  The electronic properties of a graphene sheet with attached hydrogen atoms is
studied using a modified Falicov-Kimball model on the honeycomb lattice. It is
shown that in the ground state this system separates into two phases: fully
hydrogenated graphene (graphane) and hydrogen-free graphene. The
graphene-graphane boundary acquires a positive interface tension. Therefore,
the graphene-graphane interface becomes a straight line, slightly rippled by
thermal fluctuations. A smooth interface may be useful for the fabrication of
mesoscopic graphene-based devices.
