Classification of topological insulators and superconductors in the presence of reflection symmetry
Classification of topological insulators and superconductors in the presence of reflection symmetry
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DOI：
10.1103/physrevb.88.075142
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发表时间：
2013-08-26
影响因子：
3.7
通讯作者：
Ryu, Shinsei
中科院分区：
文献类型：
--
作者：
Chiu, Ching-Kai;Yao, Hong;Ryu, Shinsei
我们讨论的拓扑分类的绝缘体和超导体中存在的两个（非空间）离散对称性的Altland-Zirnbauer分类和空间反射对称性在任何空间维度。通过使用最小矩阵维数的Dirac Hamilton体的结构和拓扑不变量的显式构造，我们提供了完整的分类，它仍然具有与原始Altland-Zirnbauer分类相同的维数周期性.反射对称保护拓扑绝缘体和超导体的分类关键取决于反射对称操作的实现方式。当引入一个边界，这是反映到自己，这些非平凡的拓扑绝缘体和超导体支持本地化的边界处的无隙模式。
We discuss a topological classification of insulators and superconductors in the presence of both (nonspatial) discrete symmetries in the Altland-Zirnbauer classification and spatial reflection symmetry in any spatial dimensions. By using the structure of bulk Dirac Hamiltonians of minimal matrix dimensions and explicit constructions of topological invariants, we provide the complete classification, which still has the same dimensional periodicities with the original Altland-Zirnbauer classification. The classification of reflection-symmetry-protected topological insulators and superconductors depends crucially on the way reflection symmetry operation is realized. When a boundary is introduced, which is reflected into itself, these nontrivial topological insulators and superconductors support gapless modes localized at the boundary.