Metal-Insulator Transition from Graphene to Graphane

Graphane is obtained by perfectly hydrogenating graphene. There exists an intermediate material, partially hydrogenated graphene (which we call hydrographene), interpolating from pure graphene to pure graphane. Employing a graph theoretical approach to the site-percolation model, we present an intuitive and physical picture revealing a percolation transition from graphene to graphane. It is demonstrated that hydrographene shows a bulk ferromagnetism based on the Lieb theory. We also propose a weighted percolation model in order to take into account the tendency of hydrogenation to cluster.