发表机构
Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所引力物理与量子信息中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文为具有二重旋转和时间反演对称性的二维自旋绝缘体提出离散的Z2不变量，基于第二Stiefel-Whitney数，并证明其规范不变性，与Kane-Mele指标区分，完善稳定分类。
AI 中文摘要
我们回顾了Stiefel-Whitney不变量，并给出了二维自旋绝缘体在二重旋转和时间反演对称性（层群$p1121'$）下的一个额外$\mathbb{Z}_2$不变量的离散表述。一个奇异规范变换指定了布里渊环面商空间上的一个实向量丛，其第二Stiefel-Whitney数定义了该不变量。我们推导了该不变量对辅助规范函数选择的依赖性，并证明了它在布洛赫标架变化下的不变性以及在直和下的可加性。离散公式使用独立选择的布洛赫标架的重叠以及半布里渊区边界上对称兼容的$\mathrm{Pin}_+$提升。原子和拓扑绝缘体模型说明了该公式，并将该额外不变量与Kane-Mele指标区分开来。连同三个量子化的$\mathbb{Z}_2$部分极化和填充数，它标记了已知的稳定分类$\mathbb{Z}\oplus\mathbb{Z}_2^{\oplus 4}$。
英文摘要
We review Stiefel--Whitney invariants and give a discrete formulation of an additional $\mathbb{Z}_2$ invariant for two-dimensional spinful insulators with twofold rotation and time-reversal symmetries (layer group $p1121'$). A singular gauge transformation specifies a real bundle over the quotient of the Brillouin torus, whose second Stiefel--Whitney number defines the invariant. We derive its dependence on the choice of auxiliary gauge function and prove invariance under changes of Bloch frame and additivity under direct sums. The discrete formula uses overlaps of independently chosen Bloch frames and symmetry-compatible $\mathrm{Pin}_+$ lifts on the boundary of a half Brillouin zone. Atomic and topological-insulator models illustrate the formula and distinguish the additional invariant from the Kane--Mele index. Together with three quantized $\mathbb{Z}_2$ partial polarizations and the filling number, it labels the known stable classification $\mathbb{Z}\oplus\mathbb{Z}_2^{\oplus 4}$.
Comments24 pages
