标题： 分形性引起的拓扑结构 显示英文标题

标题： Fractality-induced Topology

摘要： 分形几何以自相似图案和非整数维度为特征，为探索物质的拓扑相提供了一个引人入胜的平台。 在本工作中，我们引入了一个理论框架，利用等谱约化来有效简化复杂的分形结构，揭示了存在拓扑保护的边界和角态。 我们的方法表明，即使在没有传统驱动机制（如磁场或自旋-轨道耦合）的情况下，分形也可以支持拓扑相。 等谱约化不仅阐明了潜在的拓扑特性，还使该框架广泛适用于各种分形系统。 此外，我们的研究结果表明，这些拓扑相可能在自然界中发现的具有分形结构的材料中自然出现。 这项工作为设计基于分形的拓扑材料开辟了新的途径，推动了对复杂自相似几何中拓扑学的理论理解和实验探索。 显示英文摘要

摘要： Fractal geometries, characterized by self-similar patterns and non-integer dimensions, provide an intriguing platform for exploring topological phases of matter. In this work, we introduce a theoretical framework that leverages isospectral reduction to effectively simplify complex fractal structures, revealing the presence of topologically protected boundary and corner states. Our approach demonstrates that fractals can support topological phases, even in the absence of traditional driving mechanisms such as magnetic fields or spin-orbit coupling. The isospectral reduction not only elucidates the underlying topological features but also makes this framework broadly applicable to a variety of fractal systems. Furthermore, our findings suggest that these topological phases may naturally occur in materials with fractal structures found in nature. This work opens new avenues for designing fractal-based topological materials, advancing both theoretical understanding and experimental exploration of topology in complex, self-similar geometries.