Role of diffusive surface scattering in nonlocal plasmonics

TL;DR

This paper analyzes the GNOR theory for nonlocal plasmonics, linking its key parameters to microscopic surface-response functions, and clarifies its applicability and limitations in describing plasmon damping and frequency shifts.

Contribution

It provides a microscopic justification for the GNOR model's diffusion term and connects it to the Feibelman $d$ parameter, enhancing its theoretical foundation.

Findings

Quantifies the hydrodynamic convection-diffusion constant in GNOR.

Links the diffusion term to the Feibelman $d$ parameter.

Clarifies the model's validity range and limitations.

Abstract

The recent generalised nonlocal optical response (GNOR) theory for plasmonics is analysed, and its main input parameter, namely the complex hydrodynamic convection-diffusion constant, is quantified in terms of enhanced Landau damping due to diffusive surface scattering of electrons at the surface of the metal. GNOR has been successful in describing plasmon damping effects, in addition to the frequency shifts originating from induced-charge screening, through a phenomenological electron diffusion term implemented into the traditional hydrodynamic Drude model of nonlocal plasmonics. Nevertheless, its microscopic derivation and justification is still missing. Here we discuss how the inclusion of a diffusion-like term in standard hydrodynamics can serve as an efficient vehicle to describe Landau damping without resorting to computationally demanding quantum-mechanical calculations, and establish a direct link between this term and the Feibelman $d$ parameter for the centroid of charge. Our approach provides a recipe to connect the phenomenological fundamental GNOR parameter to a frequency-dependent microscopic surface-response function. We therefore tackle one of the principal limitations of the model, and further elucidate its range of validity and limitations, thus facilitating its proper application in the framework of nonclassical plasmonics.