标题： $\mathbb{Z}_2$由格林函数对角零点得到的拓扑不变量 显示英文标题

标题： $\mathbb{Z}_2$ topological invariants from the Green's function diagonal zeros

摘要： 我们研究了格林函数的解析性质与$\mathbb{Z}_2$拓扑绝缘体之间的关系，重点放在三维反演对称系统上。我们表明，在轨道基底中，格林函数的对角零点提供了一种直接且直观的方法来计算强和弱$\mathbb{Z}_2$拓扑不变量。我们引入了布里渊区中对角零点交叉面的概念，并证明它将具有相反宇称的TRIM（时间反演不变动量）分隔开，在两能带模型中，这使得通过计数两侧的相关TRIM来直观地计算$\mathbb{Z}_2$不变量成为可能。在三能带系统中，除了在非平凡两能带系统的带隙中添加平凡能带的情况外，类似性质始终成立，这与脆弱拓扑绝缘体的带拓扑特性相呼应。我们的工作可能为利用ARPES测量实验测定$\mathbb{Z}_2$拓扑不变量开辟途径。 显示英文摘要

摘要： We investigate the relationship between the analytical properties of the Green's function and $\mathbb{Z}_2$ topological insulators, focusing on three-dimensional inversion-symmetric systems. We show that the diagonal zeros of the Green's function in the orbital basis provide a direct and visual way to calculate the strong and weak $\mathbb{Z}_2$ topological invariants. We introduce the surface of crossings of diagonal zeros in the Brillouin zone, and show that it separates TRIMs of opposite parity in two-band models, enabling the visual computation of the $\mathbb{Z}_2$ invariants by counting the relevant TRIMs on either side. In three-band systems, a similar property holds in every case except when a trivial band is added in the band gap of a non-trivial two-band system, reminiscent of the band topology of fragile topological insulators. Our work could open avenues to experimental measurements of $\mathbb{Z}_2$ topological invariants using ARPES measurements.