Electric-field-induced penetration of edge states at the interface between monolayer and bilayer graphene

The edge states in a hybrid system of single-layer and double-layer graphene are studied theoretically in a tight-binding model. The edge states on one side of the interface between single-layer and double-layer graphene are shown to penetrate into the single-layer region when a perpendicular electric field is applied, while they are localized in the double-layer region without an electric field. The edge states on the other 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 edge state at the boundary between single-layer and double-layer graphene.