Friction of the surface plasmon by high-energy particle-hole pairs: Are memory effects important?

TL;DR

This paper models the damping of surface plasmons in metallic nanoparticles as a system coupled to an environment of high-energy particle-hole pairs, highlighting the Markovian nature of the bath for particles larger than 1 nm.

Contribution

It introduces a simplified model separating low- and high-energy excitations to describe plasmon damping and estimates the timescales where memory effects are negligible.

Findings

Surface plasmon damping can be modeled by a single degree of freedom coupled to an environment.

High-energy particle-hole pairs form an effective dissipative bath within nanoparticles.

Markovian dynamics are valid for nanoparticles larger than approximately 1 nm.

Abstract

We show that the dynamics of the surface plasmon in metallic nanoparticles damped by its interaction with particle-hole excitations can be modelled by a single degree of freedom coupled to an environment. In this approach, the fast decrease of the dipole matrix elements that couple the plasmon to particle-hole pairs with the energy of the excitation allows a separation of the Hilbert space into low- and high-energy subspaces at a characteristic energy that we estimate. A picture of the spectrum consisting of a collective excitation built from low-energy excitations which interacts with high-energy particle-hole states can be formalised. The high-energy excitations yield an approximate description of a dissipative environment (or "bath") within a finite confined system. Estimates for the relevant timescales establish the Markovian character of the bath dynamics with respect to the surface plasmon evolution for nanoparticles with a radius larger than about 1 nm.