2022/05/09 by Shengjie Zheng, Zheng, Shengjie, Xianfeng Man +15
Engineering · Physics and Astronomy · #Acoustic Wave Phenomena Research #Applied Physics (physics.app-ph) #FOS: Physical sciences #Materials Science (cond-mat.mtrl-sci) #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Topological Materials and Phenomena
paper · pdf · doi:10.48550/arxiv.2205.04089
openalex publication_date 2022/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 largely unexplored. Fractals, being nearly the same at different scales, are one of the intriguing complex geometries with non-integer dimensions. Here, we demonstrate acoustic Sierpiński fractal topological insulators with unconventional higher-order topological phenomena via consistent theory and experiments. We discover abundant topological edge and corner states emerging in our acoustic systems due to the rich edge and corner boundaries inside the fractals. Interestingly, the numbers of the edge and corner states scale the same as the bulk states with the system size and the exponents coincide with the Hausdorff fractal dimension of the Sierpiński carpet. Furthermore, the emergent corner states exhibit unconventional spectrum and wave patterns. Our study opens a pathway toward topological states in fractal geometries.