Quantum plasmonics through retarded Coulomb coupling to graphene electrons

The retarded Coulomb couping of the surface plasmon mode to the collective excitation of Dirac electrons in a neighboring graphene monolayer is investigated and the characteristics of the resulting hybrid quantum- plasmon modes are discussed. The unique dispersion relations of these quantum-plasmon modes are expected to be experimentally observable. For double-layer graphene, the interplay between the interlayer Coulomb interaction and the retarded coupling of a surface plasmon mode to each sheet is obtained. As a significant correction to the static dielectric function of the host cladding layer on top of the conductor surface, the effective scattering matrix for coupled double-layer graphene and a thick conductor is obtained for constructing an effective-medium theory, which includes the role of both the Coulomb interaction between electrons in different graphene sheets and the retarded Coulomb coupling of these layers to the conductor. A scattering matrix can be employed for an effective-medium theory to calculate the optical properties of inserted conducting nanodots and nanorods between graphene and a conductor which can be applied to a super-resolution near-field imaging beyond the diffraction limit for functionalized biomolecules attached to these nanodots and nanorods.