DataSheet1_Ideal hourglass nodal loop state in the monolayer lithium hydrosulfide.docx

In recent years, the exploration of topological states within two-dimensional materials has emerged as a compelling focus, complementing their three-dimensional counterparts. Through theoretical calculations, we unveil the exceptional topological state in the monolayer lithium hydrosulfide, where an ideal hourglass nodal loop is identified. Notably, this nodal loop is characterized by only four bands, representing the simplest configuration for realizing hourglass dispersion. We provide detailed symmetry arguments alongside model calculations to elucidate the formation mechanism of the nodal loop and its corresponding hourglass dispersion. Moreover, the associated edge states are not only well-separated from the bulk band projection but also persist consistently throughout the Brillouin zone. Due to the lightweight constitutive elements of this material, both the hourglass dispersion and the edge states remain robust even in the presence of spin-orbit coupling. To enhance its practical applicability, we have evaluated various mechanical parameters, analyzing their anisotropic behaviors. Furthermore, we examined the material’s response to strain conditions under both compressive and tensile stress, uncovering distinct variations in energy, size, and the hourglass dispersion of the nodal loop. Overall, the hourglass nodal loop state explored in this study, along with the proposed material candidate, provides a strong foundation for future experimental investigations. This research potentially paves the way for significant advancements within this emerging field.

近年来，二维材料中的拓扑态（topological states）研究已成为备受瞩目的前沿热点，作为三维对应体系的重要补充。本研究通过理论计算，在单层硫氢化锂（monolayer lithium hydrosulfide）中揭示了一种独特的拓扑态，其中存在理想的沙漏形节线环（hourglass nodal loop）。值得注意的是，该节线环仅由四条能带构成，是实现沙漏型色散的最简构型。我们结合详尽的对称性分析与模型计算，阐明了该节线环的形成机制及其对应的沙漏型色散特性。此外，其关联的边缘态不仅与体带投影实现了良好分离，且在整个第一布里渊区（Brillouin zone）中始终稳定存在。由于该材料的组成元素质量较轻，即使考虑自旋轨道耦合（spin-orbit coupling），沙漏型色散与边缘态仍能保持鲁棒性。为提升其实际应用潜力，我们评估了多种力学参数，并分析了其各向异性行为。进一步地，我们还研究了该材料在压应力与拉应力下的应变响应，揭示了节线环的能量、尺寸以及沙漏型色散均发生了显著变化。总体而言，本研究中探索的沙漏形节线环态与所提出的候选材料，为后续实验研究奠定了坚实基础，有望为该新兴领域的重大进展开辟道路。