Journal
SCIENCE BULLETIN
Volume 67, Issue 20, Pages 2069-2075Publisher
ELSEVIER
DOI: 10.1016/j.scib.2022.09.020
Keywords
Higher-order topological states; Topological fractals; Sierpinski carpet; Fractal dimensions; Acoustic metamaterials
Categories
Funding
- National Natural Science Foundation of China [12125504, 12072108, 51621004, 51905162]
- Priority Academic Program Development (PAPD) of Jiangsu Higher Education Institutions
- Hunan Provincial Natural Science Foundation of China [2021JJ40626]
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This study demonstrates fractal higher-order topological states in an acoustic metamaterial and uncovers abundant topological edge and corner states. The numbers of these states exponentially depend on the system size, with the leading exponent being the Hausdorff fractal dimension of the Sierpinski carpet. Furthermore, the study reveals unconventional spectrum and rich wave patterns of the corner states.
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 Sierpinski 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 Sierpinski 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. (c) 2022 Science China Press. Published by Elsevier B.V. and Science China Press. All rights reserved.
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