论文标题
pfaffian不变性识别磁阻塞的原子绝缘子
Pfaffian invariant identifies magnetic obstructed atomic insulators
论文作者
论文摘要
我们得出了一个$ \ mathbb {z} _4 $拓扑不变的，它延伸了超出对称性特征值和威尔逊循环，并用$ C_4 \ Mathcal {t} $ Symmetry对二维绝缘子进行分类。为了制定这个不变的，我们考虑了一个不可还原的布里渊区，并限制了构成其边界的开放式威尔逊线的光谱。我们通过在高对称力臂上使用Pfaffian来固定威尔逊线的量规歧义。结果，我们区分了四个$ C_4 \ MATHCAL {T} $ - 受保护的原子绝缘子，每个绝缘子都绝热连接到不同的原子限制。我们通过构建原子极限哈密顿量和$ C_4 \ Mathcal {t} $ - 对称模型，建立不变相位和阻塞相之间的对应关系。该相图显示，$ C_4 \ Mathcal {T} $绝缘子允许$ \ pm 1 $和$ 2 $变化的变化，其中后者被对称指标忽略了。
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.
