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The edge states in the hybrid system of single-layer and double-layergraphene are studied in the tight-binding model theoretically. The edge statesin one side of the interface between single-layer and double-layer graphene areshown to penetrate into the single-layer region when the perpendicular electricfield is applied, while they are localized in the double-layer region withoutelectric field. The edge states in another side of the interface are localizedin the double-layer region independent of the electric field. Thisfield-induced penetration of the edge states can be applied to switchingdevices. We also find a new type of the edge states at the boundary betweensingle-layer and the double-layer graphene.

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