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Hydrogen adsorption on graphene in commensurate periodic arrangements leads to bandgap opening at the Dirac point and the emergence of dispersionless midgap bands. We study these bandgap effects and their dependence on periodicity for a single hydrogen adsorbate on periodic graphene supercells using spin-polarized density-functional theory calculations. Our results show that for certain periodicities, marked by a scale factor of three, the bandgap is suppressed to a great extent, and has a special level structure around the neutrality point. We present explanations for the origin of the changes to the band structure in terms of the ab initio Hamiltonian matrix. This method may be used to obtain a more accurate tight-binding description of single hydrogen adsorption on graphene.
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