We study positions of chiral hinge states in higher-order topological insulators (HOTIs) with inversion symmetry. First, we exhaust all possible configurations of the hinge states in the HOTIs in all type-I magnetic space groups with inversion symmetry by studying dependence of the sign of the surface Dirac mass on surface orientations. In particular, in the presence of glide symmetry, for particular surface orientations, the surface Dirac mass changes sign by changing the surface terminations. By applying this result to a layered antiferromagnet, we find a difference in the hinge states between the cases with an even and odd number of layers. In the case of an even number of layers, which does not preserve inversion symmetry, positions of hinge states are not inversion symmetric. Nonetheless, these inversion-asymmetric hinge states result from the bulk topology. We show that their inversion-asymmetric configurations are uniquely determined from the symmetries and the topological invariant.

中文翻译：

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Z4保护的拓扑手性铰链态的反演理论及其在层状反铁磁体中的应用

我们研究具有反演对称性的高阶拓扑绝缘体（HOTI）中的手性铰链状态的位置。首先，通过研究表面狄拉克质量的符号对表面取向的依赖性，我们以反对称性穷尽了所有I型磁性空间群中HOTI中铰链状态的所有可能构型。特别地，在滑行对称存在的情况下，对于特定的表面取向，表面狄拉克质量通过改变表面终端来改变符号。通过将此结果应用于分层反铁磁体，我们发现在具有偶数层和奇数层的情况下，铰链状态之间存在差异。在偶数层的情况下，其不保持反转对称性，铰链状态的位置不是反转对称的。尽管如此，这些反不对称的铰链状态是由于体拓扑结构导致的。我们表明，它们的反演非对称构型是由对称性和拓扑不变性唯一确定的。