Quantum hydrodynamic model for noble metal nanoplasmonics

Abstract

The quantum hydrodynamic model (QHDM) has become a versatile and efficient tool for plasmonics at nanometer and even subnanometer length scales, but the theory is principally applicable only to simple metals. For the most common plasmonic materials, i.e., noble metals, QHDM has not been duly justified to describe their optical responses. In particular, when noble metal structures interface with dielectric materials, electron spillover plays an important role. Although a background optical permittivity is usually invoked in Amp\`ere's law to encompass the $d$-band electrons' effect on optical responses in a direct manner, their indirect effects, e.g., acting via conduction electrons, still remain elusive. Here we identify these indirect effects and develop a near-field potential ${U}_{\mathrm{aff}}$ refined QHDM (U-QHDM), in which the $d$-band electrons' effects on the conduction electrons are recognized and the electrostatic properties of dielectric are incorporated. We report the detailed procedures of calibrating U-QHDM. Material-independent model parameters are fitted with density functional theory (DFT) calculations for simple metals. Last, the calibrated U-QHDM is benchmarked against DFT and time-dependent DFT within stabilized jellium model for Ag, Au, and Al nanostructures interfacing with dielectrics. We expect U-QHDM will be a valuable asset for the rapidly developing field of extreme nanophotonics.