Zak phase of 1-D electrostatically gated graphene grating and optical properties of plasmonic edge state*

We design periodic metal gates on top of a hBN/Graphene/hBN sandwich heterostructure to modulate local graphene conductivity. We investigated properties of graphene surface plasmon(GSP) of a doubly gated graphene. Stop bands due to GSP modes mixing can be controlled by electrostatic doping. Topology of each plasmon band can be characterized by a Zak phase. When two insulators of a same bandgap but distinct Zak phases are joined together, an edge state in the bandgap has been observed in many physical systems. The edge state observed on our graphene grating platform presents an anisotropic dipole moment. While it radiating into the left or right in the forward direction offers an interrogation approach for band topologies of component graphene gratings, the angle of radiation remains a tunable property that depends on an interplay of the mode's resonant frequency, the bandgap width, its mid-gap frequency and the dimensions of metal gates. Due to its capability of active tuning, this may serve as a stepping stone on the way toward active control of surface plasmon band structures for optical communication, wavefront steering or sensing applications.