Energy-Based Plasmonicity Index to Characterize Optical Resonances in Nanostructures

Resonances sustained by plasmonic nanoparticles provide extreme electric field confinement and enhancement into the deep subwavelength domain for a plethora of applications. Recent progress in nanofabrication made it even possible to tailor the properties of nanoparticles consisting of only a few hundred atoms. These nanoparticles support both single-particle-like resonances and collective plasmonic charge density oscillations. Prototypical systems sustaining both features are graphene nanoantennas. In pushing the frontier of nanoscience, traditional identification, and classification of such resonances is at stake again. We show that in such nanostructures, the concerted electron cloud oscillation in real space does not necessarily come along with collective dynamics of conduction band electrons in energy space. This unveils an urgent need for a discussion of how a plasmon in nanostructures should be defined. Here, we propose to define it relying on energy space dynamics. The unambiguous identification of the plasmonic nature of a resonance is crucial to find out whether desirable plasmon-assisted features, such as frequency conversion processes, can be expected from a resonance. We elaborate an energy-based figure of merit that classifies the nature of resonances in nanostructures, motivated by tight binding simulations with a toy model consisting of a linear chain of atoms. We apply afterward the proposed figure of merit to a doped hexagonal graphene nanoantenna, which is known to support plasmons in the near infrared and single-particle-like transitions in the visible.