Adsorption of Hydrogen in Graphene without Band Gap Opening at the Dirac Point

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.