Observation of fractal higher-order topological states in acoustic metamaterials

作     者：Shengjie Zheng Xianfeng Man Ze-Lin Kong Zhi-Kang Lin Guiju Duan Ning Chen Dejie Yu Jian-Hua Jiang Baizhan Xia 郑圣洁;满先锋;孔泽霖;林志康;段桂菊;陈宁;于德介;蒋建华;夏百战

作者机构：State Key Laboratory of Advanced Design and Manufacturing for Vehicle BodyHunan UniversityChangsha 410082China College of Mechanical and Electrical EngineeringChangsha UniversityChangsha 410022China Institute of Theoretical and Applied PhysicsSchool of Physical Science and Technology&Collaborative Innovation Center of Suzhou Nano Science and TechnologySoochow UniversitySuzhou 215006China 

出 版 物：《Science Bulletin》 (科学通报（英文版）)

年 卷 期：2022年第67卷第20期

页      面：2069-2075,M0004页

核心收录：

学科分类：08[工学] 080501[工学-材料物理与化学] 0805[工学-材料科学与工程（可授工学、理学学位）] 

基　　金：supported by the National Natural Science Foundation of China(12125504,12072108,51621004,and 51905162) the Priority Academic Program Development(PAPD)of Jiangsu Higher Education Institutions the Hunan Provincial Natural Science Foundation of China(2021JJ40626) 

主　　题：Higher-order topological states Topological fractals Sierpinski carpet Fractal dimensions Acoustic metamaterials 

摘      要：Topological phases of matter have been extensively investigated in solid-state materials and classical wave systems with integer dimensions. However, topological states in non-integer dimensions remain almost unexplored. Fractals, being self-similar on different scales, are one of the intriguing complex geometries with non-integer dimensions. Here, we demonstrate fractal higher-order topological states with unprecedented emergent phenomena in a Sierpin? ski acoustic metamaterial. We uncover abundant topological edge and corner states in the acoustic metamaterial due to the fractal geometry. Interestingly,the numbers of the edge and corner states depend exponentially on the system size, and the leading exponent is the Hausdorff fractal dimension of the Sierpin? ski carpet. Furthermore, the results reveal the unconventional spectrum and rich wave patterns of the corner states with consistent simulations and experiments. This study thus unveils unconventional topological states in fractal geometry and may inspire future studies of topological phenomena in non-Euclidean geometries.