  Devising ways of opening a band gap in graphene to make charge-carrier masses
finite is essential for many applications. Recent experiments with graphene on
hexagonal boron nitride (h-BN) offer tantalizing hints that the weak
interaction with the substrate is sufficient to open a gap, in contradiction of
earlier findings. Using many-body perturbation theory, we find that the small
observed gap is what remains after a much larger underlying quasiparticle gap
is suppressed by incommensurability. The sensitivity of this suppression to a
small modulation of the distance separating graphene from the substrate
suggests ways of exposing the larger underlying gap.
