  We study graphene antidot lattices (GALs) in magnetic fields. Using a
tight-binding model and a recursive Green's function technique that we extend
to deal with periodic structures, we calculate Hofstadter butterflies of GALs.
We compare the results to those obtained in a simpler gapped graphene model. A
crucial difference emerges in the behaviour of the lowest Landau level, which
in a gapped graphene model is independent of magnetic field. In stark contrast
to this picture, we find that in GALs the band gap can be completely closed by
applying a magnetic field. While our numerical simulations can only be
performed on structures much smaller than can be experimentally realized, we
find that the critical magnetic field for which the gap closes can be directly
related to the ratio between the cyclotron radius and the neck width of the
GAL. In this way, we obtain a simple scaling law for extrapolation of our
results to more realistically sized structures and find resulting quenching
magnetic fields that should be well within reach of experiments.
