Topological constraints on the electronic band structure of a hexagonal lattice in a magnetic field

The impact of projective lattice symmetry on electronic band structures has attracted significant attention in recent years, particularly in light of growing experimental studies of two-dimensional hexagonal materials in magnetic fields. Yet, most theoretical work to date has focused on the square lattice due to its relative simplicity. In this work, we investigate the role of projective lattice symmetry in a hexagonal lattice with rational magnetic flux, emphasizing the resulting topological constraints on the electronic band structure. We show that, at pi flux, the symmetry in the hexagonal lattice enforces novel Dirac band touchings at E not equal to zero, and for general rational flux it constrains the number of Dirac points at E = 0. We further analyze the symmetry-imposed constraints on the Chern numbers of both isolated gapped bands and band multiplets connected by Dirac-point touchings. Our results demonstrate that these constraints in the hexagonal lattice differ substantially from those in the square lattice.