A periodic metagate is designed on top of a boron nitride-graphene heterostructure to modulate the local carrier density distribution on the monolayer graphene. This causes the bandgaps of graphene surface plasmon polaritons to emerge because of either the interaction between the plasmon modes, which are mediated by the varying local carrier densities, or their interaction with the metal gates. Using the example of a double-gate graphene device, we discuss the tunable band properties of graphene plasmons due to the competition between these two mechanisms. Because of this, a bandgap inversion, which results in a Zak phase switching, can be realized through electrostatic gating. Here we also show that an anisotropic plasmonic topological edge state exists at the interface between two graphene gratings of different Zak phases. While the orientation of the dipole moments can differentiate the band topologies of each graphene grating, the angle of radiation remains a tunable property. This may serve as a stepping stone toward active control of the band structures of surface plasmons for potential applications in optical communication, wave steering, or sensing.
