旋转拓扑态：理论与材料实现
Rotation topological states: theory and material realization
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中文总结 AI 辅助
研究旋转对称性系统中拓扑态，通过希尔伯特空间分解提出新型\(\mathbb{Z}_2^n\)拓扑不变量理论，以体相CsCl为例，经计算和分析表明其有非平凡拓扑不变量及表面双Weyl点，该不变量可细化对称保护拓扑相，助于发现被忽略的拓扑态。
中文摘要 AI 辅助
传统拓扑材料表征依赖于占据能带计算拓扑不变量。当系统具有旋转对称性时，占据希尔伯特空间可分解为多个由不同旋转本征值标记的子空间。我们表明这种分解揭示了由新型\(\mathbb{Z}_2^n\)拓扑不变量表征的隐藏拓扑态，传统\(\mathbb{Z}_2\)不变量可能无法检测到旋转子空间中的拓扑。时间反演对称性使共轭旋转本征值配对，保证两个子空间有相同\(\mathbb{Z}_2\)不变量，使拓扑对传统全局不变量总是隐藏的。我们阐述了旋转子空间拓扑理论，并在体相CsCl中展示其材料实现。通过第一性原理计算和对称性分析表明，传统方法诊断为拓扑平凡的体相CsCl，沿\(\Gamma\)-R路径具有非平凡\(\mathbb{Z}_2^3\)不变量，沿\(\Gamma\)-Z和M-R路径具有非平凡\(\mathbb{Z}_2^4\)不变量，分别在(111)和(001)表面导致双Weyl点。这里提出的子空间\(\mathbb{Z}_2^n\)不变量是对称保护拓扑相的必要细化，将有助于识别现有诊断忽略的一大类拓扑态。
英文摘要
The conventional characterization of topological materials relies on topological invariants calculated from the entire set of occupied bands. However, when a system possesses rotational symmetry, the occupied Hilbert space can be decomposed into multiple subspaces labeled by distinct rotation eigenvalues. We show that this decomposition reveals hidden topological states characterized by a novel $\mathbb{Z}_2^n$ topological invariant, where $n$ is the number of subspaces, while the conventional $\mathbb{Z}_2$ invariant may fail to detect the topology hidden in the rotation subspaces. Remarkably, time-reversal symmetry pairs conjugate rotation eigenvalues and guarantees that the two subspaces have the same $\mathbb{Z}_2$ invariants, making the topology always hidden from the conventional global invariant. We formulate the theory of rotation-subspace topology and demonstrate its material realization in bulk CsCl. Using first-principles calculations and symmetry analysis, we show that bulk CsCl, which is diagnosed as topologically trivial by the conventional approach, features a nontrivial $\mathbb{Z}_2^3$ invariant along the $Γ$-R path and a nontrivial $\mathbb{Z}_2^4$ invariant along the $Γ$-Z and M-R paths, leading to double Weyl points on the (111) and (001) surfaces, respectively. The subspace $\mathbb{Z}_2^n$ invariant proposed here serves as a necessary refinement for symmetry-protected topological phases and will facilitate the identification of a large class of topological states overlooked by existing diagnostics.
