A hybrid quantum–classical theory for predicting terahertz charge-transfer plasmons in metal nanoparticles on graphene

Metal nanoparticle (NP) complexes lying on a single-layer graphene surface are studied with a developed original hybrid quantum-classical theory using the Finite Element Method (FEM) that is computationally cheap. Our theory is based on the motivated assumption that the carrier charge density in the doped graphene does not vary significantly during the plasmon oscillations. Charge transfer plasmon (CTP) frequencies, eigenvectors, quality factors, energy loss in the NPs and in graphene, and the absorption power are aspects that are theoretically studied and numerically calculated. It is shown the CTP frequencies reside in the terahertz range and can be represented as a product of two factors: the Fermi level of graphene and the geometry of the NP complex. The energy losses in the NPs are predicted to be inversely dependent on the radius R of the nanoparticle, while the loss in graphene is proportional to R and the interparticle distance. The CTP quality factors are predicted to be in the range ∼10-100. The absorption power under CTP excitation is proportional to the scalar product of the CTP dipole moment and the external electromagnetic field. The developed theory makes it possible to simulate different properties of CTPs 3-4 orders of magnitude faster compared to the original FEM or the finite-difference time domain method, providing possibilities for predicting the plasmonic properties of very large systems for different applications.