Resonance shifts and spill-out effects in self-consistent hydrodynamic nanoplasmonics

TL;DR

This paper introduces a Self-Consistent Hydrodynamic Model (SC-HDM) that incorporates electron density spill-out effects in nanoplasmonics, providing accurate optical response predictions that align with experiments and quantum methods, while being computationally efficient.

Contribution

The paper develops a generalized hydrodynamic model including density gradients, enabling natural spill-out effects and accurate plasmonic predictions without fully quantum approaches.

Findings

Accurately predicts resonance shifts in Na and Ag nanowires.

Quantitative agreement with experiments and quantum methods.

Applicable to larger nanoplasmonic systems with full retardation effects.

Abstract

The standard hydrodynamic Drude model with hard-wall boundary conditions can give accurate quantitative predictions for the optical response of noble-metal nanoparticles. However, it is less accurate for other metallic nanosystems, where surface effects due to electron density spill-out in free space cannot be neglected. Here we address the fundamental question whether the description of surface effects in plasmonics necessarily requires a fully quantum-mechanical approach, such as time-dependent density-functional theory (TD-DFT), that goes beyond an effective Drude-type model. We present a more general formulation of the hydrodynamic model for the inhomogeneous electron gas, which additionally includes gradients of the electron density in the energy functional. In doing so, we arrive at a Self-Consistent Hydrodynamic Model (SC-HDM), where spill-out emerges naturally. We find a redshift for the optical response of Na nanowires, and a blueshift for Ag nanowires, which are both in quantitative agreement with experiments and more advanced quantum methods. The SC-HDM gives accurate results with modest computational effort, and can be applied to arbitrary nanoplasmonic systems of much larger sizes than accessible with TD-DFT methods. Moreover, while the latter typically neglect retardation effects due to time-varying magnetic fields, our SC-HDM takes retardation fully into account.