Topological classification with additional symmetries from Clifford algebras
Topological classification with additional symmetries from Clifford algebras
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DOI：
10.1103/physrevb.88.125129
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发表时间：
2013-09-20
影响因子：
3.7
通讯作者：
Furusaki, Akira
中科院分区：
文献类型：
--
作者：
Morimoto, Takahiro;Furusaki, Akira
我们分类拓扑绝缘体和超导体在存在额外的对称性，如反射或镜像对称。对于10个Altland-Zirnbauer对称类的每一个成员，我们都有一个Clifford代数，它由一般（时间反演、粒子-空穴或手征）对称性和其他对称性的算子定义，以及代表拓扑绝缘体和超导体的狄拉克哈密顿量中的伽马矩阵。遵循Kitaev的方法，我们通过检查所有可能的不同狄拉克质量项，可以添加到Clifford代数的发电机集合中，对非相互作用的费米子在额外的对称性下的带隙相位进行分类。我们发现，施加额外的对称性的效果改变对称类，并导致拓扑绝缘体和超导体的周期表中的变化。我们的结果与Chiu，Yao和Ryu最近报道的反射对称下的分类一致[Phys. Rev. B 88，075142（2013）]。几个例子进行了讨论，包括拓扑晶体绝缘体与镜像陈数和镜像超导体。
We classify topological insulators and superconductors in the presence of additional symmetries such as reflection or mirror symmetries. For each member of the 10 Altland-Zirnbauer symmetry classes, we have a Clifford algebra defined by operators of the generic (time-reversal, particle-hole, or chiral) symmetries and additional symmetries, together with gamma matrices in Dirac Hamiltonians representing topological insulators and superconductors. Following Kitaev's approach, we classify gapped phases of noninteracting fermions under additional symmetries by examining all possible distinct Dirac mass terms which can be added to the set of generators of the Clifford algebra. We find that imposing additional symmetries in effect changes symmetry classes and causes shifts in the periodic table of topological insulators and superconductors. Our results are in agreement with the classification under reflection symmetry recently reported by Chiu, Yao, and Ryu [Phys. Rev. B 88, 075142 (2013)]. Several examples are discussed including a topological crystalline insulator with mirror Chern numbers and mirror superconductors.