Thermodynamically stable single-side hydrogenated graphene

The single-sided hydrogenation of graphene was examined by combining the cluster expansion method with density-functional theory to find that hydrogen atoms prefer to form one-dimensional chains, leading to ripples made up of sp(2) carbon atoms between them. The formation of such novel structures is due to the competition between electronic kinetic energy and elastic strain energy. Surprisingly, the single-sided hydrogenation of graphene is thermodynamically stable at low hydrogen coverage, and some hydrogenated graphenes are semiconducting, similar to graphene nanoribbons. The new single-side hydrogenated graphene structures account for several puzzling experimental observations. In addition, we propose a low-energy single-side fluorinated graphene structure.