  The band gap of periodically-doped graphene with hydrogen is investigated. It
is found through a tight-binding model (TB) that for certain periodicities,
called here NGPs (non-gap periodicities), no gap is opened at the Dirac point.
This result is confirmed by Density Functional Theory (DFT) calculations. DFT
results show that a tiny gap is opened for NGPs due to exchange effects, not
taken into account in the TB model. However, this tiny gap is one or two orders
of magnitude smaller than the gap opened for other periodicities different from
NGPs. This finding opens up a new path for band gap engineering experiments in
graphene.
