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 sp² 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.