Asymptotics of surface-plasmon redshift saturation at sub-nanometric separations

TL;DR

This paper provides an asymptotic analysis of plasmon resonance redshift saturation at extremely small gaps, revealing a nonlocal mechanism that effectively widens the gap and sets a lower bound on resonance frequency.

Contribution

It introduces a simple asymptotic formula capturing nonlocal effects causing plasmon redshift saturation at subnanometric gaps, supported by physical interpretation and agreement with numerical data.

Findings

Nonlocality manifests as an effective potential discontinuity.

Resonance frequency asymptotics are renormalized, providing a lower bound.

The model agrees with numerical computations for nanowire and nanosphere dimers.

Abstract

Many promising nanophotonics endeavours hinge upon the unique plasmonic properties of nanometallic structures with narrow non-metallic gaps, which support super-concentrated bonding modes that singularly redshift with decreasing separations. In this letter, we present a descriptive physical picture, complemented by elementary asymptotic formulae, of a nonlocal mechanism for plasmon-redshift saturation at subnanometric gap widths. Thus, by considering the electron-charge and field distributions in the close vicinity of the metal-vacuum interface, we show that nonlocality is asymptotically manifested as an effective potential discontinuity. For bonding modes in the near-contact limit, the latter discontinuity is shown to be effectively equivalent to a widening of the gap. As a consequence, the resonance-frequency near-contact asymptotics are a renormalisation of the corresponding local ones. Specifically, the renormalisation furnishes an asymptotic plasmon-frequency lower bound that scales with the $1/4$-power of the Fermi wavelength. We demonstrate these remarkable features in the prototypical cases of nanowire and nanosphere dimers, showing agreement between our elementary expressions and previously reported numerical computations.