Energy-Based Plasmonicity Index to Characterize Optical Resonances in Nanostructures

Abstract

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 nano particles 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. Repository KITopenDies ist ein Postprint/begutachtetes Manuskript.

Plasmons: untangling the classical, experimental, and quantum mechanical definitions

“…42 Based on these early observations, there has been great interest in using quantum mechanical calculations to understand the emergence of plasmonic properties and in developing techniques to characterize whether nanoclusters have plasmonic or excitonic properties. 43,44,46,47,104,105 These different characterization methods focus on various aspects of the definition of plasmons from classical electrodynamics, and in some cases multiple characterization approaches attempt to quantify similar aspects of the electrodynamics definition. Here, we summarize the main characterization techniques and then focus on their application to prototypical linear metal nanowires, which are widely used as model systems.…”

“…A related characterization method is based on quantifying the energy distribution of excitations contributing each excited state, resulting in an energy-based plasmonicity index (EPI). 47 This index is based on the off-diagonal density matrix elements r o mn coupling electron configurations m and n for an excited state with energy o within a time-dependent framework. The elements r o mn are essentially equivalent to the weights of excitations l mn within a frequency-domain framework.…”

“…The energy-based plasmonicity index (EPI), which quantifies the distribution of the excitations contributing to an excited state, has been applied to the longitudinal excited states of a 70 atom nanowire within a tight-binding model. 47 This model includes only the conduction electrons and uses an empirical coupling between neighboring atoms; electron-electron repulsion is neglected. Because of these simplifications, the model predicts a series of longitudinal absorption peaks (Fig.…”

“…These discrepancies highlight the need for more work to define consistent criteria for plasmons and determine what criteria best reflect the features used experimentally to determine whether states are plasmonic. 47 Energy distribution M 70 Moderate to high -Lambda scaling 49 Coupling between excitations Na 20 High -…”

“…Many of these nanoclusters are also small enough to study using quantum mechanical models, giving detailed insight into their properties. [39][40][41] As these developments have converged, there have been many distinct but overlapping definitions proposed for how to identify plasmons within a quantum mechanical framework, [42][43][44][45][46][47][48][49] which has led to confusion in the field.…”