Topological classification with additional symmetries from Clifford algebras

By T. Morimoto, A. Furusaki. 2013

197 citations recorded by the source corpus.

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 non-interacting 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 et al. Several examples are discussed including a topological crystalline insulator with mirror Chern numbers and mirror superconductors.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/578e6a23d1548a67f6f7625dff9237897d6b561d

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In Atomic and Molecular Physics, and Optics

1. K. Kawabata
2. S. Higashikawa
3. Masahito Ueda
4. Z. Gong
5. Luka Trifunovic
6. K. Takasan
7. P. Brouwer
8. Yuto Ashida

In Condensed Matter Physics

1. K. Kawabata
2. Masahito Ueda
3. Z. Gong
4. Luka Trifunovic
5. P. Brouwer
6. Yuto Ashida

Citations in the corpus

• Topological Phases of Non-Hermitian Systems (2018, methodology): “For the latter two classes, we can construct Σðσ0 ⊗ ΓÞ 1⁄4 σz ⊗ Γ; this operator gives 1 upon squaring and commutes with all the elements in the original Clifford algebra excluding Σ, which implies that the topological number of classes BDI and CII simply gets doubled, since σz ⊗ Γ has two different”
• Higher-Order Bulk-Boundary Correspondence for Topological Crystalline Phases (2018, methodology): “Shiozaki and Sato [21] extend the tenfold-way classes to include an additional crystalline unitary symmetry [8,9,16], unitary antisymmetry, antiunitary symmetry, or antiunitary antisymmetry S.”