Resonance shifts and spill-out effects in self-consistent hydrodynamic nanoplasmonics

Abstract

The standard hydrodynamic Drude model with hard-wall boundary conditions can give accurate quantitative predictions for the optical response of noble-metal nanoparticles. However, it is less accurate for other metallic nanosystems, where surface effects due to electron density spill-out in free space cannot be neglected. Here we address the fundamental question whether the description of surface effects in plasmonics necessarily requires a fully quantum-mechanical ab initio approach. We present a self-consistent hydrodynamic model (SC-HDM), where both the ground state and the excited state properties of an inhomogeneous electron gas can be determined. With this method we are able to explain the size-dependent surface resonance shifts of Na and Ag nanowires and nanospheres. The results we obtain are in good agreement with experiments and more advanced quantum methods. The SC-HDM gives accurate results with modest computational effort, and can be applied to arbitrary nanoplasmonic systems of much larger sizes than accessible with ab initio methods.

A classical treatment of optical tunneling in plasmonic gaps: extending the quantum corrected model to practical situations

“…Other approaches to introduce nonlocality have been recently discussed, such as adding an extra dielectric layer of well dened properties to mimic the nonlocal displacement of the centroid of charge at the surface, 88 including extra nonlocal dissipation terms, 84 or considering more accurately the electron density prole at the interfaces. 89 hydrodynamic description and with or without inclusion of the interparticle electron tunneling within the QCM. In all the calculations, we solved the classical electromagnetic Maxwell's equations to obtain the optical response of the system.…”

“…86,87 Some approaches have proposed the recovery of nonlocal results by a convenient rescaling of the local distances 86,87 and thicknesses 88 at the metal interfaces, providing good descriptions of the plasmon energies and dispersions in nanometric gaps. Recently, the inclusion of the realistic density prole above the surface into the NLHD description has allowed the retrieval of full quantum and experimental results both for d-electron and simple metals, 89 at an increased computational cost. While the above treatments address nonlocal screening, it has only been recently that the charge transfer between the particles due to quantum tunneling could be accounted for within the classical treatment appropriate for large systems.…”

Third-harmonic generation in the presence of classical nonlocal effects in gap-plasmon nanostructures

“…For example, in physical systems, the geometrical dimensions may exceed several hundreds of nanometers, making the computational domain for quantum calculations prohibitive. Another promising approach could be the generalization of the hydrodynamic model to take into a account a more sophisticated description of the free-electron gas internal energy 43 . Such a description would be more adequate to describe surface phenomena and at the same time it could be applied to macroscopical systems.…”

Hydrodynamic theory for quantum plasmonics: Linear-response dynamics of the inhomogeneous electron gas

“…The scheme can also be applied to more complex geometries, such as cylinders demonstrated in Ref. [69].…”

“…It has been demonstrated that the QHT can predict the work function and surface energy well [58,67], capture the important features of the linear excitations of free electron gas [54], and predict the nonlinear dynamics [68]. Recently, the QHT has been employed to investigate the surface plasmon response of two-dimensional (2D) nanowires of both simple metal (sodium) and noble metal (silver), and successfully predicts the dimension-dependent SP resonance shift [69]. However, a comprehensive understanding of the QHT is still needed.…”