Understanding fragile topology Exploiting topological features in materials is being pursued as a route to build in robustness of particular properties. Stemming from crystalline symmetries, such topological protection renders the properties robust against defects and provides a platform of rich physics to be studied. Recent developments have revealed the existence of so-called fragile topological phases, where the means of classification due to symmetry is unclear. Z.-D. Song et al. and Peri et al. present a combined theoretical and experimental approach to identify, classify, and measure the properties of fragile topological phases. By invoking twisted boundary conditions, they are able to describe the properties of fragile topological states and verify the expected experimental signature in an acoustic crystal. Understanding how fragile topology arises could be used to develop new materials with exotic properties. Science, this issue p. 794, p. 797 A better understanding of fragile topological phases could lead to the development of materials with exotic properties. Symmetries crucially underlie the classification of topological phases of matter. Most materials, both natural as well as architectured, possess crystalline symmetries. Recent theoretical works unveiled that these crystalline symmetries can stabilize fragile Bloch bands that challenge our very notion of topology: Although answering to the most basic definition of topology, one can trivialize these bands through the addition of trivial Bloch bands. Here, we fully characterize the symmetry properties of the response of an acoustic metamaterial to establish the fragile nature of the low-lying Bloch bands. Additionally, we present a spectral signature in the form of spectral flow under twisted boundary conditions.

中文翻译：

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声学超材料中脆弱拓扑的实验表征

理解脆弱拓扑 正在寻求利用材料中的拓扑特征作为建立特定属性稳健性的途径。源于晶体对称性，这种拓扑保护使得这些特性对缺陷具有强大的抵抗力，并提供了一个丰富的物理研究平台。最近的发展揭示了所谓的脆弱拓扑相的存在，其中由于对称性而导致的分类方法尚不清楚。Z.-D。宋等人。和佩里等人。提出了一种结合理论和实验的方法来识别、分类和测量脆弱拓扑相的特性。通过调用扭曲边界条件，他们能够描述脆弱拓扑状态的特性并验证声学晶体中的预期实验特征。了解脆弱拓扑是如何产生的，可用于开发具有奇异特性的新材料。科学，这个问题 p。794 页。797 更好地了解脆弱的拓扑相可能会导致具有奇异特性的材料的开发。对称性是物质拓扑相分类的关键基础。大多数材料，无论是天然材料还是建筑材料，都具有晶体对称性。最近的理论工作表明，这些晶体对称性可以稳定脆弱的 Bloch 带，这对我们的拓扑学概念提出了挑战：虽然回答了拓扑学的最基本定义，但可以通过添加平凡的 Bloch 带来使这些带变得不重要。这里，我们充分表征了声学超材料响应的对称特性，以确定低洼布洛赫带的脆弱性。此外，我们在扭曲边界条件下以光谱流的形式呈现光谱特征。