Charge transfer plasmons in nanoparticle arrays on graphene: Theoretical development

Abstract

The properties of charge transfer plasmons (CTPs) in periodic metallic nanoparticle arrays (PMNPAs) on the single-layer graphene surface are studied within a computationally efficient original hybrid quantum-classical model. The model is based on the proven assumption that the carrier charge density in doped graphene remains unchanged under plasmon oscillations. Calculated CTP frequencies for two PMNPA geometries are shown to lie within the THz range and to be factorized, i.e., presented as a product of two independent factors determined by the graphene charge density and the PMNPA geometry. Equations are derived for describing the CTP frequencies and eigenvectors, i.e., oscillating nanoparticle charge values. It is shown that the CTP plasmons having a band structure containing a wave vector and a band number, like to phonons in periodic media, can be divided into an acoustic mode and optical CTP modes. For the acoustic modes, the CTP group velocity tends to zero at k→0, but reaches a value of ∼VFermi in graphene inside the Brillouin zone, while for the optical modes, the group velocity dispersion is extremely weak, although their energy is higher than the acoustic plasmon energies. It is shown that the calculated dependence of CTP frequencies on the carrier concentration in graphene is in good agreement with experimental data. We believe that the proposed model can help in designing various graphene-based terahertz nanoplasmonic devices of complex geometry due to very high computational efficiency.