# Symmetry-protected topological Hopf insulator and its generalizations

@article{Liu2016SymmetryprotectedTH, title={Symmetry-protected topological Hopf insulator and its generalizations}, author={Chunxiao Liu and Farzan Vafa and Cenke Xu}, journal={Physical Review B}, year={2016}, volume={95}, pages={161116} }

The tenfold way classification of noninteracting topological insulators represents a great success towards understanding topological states of matter. The question the authors try to address is: can all possible topological insulators be represented by the prototypes in the tenfold way classification (perhaps enriched with some extra symmetries), or are there exceptions fundamentally different from those prototypes? The Hopf insulator was considered as a special type of TI that is not obviously…

## 34 Citations

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- 2017

Topological phases of matter have been among the most active research subjects in condensed matter physics. They can be broadly classified as two major classes. The first class of phases, including…

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Abstract Topological insulators constitute one of the most intriguing phenomena in modern condensed matter theory. The unique and exotic properties of topological states of matter allow for…

## References

SHOWING 1-5 OF 5 REFERENCES

### Fractional statistics and anyon superconductivity

- Physics
- 1990

The occurrence of fractional statistics has been discovered in more and more quantum field theory models, including some of the most geometrical and canonical ones. In a remarkable case, the…

### Science 294

- 823
- 2001

### New J

- Phys. 12, 065010
- 2010

### Algebraic Topology (Cambridge

- 2002

### Annals of Mathematics 49

- 471
- 1948