论文标题
观察声学超材料中的分形拓扑状态
Observation of fractal topological states in acoustic metamaterials
论文作者
论文摘要
物质的拓扑阶段已在具有整数尺寸的固态材料和经典波系统中进行了广泛的研究。但是，非整数维度中的拓扑状态在很大程度上尚未开发。分形在不同的尺度上几乎相同，是具有非整体尺寸的有趣的复杂几何形状之一。在这里，我们通过一致的理论和实验证明了具有非常规的高阶拓扑现象，具有非常规的高阶拓扑现象。由于分形内部的边缘和角边界丰富，我们发现声学系统中出现的大量拓扑边缘和角状态。有趣的是，边缘和角状态的数量与系统大小的散装状态相同，并且指数与Sierpiński地毯的Hausdorff分形维度一致。此外，新兴角状态表现出非常规的光谱和波浪模式。我们的研究为分形几何形状的拓扑状态打开了一条途径。
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.
