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, particularly the translation, rotational, and sublattice symmetries, 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 projective lattice symmetry in the hexagonal lattice enforces Dirac band touchings at $E\ne 0$, 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.

Close

PrevNext

View figure in article

• Hexagonal close-packed
• Topological materials
• Band structure methods
• Projective symmetries