Energy gap of Kronig-Penney-type hydrogenated graphene superlattices

The electronic structure of graphene-graphane superlattices with armchair interfaces is investigated with first-principles density-functional theory. By separately varying the widths, we find that the energy gap Eg is inversely proportional to the width of the graphene strip and that the gap increases as the hydrogenated strip becomes wider due to the enhanced confinement effect. It is further demonstrated that, unlike other graphene nanostructures, the superlattices exhibit both direct and indirect band gaps without external perturbations. This peculiarity in the nature of Eg originates from the different connection structures of the symmetrized wave function at the boundary between adjacent unit cells due to the reflection symmetry of the superlattices. These findings suggest that the optical as well as electronic properties of graphene superlattices can be controlled through selective chemical functionalization.