Projective symmetry in hexagonal lattices with rational magnetic flux enforces novel non-zero-energy Dirac touchings at pi flux, constrains zero-energy Dirac points for general fluxes, and imposes distinct Chern number rules on gapped bands and multiplets.
Beyond the regime ||ti|q − |t j|q| ≤ |t k|q ≤ ||t i|q +|t j|q||, we only need to break theT 2 translation symmetry to gap the bands at E̸= 0
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Topological constraints on the electronic band structure of hexagonal lattice in a magnetic field
Projective symmetry in hexagonal lattices with rational magnetic flux enforces novel non-zero-energy Dirac touchings at pi flux, constrains zero-energy Dirac points for general fluxes, and imposes distinct Chern number rules on gapped bands and multiplets.