We report our recent theoretical studies on adsorption of hydrogen atoms on graphene. The unique properties of the "defects" introduced in this way, i.e. the formation of midgap states and magnetic textures, are studied with density-functional-theory methods and analyzed with the help of tight-binding, Hubbard and resonating valence-bond models. They are used to show how and why clustering of H atoms occurs -in ordinary surface science conditions- at all but very low (< 1 %) concentrations.

On the other hand, we also show that controlled functionalization, if feasible, can be used to design novel nanoelectronic devices. This is the case, for example, of a novel class of H-graphene structures which are predicted to have enhanced field-switching capabilities (even at low defect concentrations) because of a symmetry-induced gap opening in the band structure.

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