Dispersion of edge states and quantum confinement of electrons in graphene channels drawn on graphene fluoride

Graphene is an excellent conductor, while graphene fluoride is a wide band-gap semiconductor. We propose the formation of graphene channels embedded in graphene fluoride as a method to induce quantum confinement of charge carriers in graphene. In particular, we study the electronic structure of graphene channels drawn on the fluoride along two high-symmetry directions: the armchair and zigzag orientations. The zigzag channels are found to have dispersive one-dimensional edge bands, contrary to the case of ribbons and channels drawn on graphane, where the edge state is flat close to the Fermi level and has a very large effective mass. The effective mass of this one-dimensional edge state can be controlled by electrostatic interactions at the edge of the channel. This result indicates that the mobility of these channels can be controlled by a localized gate voltage. The armchair channel is found to be metallic or semiconducting depending on the width of the channel, in agreement with ribbons and hydrogen-limited channels.