Abstract
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. Among all currently available recipes for obtaining such response functions, the use of ab initio methods remains one of the most conspicuous trends, wherein the surface-response functions are retrieved via the metal’s non-equilibrium response to an external time-dependent perturbation. Here, we present a complementary approach to approximate one of the most appealing surface-response functions, namely the Feibelman d-parameters, yield a finite contribution even when they are calculated solely with the equilibrium properties of the metal, described under the local-response approximation (LRA) but with a spatially varying equilibrium electron density, as input. 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, ab initio methods. The analytical work presented here illustrates how microscopic surface-response functions can emerge out of entirely local electrodynamic considerations.
Highlights
The plasmonic response of metallic nanostructures is commonly explored within the framework of classical electrodynamics [1], typically describing the free electrons of metals classically within the Drude-like local-response approximation (LRA) [2]
The microscopic and analytical understanding of ε(r, r′) is in general limited to bulk considerations within the random-phase approximation (RPA) or the hydrodynamic model (HDM) [4, 5, 27, 41, 46, 47]
Inspired by the long-established traditions in the electrodynamics of composite dielectric problems [49], it is common in plasmonics [2] to invoke yet another approximation: the step-like, abrupt surface termination of the metal, thereby neglecting any microscopic inhomogeneities in the vicinity of the surface [ defined by z = 0, without loss of generality, with the metal and the dielectric each occupying the z < 0 and z > 0 half-spaces, respectively (Figure 1a)]
Summary
The plasmonic response of metallic nanostructures is commonly explored within the framework of classical electrodynamics [1], typically describing the free electrons of metals classically within the Drude-like local-response approximation (LRA) [2]. We explicitly show that even when using a local-response approach along with the equilibrium electron densityprofile alone as input, there is a finite contribution to the metallic surface-response functions provided that the (equilibrium) electron density varies smoothly from its bulk value deep inside the metal to zero near the metal’s surface [41,42,43] (as opposed to terminating abruptly at it) Such an approach, despite its simplicity and inherent limitations, could facilitate new physical insights into the electrodynamic fingerprints associated with quantum spill-out/spill-in, without resorting to computationally demanding ab initio methods. The microscopic and analytical understanding of ε(r, r′) is in general limited to bulk considerations within the random-phase approximation (RPA) or the hydrodynamic model (HDM) [4, 5, 27, 41, 46, 47]
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