Quantum spill out in few-nanometer metal gaps: Effect on gap plasmons and reflectance from ultrasharp groove arrays

TL;DR

This paper investigates how quantum electron spill-out affects gap plasmons and reflectance in ultrasharp metal grooves, revealing significant deviations from classical models and aligning better with experimental data.

Contribution

It introduces a fully quantum mechanical model to study electron spill-out effects on gap plasmons and reflectance, improving accuracy over classical approaches.

Findings

Spill-out causes the mode index to approach the bulk refractive index as gaps vanish.

Spill-out increases plasmonic absorption in nanometer gaps.

Reflectance predictions with spill-out match experiments better than classical models.

Abstract

Plasmons in ultranarrow metal gaps are highly sensitive to the electron density profile at the metal surfaces. Using a fully quantum mechanical approach, we study the effects of electron spill-out on gap plasmons and reflectance from ultrasharp metal grooves. We demonstrate that the mode index of ultranarrow gap plasmons converges to the bulk refractive index in the limit of vanishing gap and, thereby, rectify the unphysical divergence found in classical models. Surprisingly, spill-out also significantly increases the plasmonic absorption for few-nanometer gaps and lowers the reflectance from arrays of ultrasharp metal grooves. These findings are explained in terms of enhanced gap plasmon absorption taking place inside the gap 1-2 {\AA} from the walls and delocalization near the groove bottom. Reflectance calculations taking spill-out into account are shown to be in much better agreement with measurements compared with classical models.