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Edge Saturation effects on the magnetism and band gaps in multilayer graphene ribbons and flakes

Using a density functional theory based electronic structure method and semi-local density approximation, we study the interplay of geometric confinement, magnetism and external electric fields on the electronic structure and the resulting band gaps of multilayer graphene ribbons whose edges are saturated with molecular hydrogen (H$_2$) or hydroxyl (OH) groups. We discuss the similarities and differences of computed features in comparison with the atomic hydrogen (or H-) saturated ribbons and flakes. For H$_2$ edge-saturation, we find \emph{shifted} labeling of three armchair ribbon classes and magnetic to non-magnetic transition in narrow zigzag ribbons whose critical width changes with the number of layers. Other computed characteristics, such as the existence of a critical gap and external electric field behavior, layer dependent electronic structure, stacking-dependent band gap induction and the length confinement effects remain qualitatively same with those of H-saturated ribbons.