Low-voltage controlling high order plasmonic modes based on graphene/metal electrodes

•High order plasmonic modes, including even and odd ones, are efficiently excited.•Metallic slits break the structural symmetry of the graphene ribbon system.•Low voltages can be realized by using nanosized space gate electrodes.•A low-voltage controlling multi-band absorber are successfully designed.•The proposed structure is useful for low-voltage controlled THz plasmonic devices.