Complex edge effects in graphene nanoribbons due to hydrogenation

We have performed density-functional calculations as well as employed a tight-binding theory, to study the effect of hydrogenation of zigzag graphene nanoribbons (ZGNR). We show that each edge C atom bonded with 2 H atoms open up a gap and magnetism collapses for small widths of the nanoribbon. However, a re-entrant magnetism accompanied by a metallic electronic structure is observed from eight rows and thicker nanoribbons. The electronic structure and magnetic state are quite complex for this type of termination, with $sp^{3}$ bonded edge atoms being nonmagnetic whereas the nearest neighboring atoms are metallic and magnetic. We have also evaluated the phase stability of several thicknesses of ZGNR and demonstrate that $sp^{3}$ bonded edge atoms with 2 H atoms at the edge can be stabilized over 1 H atom terminated edge at high temperatures and pressures.