Collective quantum approach to resonant photo-plasmonic effect

Abstract

In this research, we investigate the resonant photo-plasmonic effect in the framework of the dual length-scale driven damped collective quantum excitations of the spill-out electrons at the metal surface. The bulk plasmon and the spill-out electron excitations are modeled using the Hermitian and the damped non-Hermitian effective Schrödinger–Poisson systems, respectively, matched appropriately at the metal–vacuum boundary. It is shown that, when driven by an external field, the system behaves quite analogous to the driven damped mechanical oscillations in the wavenumber domain, causing the spill-out electron collective excitation resonance. However, in the current model, the resonance takes place due to matching of the wavenumber of the driving pseudoforce with that of the spill-out electron excitations, which can be either due to single-electron or collective oscillations. Hence, the RPP effect considered here leads to both conventional resonant photo-electric and the photo-plasmonic effects due to the dual-tone nature of collective quantum oscillations. The current model may be extended to a similar resonance effect in nanometer-sized metal surfaces with a non-planar geometry. A new equation of state for the electron number density of spill-out electrons is obtained, which limits the plasmonic response in high-density and low-temperature regime due to the small transition probability of electrons to the spill-out energy band.