Squaring the fermion: The threefold way and the fate of zero modes

@article{Xu2020SquaringTF,
  title={Squaring the fermion: The threefold way and the fate of zero modes},
  author={Qiao-Ru Xu and Vincent P. Flynn and Abhijeet Alase and Emilio Cobanera and Lorenza Viola and Gerardo Guzman Ortiz},
  journal={Physical Review B},
  year={2020},
  volume={102},
  pages={125127}
}
In the spirit of Dirac's derivation of a fermionic theory by ``taking the square root'' of the bosonic Klein-Gordon equation, the authors present here a squaring procedure, mapping fermionic to bosonic theories, that helps establish a threefold-way topological classification of stable noninteracting bosonic matter. The ephemeral nature of boundary states and the topological triviality of noninteracting, zero-temperature bosonic phases are supported by three no-go theorems, although excitations… 
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