包含超越最近邻相互作用的一维晶格中常规卷绕数计算的失效
Breakdown of Conventional Winding Number Calculation in One-Dimensional Lattices with Interactions Beyond Nearest Neighbors
AI总结：
本文理论与实验证明在含超越最近邻相互作用的机械SSH模型中，TPDWSs数量可高于卷绕数，导致常规预测失效，并提出利用Berry connection实现精确表征。
摘要：
拓扑绝缘体有望在电子、光子和声子系统中实现新奇的量子现象。传统上，拓扑指数（如卷绕数）被用于预测拓扑绝缘体中受拓扑保护的畴壁态（TPDWSs）的数量，这是被称为体边对应的拓扑现象的标志。在此，我们从理论和实验上证明，在机械Su-Schrieffer-Heeger（SSH）模型中，TPDWSs的数量可以高于卷绕数，这取决于超越最近邻相互作用的强度，揭示了卷绕数预测的失效。或者，我们借助Berry connection来准确表征SSH系统中TPDWSs的数量和空间特征，这进一步被Jackiw-Rebbi理论所证实，证明多个TPDWSs对应于体Dirac cones。我们的发现加深了对复杂网络动力学的理解，并为涉及局部振动的潜在应用（如药物递送和量子计算）中精确预测TPDWS提供了广义范式。
英文摘要：
Topological insulators hold promises to realize exotic quantum phenomena in electronic, photonic, and phononic systems. Conventionally, topological indices, such as winding numbers, have been used to predict the number of topologically protected domain-wall states (TPDWSs) in topological insulators, a signature of the topological phenomenon called bulk-edge correspondence. Here, we demonstrate theoretically and experimentally that the number of TPDWSs in a mechanical Su-Schrieffer-Heeger (SSH) model can be higher than the winding number depending on the strengths of beyond-nearest-neighbor interactions, revealing the breakdown of the winding number prediction. Alternatively, we resort to the Berry connection to accurately characterize the number and spatial features of TPDWSs in SSH systems, further confirmed by the Jackiw-Rebbi theory proving that the multiple TPDWSs correspond to the bulk Dirac cones. Our findings deepen the understanding of complex network dynamics and offer a generalized paradigm for precise TPDWS prediction in potential applications involving localized vibrations, such as drug delivery and quantum computing.
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