Topology is the branch of mathematics studying the properties of an object that are preserved under continuous deformations. Quite remarkably, the powerful theoretical tools of topology have been applied over the past few years to study the electronic band structure of crystals. Topological band theory can explain and predict topological phase transitions in a material, and the unusual robustness of certain band structure shapes, such as Dirac cones, against small perturbations. These findings have also unveiled a new phase of matter—topological insulators—whose exotic transport properties at their boundaries are topologically protected against imperfections and disorder. The fascinating features of topological boundary states have triggered the search for their analogs in classical wave physics. Here, we focus on the peculiar features of two-dimensional topological insulators for sound and mechanical waves. Two-dimensional Dirac cones and phononic topological insulators can emerge under certain conditions in periodic acoustic metamaterials, demonstrating great potential for acoustic and mechanical systems to demonstrate, over a tabletop platform, complex fundamental phenomena driven by topological concepts. In addition, these discoveries offer a direct path toward new technologies for enhanced sound control and manipulation.

中文翻译：

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二维拓扑声音

拓扑学是数学的一个分支，研究物体在连续变形下保持不变的特性。值得注意的是，在过去几年中，强大的拓扑理论工具已被应用于研究晶体的电子能带结构。拓扑能带理论可以解释和预测材料中的拓扑相变，以及某些能带结构形状（例如狄拉克锥）对小扰动的异常鲁棒性。这些发现还揭示了物质的新相——拓扑绝缘体——其边界处的奇异传输特性在拓扑上受到保护，不会出现缺陷和无序。拓扑边界态的迷人特征引发了在经典波物理学中寻找它们的类似物。这里，我们专注于声波和机械波的二维拓扑绝缘体的独特特征。二维狄拉克锥和声子拓扑绝缘体可以在特定条件下出现在周期性声学超材料中，展示了声学和机械系统在桌面平台上展示由拓扑概念驱动的复杂基本现象的巨大潜力。此外，这些发现为增强声音控制和操纵的新技术提供了一条直接途径。由拓扑概念驱动的复杂基本现象。此外，这些发现为增强声音控制和操纵的新技术提供了一条直接途径。由拓扑概念驱动的复杂基本现象。此外，这些发现为增强声音控制和操纵的新技术提供了一条直接途径。