Topological Phases Protected by Point Group Symmetry

By Hao Song, Sheng-Jie Huang, Liang Fu, M. Hermele. 2016

166 citations recorded by the source corpus.

We consider symmetry protected topological (SPT) phases with crystalline point group symmetry, dubbed point group SPT (pgSPT) phases. We show that such phases can be understood in terms of lower-dimensional topological phases with on-site symmetry, and can be constructed as stacks and arrays of these lower-dimensional states. This provides the basis for a general framework to classify and characterize bosonic and fermionic pgSPT phases, that can be applied for arbitrary crystalline point group symmetry and in arbitrary spatial dimension. We develop and illustrate this framework by means of a few examples, focusing on three-dimensional states. We classify bosonic pgSPT phases and fermionic topological crystalline superconductors with $Z_2^P$ (reflection) symmetry, electronic topological crystalline insulators (TCIs) with ${\rm U}(1) \times {Z}_2^P$ symmetry, and bosonic pgSPT phases with $C_{2v}$ symmetry, which is generated by two perpendicular mirror reflections. We also study surface properties, with a focus on gapped, topologically ordered surface states. For electronic TCIs we find a $Z_8 \times Z_2$ classification, where the $Z_8$ corresponds to known states obtained from non-interacting electrons, and the $Z_2$ corresponds to a "strongly correlated" TCI that requires strong interactions in the bulk. Our approach may also point the way toward a general theory of symmetry enriched topological (SET) phases with crystalline point group symmetry.

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

View Paper: https://www.semanticscholar.org/paper/a412697685de4ce2c683aa670feedd268d442afc

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. Luka Trifunovic
2. P. Brouwer
3. Ashvin Vishwanath
4. E. Khalaf
5. Ryan Thorngren
6. H. Po
7. Chong Wang
8. R. Ma

In Condensed Matter Physics

1. Luka Trifunovic
2. P. Brouwer
3. Ryan Thorngren
4. R. Ma
5. Chong Wang
6. D. Else
7. H. Po
8. Ashvin Vishwanath

Citations in the corpus

• Higher-Order Bulk-Boundary Correspondence for Topological Crystalline Phases (2018, background): “[48,53,54,63] is a realization of the order-raising homomorphism.”
• Average Symmetry-Protected Topological Phases (2022, background): “In real space, this state can be adiabatically deformed to a particularly simple limit[20]: on the mirror reflection plane z = 0, we decorate an integer quantum Hall (IQHE) state with σxy = 1, and on the other reflection-invariant plane at z = L/2 ∼ −L/2 (where L is the system size, and periodic bou”
• Gauging spatial symmetries and the classification of topological crystalline phases (2016, background): “[55], there should be a Z2 ⊕ Z2 classification corresponding to the residual Z2 charges at the two fixed points (see Fig.”
• Symmetry Indicators and Anomalous Surface States of Topological Crystalline Insulators (2017, background): “Curiously, on more general grounds, it has been suggested that many, if not all, crystalline symmetry-protected topological phases can be understood in terms of a similar construction, upon the replacement of lattice translation by other crystalline symmetries [16,23,38,39,41,42].”