The lattice geometry induced second-order topological corner states in breathing Kagome lattice have attracted enormous research interests, while the realistic breathing Kagome materials identified as second-order topological insulators are still lacking. Here, we report by first-principles calculations the second-order topological states emerging in two-dimensional d-orbital breathing Kagome crystals, i.e., monolayer niobium/tantalum chalcogenide halides M₃QX₇ (M = Nb, Ta; Q = S, Se, Te; X = Cl, Br, I). We find that the orbital degree of freedom of d orbitals can give rise to multiple sets of corner states. Combining fraction corner anomaly, orbital components and real space distribution of the corner states, we can also identify the topology of these corner states. Our work not only extends the lattice geometry induced second-order topological states to realistic materials, but also builds a clear and complete picture on their multiple sets of second-order topological states.

呼吸 Kagome 晶格中的晶格几何诱导二阶拓扑角态引起了巨大的研究兴趣，而被确定为二阶拓扑绝缘体的真实呼吸 Kagome 材料仍然缺乏。在这里，我们通过第一性原理计算报告二维d轨道呼吸 Kagome 晶体中出现的二阶拓扑状态，即单层铌/钽硫族化物卤化物 M ₃ QX ₇（M = Nb，Ta；Q = S， Se、Te；X = Cl、Br、I)。我们发现d的轨道自由度轨道可以产生多组角态。结合分数角异常、轨道分量和角态的实空间分布，我们还可以识别这些角态的拓扑结构。我们的工作不仅将晶格几何诱导的二阶拓扑状态扩展到现实材料，而且在它们的多组二阶拓扑状态上建立了清晰和完整的图像。