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We study the band structure of electrons hopping on a honeycomb lattice with1/q (q integer) flux quanta through each elementary hexagon. In the nearestneighbor hopping model the two bands that eventually form the n = 0 Landaulevel have 2q zero energy Dirac touchings. In this work, we study theconditions needed for these Dirac points and their stability to variousperturbations. We prove that these touchings and their locations are guaranteedby a combination of an anti-unitary particle-hole symmetry and the latticesymmetries of the honeycomb structure. We also study the stability of the Diractouchings to one-body perturbations that explicitly lower the symmetry.

Stability of zero energy Dirac touchings in the honeycomb Hofstadter problem