论文标题
使用受$ K $ - 理论启发的实验协议在金属中揭示拓扑
Revealing Topology in Metals using Experimental Protocols Inspired by $K$-Theory
论文作者
论文摘要
拓扑金属是带有无间隙带结构和非平凡边缘环境共振的特殊导电材料，其发现证明是难以捉摸的，因为在这种情况下，传统的拓扑分类方法不适用。受到最新理论发展的启发，即从$ c^*$ - 代数的领域利用技术来识别拓扑金属\ cite {cerjan_local_2021}，在这里，我们直接观察到无差异的声学晶体中的拓扑现象，并提供了一般的实验技术来证明其拓扑。具体而言，我们不仅观察到拓扑声学金属中的鲁棒边界局部化状态，而且还重新解释了一个复合算子，从数学上衍生出源自问题的K理论，作为一个新的哈米尔顿人，其物理实现使我们能够直接观察拓扑光谱流并测量拓扑不变的拓扑。我们的观察结果和实验方案可能会为发现缺乏散装带隙的各种人造和天然材料的拓扑行为提供见解。
Topological metals are special conducting materials with gapless band structures and nontrivial edge-localized resonances, whose discovery has proved elusive because the traditional topological classification methods do not apply in this context. Inspired by recent theoretical developments that leveraged techniques from the field of $C^*$-algebras to identify topological metals \cite{cerjan_local_2021}, here, we directly observe topological phenomena in gapless acoustic crystals and provide a general experimental technique to demonstrate their topology. Specifically, we not only observe robust boundary-localized states in a topological acoustic metal, but also re-interpret a composite operator, mathematically derived from the K-theory of the problem, as a new Hamiltonian, whose physical implementation allows us to directly observe a topological spectral flow and measure the topological invariants. Our observations and experimental protocols may offer insights for discovering topological behavior across a wide array of artificial and natural materials that lack bulk band gaps.
