Pfaffian不变量识别磁性受阻原子绝缘体
Pfaffian invariant identifies magnetic obstructed atomic insulators
AI总结：
本文提出基于Pfaffian的$\mathbb{Z}_4$拓扑不变量，通过约束不可约布里渊区边界开放Wilson线谱，识别四种受$C_4\mathcal{T}$保护的磁性受阻原子绝缘体。
摘要：
我们推导了一个超越对称本征值和Wilson回路的$\mathbb{Z}_4$拓扑不变量，用于对具有$C_4 \mathcal{T}$对称性的二维绝缘体进行分类。为构建该不变量，我们考虑一个不可约布里渊区，并约束构成其边界的开放Wilson线的谱。我们利用高对称动量处的Pfaffian来消除Wilson线的规范歧义。由此，我们区分了四种受$C_4 \mathcal{T}$保护的原子绝缘体，每一种都绝热连接到不同的原子极限。我们通过构建原子极限哈密顿量以及在它们之间插值的$C_4 \mathcal{T}$对称模型，建立了不变量与受阻相之间的对应关系。相图表明，$C_4 \mathcal{T}$绝缘体允许不变量发生$\pm 1$和$2$的变化，其中后者被对称指标所忽略。
英文摘要：
We derive a $\mathbb{Z}_4$ topological invariant that extends beyond symmetry eigenvalues and Wilson loops and classifies two-dimensional insulators with a $C_4 \mathcal{T}$ symmetry. To formulate this invariant, we consider an irreducible Brillouin zone and constrain the spectrum of the open Wilson lines that compose its boundary. We fix the gauge ambiguity of the Wilson lines by using the Pfaffian at high symmetry momenta. As a result, we distinguish the four $C_4 \mathcal{T}$-protected atomic insulators, each of which is adiabatically connected to a different atomic limit. We establish the correspondence between the invariant and the obstructed phases by constructing both the atomic limit Hamiltonians and a $C_4 \mathcal{T}$-symmetric model that interpolates between them. The phase diagram shows that $C_4 \mathcal{T}$ insulators allow $\pm 1$ and $2$ changes of the invariant, where the latter is overlooked by symmetry indicators.
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