Competition between surface screening and size quantization for surface plasmons in nanoparticles

We present a theoretical model for analyzing the size dependence of the surface plasmon resonance of metallic nanospheres in a range of sizes down to a single nanometer. Within this model, we explicitly show how different microscopic mechanisms, namely quantization due to size (quantum size effect (QSE)) and dynamical surface screening, affect the energy of the surface plasmon. We demonstrate that the latter mechanism, 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 material parameters, QSE may only be observed for ultra-small 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.