# Stability of zero energy Dirac touchings in the honeycomb Hofstadter problem

## TL;DR

This paper investigates the stability of zero energy Dirac points in the band structure of electrons on a honeycomb lattice under magnetic flux, revealing symmetry conditions that protect these touchings.

## Contribution

It demonstrates that Dirac touchings are protected by anti-unitary particle-hole symmetry and lattice symmetries, and analyzes their robustness to symmetry-lowering perturbations.

## Key findings

- Dirac touchings are guaranteed by combined symmetry conditions.
- Locations of Dirac points are symmetry-dependent.
- Dirac points exhibit stability under certain perturbations.

## Abstract

We study the band structure of electrons hopping on a honeycomb lattice with 1/q (q integer) flux quanta through each elementary hexagon. In the nearest neighbor hopping model the two bands that eventually form the n = 0 Landau level have 2q zero energy Dirac touchings. In this work, we study the conditions needed for these Dirac points and their stability to various perturbations. We prove that these touchings and their locations are guaranteed by a combination of an anti-unitary particle-hole symmetry and the lattice symmetries of the honeycomb structure. We also study the stability of the Dirac touchings to one-body perturbations that explicitly lower the symmetry.