Plasmons do not go that quantum

TL;DR

This paper presents a theoretical model analyzing how microscopic mechanisms like quantization and electron spill-out influence the surface plasmon resonance in metallic nanospheres, showing spill-out effects can dominate at certain sizes.

Contribution

The model explicitly compares size quantization and electron spill-out effects, revealing spill-out can significantly alter plasmon energies and dominate in nanoparticles larger than previously thought.

Findings

Electron spill-out effects can shift plasmon energies significantly.

QSE effects are only observable in particles closer to 1 nm.

Model aligns quantitatively with recent experimental data.

Abstract

We develop a theoretical model of the surface plasmon resonance of metallic nanospheres in the size range down to the single nanometer size. Within this model we explicitly show how different microscopic mechanisms, namely quantization due to size (QSE) and electron spill-out, affect the energy of the surface plasmon. We demonstrate, that electron spill-out effects, which can move the surface plasma energy both toward the red or the blue, can be comparable to or even stronger than QSE. Thus, depending on circumstances, QSE may only be observed for ultrasmall metal nanoparticles much closer to 1 nm in size than to 10 nm. Results presented herein are in quantitative agreement with recent published experimental results for Ag and Au.