Influence of the electron spill-out and nonlocality on gap-plasmons in the limit of vanishing gaps

TL;DR

This paper investigates how electron spill-out and nonlocal effects influence gap-plasmon propagation in ultra-narrow metal gaps, highlighting the importance of quantum models over local responses for accurate predictions.

Contribution

It compares local and quantum hydrodynamic models, demonstrating the necessity of nonlocal effects for correct behavior as gaps vanish.

Findings

Quantum hydrodynamic model accurately predicts behavior in vanishing gaps.

Local models overestimate losses and show divergence issues.

Effective gap width can approximate quantum effects in local models.

Abstract

We study the effect of electron spill-out and of nonlocality on the propagation of light inside a gap between two semi-infinite metallic regions. We compare the predictions of a local response model taking into account only the spill-out, to the predictions of a quantum hydrodynamic model able to take both phenomena into account. We show that only the latter is able to correctly retrieve the correct limit when the gap closes, while the local model suffers from undesirable features (divergence of the fields, overestimation of the losses). Finally, we show that, to a certain extent, the correct results can be retrieved using a simple local approach without spill-out or conventional Thomas-Fermi approximation, but considering an effective gap width.