发表机构
School of Physics, Peking University（北京大学物理学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究三维\(S_4\)对称轴子绝缘体中轴子不变量与\(S_4\)对称指标的等价性，通过陈 - 西蒙斯表达式等方法，经稳定约化、计算映射度等步骤，用最小紧束缚模型验证，弥合理论差距并扩展等价性。
AI 中文摘要
对于三维陈数为零的\(S_4\)对称轴子绝缘体，建立了轴子不变量与\(S_4\)对称指标之间的等价性。从磁电极化率的陈 - 西蒙斯表达式出发，\(2P_3 = \theta / \pi\)用\(S_4\)缝合矩阵重写。稳定约化到行列式为一的双带块后，不变量表示为从布里渊区到\(SU(2)\)的映射度。通过\(S_4\)在四个\(S_4\)不变动量处的本征值计算度模二，并证明其与对称指标\(z_2\)一致。一个最小紧束缚模型验证了\(2P_3\)与\(z_2\)之间的对应关系。该结果弥合了轴子响应的拓扑场论描述与对称指标的拓扑能带论分类之间的差距，并将已知的响应 - 指标等价性从反酉设置扩展到酉的、取向反转的旋转反演对称\(S_4\)。
英文摘要
The equivalence between the axion invariant and the $S_4$ symmetry indicator is established for three-dimensional $S_4$-symmetric axion insulators with vanishing three-dimensional Chern numbers. Starting from the Chern-Simons expression for the magnetoelectric polarizability, $2P_3=θ/π$ is rewritten in terms of the $S_4$ sewing matrix. After stable reduction to determinant-one two-band blocks, the invariant is expressed as the degree of a map from the Brillouin zone to $SU(2)$. The degree modulo two is then evaluated from the $S_4$ eigenvalues at the four $S_4$-invariant momenta and is shown to coincide with the symmetry indicator $z_2$. A minimal tight-binding model with $S_4$ symmetry verifies the correspondence between $2P_3$ and $z_2$ throughout its phase diagram. The result closes a gap between the topological-field-theory description of the axion response and the topological-band-theory classification by symmetry indicators. It also extends the known response-indicator equivalence from antiunitary settings such as $C_nT$ symmetry to the unitary, orientation-reversing roto-inversion symmetry $S_4$.
Comments21 pages, 6 figures
