Surface-response functions obtained from equilibrium electron-density profiles

TL;DR

This paper introduces a method to derive surface-response functions, specifically Feibelman d-parameters, from equilibrium electron-density profiles, providing a simpler alternative to complex ab initio calculations in quantum nanoplasmonics.

Contribution

The paper demonstrates that surface-response functions can be obtained from equilibrium properties using local-response approximation, aligning qualitatively with more complex ab initio methods.

Findings

Feibelman d-parameters derived from equilibrium densities match ab initio results qualitatively.

Equilibrium-based approach simplifies calculations of surface-response functions.

Microscopic surface-response functions can emerge from local electrodynamics.

Abstract

Surface-response functions are one of the most promising routes for bridging the gap between fully quantum-mechanical calculations and phenomenological models in quantum nanoplasmonics. Within all the currently available recipes for obtaining such response functions, \emph{ab initio} calculations remain one of the most predominant, wherein the surface-response function are retrieved via the metal's non-equilibrium response to an external perturbation. Here, we present a complementary approach where one of the most appealing surface-response functions, namely the Feibelman $d$-parameters, yield a finite contribution even in the case where they are calculated directly from the equilibrium properties described under the local-response approximation (LRA), but with a spatially varying equilibrium electron density. Using model calculations that mimic both spill-in and spill-out of the equilibrium electron density, we show that the obtained $d$-parameters are in qualitative agreement with more elaborate, but also more computationally demanding, \emph{ab initio} methods. The analytical work presented here illustrates how microscopic surface-response functions can emerge out of entirely local electrodynamic considerations.