Frequency dependent polarizability of small metallic grains

TL;DR

This paper investigates the frequency-dependent polarizability of nano-scale metallic grains using quantum mechanics, revealing size-dependent shifts in plasmon resonance peaks and comparing results with classical models.

Contribution

Introduces a quantum mechanical model for the polarizability of metallic grains, capturing size-dependent resonance shifts and secondary peaks not explained by classical theories.

Findings

Main resonance peak is blue-shifted in quantum model.

Secondary resonances are observed around the main peak.

Blue shift varies with grain size and differs from classical predictions.

Abstract

We study the dynamic electronic polarizability of a single nano-scale spherical metallic grain using quantum mechanical approach. We introduce the model for interacting electrons bound in the grain allowing us numerically to calculate the frequency dependence of the polarizability of grains of different sizes. We show that within this model the main resonance peak corresponding to the surface plasmon mode is blue-shifted and some minor secondary resonances above and below the main peak exist. We study the behavior of blue shift as a function of grain size and compare our findings with the classical polarizability and with other results in the literature.