Role of diffusive surface scattering in nonlocal plasmonics

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.

Mesoscopic electrodynamics at metal surfaces

“…Now, this also indicates that a high-frequency diffusive contribution term would not emerge out of Boltzmann considerations applied to the homogeneous bulk system. While somewhat a lengthy discussion not repeated here, this can indeed also be shown explicitly [242]. Simply stated, bulk diffusion at optical frequencies is negligible.…”

“…So, what is then the physical mechanism behind the seemingly experimentally observed diffusion at optical frequencies? Here, surfaceenhanced Landau damping represents a surface-scattering effect beyond the bulk description of the metal [154, 156, Finally, we note that an ad hoc inclusion of surface effects in a bulk term should be done with care and one might naïvely speculate that the diffusion constant should then at least be space-dependent to only account for diffusion at the surface [242]. However, since the induced charge density resides only in the near vicinity of the surface without any significant density gradients in the bulk, the diffusion is anyway only effective near the surface.…”

“…Having already promoted the semiclassical hydrodynamic model in Section 3, where the induced charge is smeared over a length scale 𝜉, one could speculate that d ⊥ (𝜔) should somehow resemble 𝜉(𝜔). Indeed the following expressions [242]…”

“…The link from the hydrodynamic bulk description to the surface-response approach is highlighted by Eq. ( 36), while the opposite attempt at deriving hydrodynamic parameters from surface-response functions is more ambiguous [242].…”

Parameter-free quantum hydrodynamic theory for plasmonics: Electron density-dependent damping rate and diffusion coefficient

“…As is stated in Ref. [51,52], this diffusion captures the effects of both mutual interactions among the electrons and the scattering of the electrons on metal surfaces, which mimics the surface-enhanced Landau damping due to the creation of electron-hole pairs.…”