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… 

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