An eigenvalue approach to quantum plasmonics based on a self-consistent hydrodynamics method

Plasmonics has attracted much attention not only because it has useful properties such as strong field enhancement, but also because it reveals the quantum nature of matter. To handle quantum plasmonics effects, ab initio packages or empirical Feibelman d-parameters have been used to explore the quantum correction of plasmonic resonances. However, most of these methods are formulated within the quasi-static framework. The self-consistent hydrodynamics model offers a reliable approach to study quantum plasmonics because it can incorporate the quantum effect of the electron gas into classical electrodynamics in a consistent manner. Instead of the standard scattering method, we formulate the self-consistent hydrodynamics method as an eigenvalue problem to study quantum plasmonics with electrons and photons treated on the same footing. We find that the eigenvalue approach must involve a global operator, which originates from the energy functional of the electron gas. This manifests the intrinsic nonlocality of the response of quantum plasmonic resonances. Our model gives the analytical forms of quantum corrections to plasmonic modes, incorporating quantum electron spill-out effects and electrodynamical retardation. We apply our method to study the quantum surface plasmon polariton for a single flat interface.