Interplay between Electromagnetic and Coulomb Coupling

Both the transverse electromagnetic and longitudinal coulomb couplings of the surface-plasmon mode to the collective excitation of Dirac electrons are investigated. The unique features of coupled quantum-plasmon modes are demonstrated. The predicted dispersion relations of these quantum-plasmon modes should be experimentally observable. For a double-layer graphene structure, the interplay between the interlayer Coulomb forces and the electromagnetic coupling to each layer is calculated. The effective polarizability matrix for coupled double-layer graphene and a semi-infinite conductor is obtained for constructing an effective-medium theory, which includes correlation effects from the Coulomb interaction between electrons in graphene and the conductor as well as the electromagnetic field between them.