured pressure field distributions in the Cout and Cin corners for the ring with 2 unit cells. The structural parameters are the same as those in Fig. 2. The color bars in (c) and (d), and the pressure fields in (c−f) are normalized by their maxima.
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本文通讯作者
邓伟胤 副教授 华南理工大学物理与光电学院. 主要从事拓扑量子材料和声子晶体等领域的研究.
陈 刚 教授 山西大学激光光谱研究所. 主要从事超冷原子和人工微结构的理论和实验研究.
刘正猷 教授 武汉大学物理科学与技术学院. 主要从事凝聚态物理和声学等领域的研究，研究兴趣包括: 声子晶体与拓扑物理、超材料与超表面、声场调控及与颗粒相互作用等.
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