  The edge states in the hybrid system of single-layer and double-layer
graphene are studied in the tight-binding model theoretically. The edge states
in one side of the interface between single-layer and double-layer graphene are
shown to penetrate into the single-layer region when the perpendicular electric
field is applied, while they are localized in the double-layer region without
electric field. The edge states in another side of the interface are localized
in the double-layer region independent of the electric field. This
field-induced penetration of the edge states can be applied to switching
devices. We also find a new type of the edge states at the boundary between
single-layer and the double-layer graphene.
