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      Fragile Phases as Affine Monoids: Classification and Material Examples 

      Song, Zhi-Da; Elcoro Cengotitabengoa, Luis Angel ORCID; Xu, Yuan-Feng; Regnault, Nicolas; Bernevig, B. Andrei (American Physical Society, 2020-07-01)
      Topological phases in electronic structures contain a new type of topology, called fragile, which can arise, for example, when an elementary band representation (atomic limit band) splits into a particular set of bands. ...
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      Magnetic topological quantum chemistry 

      Elcoro Cengotitabengoa, Luis Angel ORCID; Wieder, Benjamin J.; Song, Zhi-Da; Xu, Yuan-Feng; Bradlyn, Barry; Bernevig, B. Andrei (Nature Research, 2021-10-13)
      [EN]The band topology of nonmagnetic crystals can be characterized by Topological Quantum Chemistry (TQC), whereas the band topology of magnetic crystals remains unexplored. Here, the authors extend TQC to the magnetic ...