The higher-order topological phases have attracted intense attention in the past years, which reveals various intriguing topological properties. Meanwhile, the enrichment of group symmetries with projective symmetry algebras redefines the fundamentals of topological matter and makes Stiefel-Whitney (SW) classes in classical wave systems possible. Here, we report the experimental realization of higher-order topological nodal loop semimetal in an acoustic system and obtain the inherent SW topological invariants. In stark contrast to higher-order topological semimetals relating to complex vector bundles, the hinge and surface states in the SW topological phase are protected by two distinctive SW topological charges relevant to real vector bundles. Our findings push forward the studies of SW class topology in classical wave systems, which also show possibilities in robust high-$Q$-resonance-based sensing and energy harvesting.

中文翻译：

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声学高阶拓扑 Stiefel-Whitney 半金属演示

高阶拓扑相在过去几年中引起了人们的强烈关注，它揭示了各种有趣的拓扑性质。同时，群对称性与射影对称代数的丰富重新定义了拓扑物质的基础，并使经典波系中的斯蒂菲尔-惠特尼（SW）类成为可能。在这里，我们报告了声学系统中高阶拓扑节点环半金属的实验实现，并获得了固有的 SW 拓扑不变量。与复杂向量丛相关的高阶拓扑半金属形成鲜明对比，SW拓扑相中的铰链和表面态受到与实向量丛相关的两个独特的SW拓扑荷的保护。我们的研究结果推动了经典波系统中 SW 类拓扑的研究，这也表明了鲁棒高波系统的可能性。$问$-基于共振的传感和能量收集。