Laplacian-Level Quantum Hydrodynamic Theory for Plasmonics

Abstract

An accurate description of the optical response of subwavelength metallic particles and nanogap structures is a key problem of plasmonics. Quantum hydrodynamic theory (QHT) has emerged as a powerful method to calculate the optical response of metallic nanoparticles (NPs) since it takes into account nonlocality and spill-out effects. Nevertheless, the absorption spectra of metallic NPs obtained with conventional QHT, i.e., incorporating Thomas-Fermi (TF) and von Weizsäcker (vW) kinetic energy (KE) contributions, can be affected by several spurious resonances at energies higher than the main localized surface plasmon (LSP). These peaks are not present in reference time-dependent density-functional-theory (TD-DFT) spectra, where, instead, only a broad shoulder exists. Moreover, we show here that these peaks incorrectly reduce the LSP peak intensity and have a strong dependence on the simulation domain size so that a proper calculation of QHT absorption spectra can be problematic. In this article, we introduce a more general QHT method accounting for KE contributions depending on the Laplacian of the electronic density ($q$), thus, beyond the gradient-only dependence of the TFvW functional. We show that employing a KE functional with a term proportional to $q^2$ results in an absorption spectrum free of spurious peaks, with LSP resonance of correct intensity and numerically stable Bennett state. Finally, we present a novel Laplacian-level KE energy functional that is very accurate for the description of the optical properties of NPs with different sizes as well as for dimers.

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• Roadmap on Nonlocality in Photonic Materials and Metamaterials
• Interrogating Quantum Nonlocal Effects in Nanoplasmonics through Electron-Beam Spectroscopy
• Nonlocal and nonadiabatic Pauli potential for time-dependent orbital-free density functional theory
• Imposing Correct Jellium Response Is Key to Predict the Density Response by Orbital-Free DFT
• Application of Madelung Hydrodynamics to Plasmonics and Nonlinear Optics in Two-Dimensional Materials
• The Uniqueness Theorem for Nonlocal Hydrodynamic Media
• Quantum-hydrodynamic modal perspective on plasmonic gap structures
• Electron spill-out effect on third-order optical nonlinearity of metallic nanostructure
• Density-Functional-Theory Perspective on the Non-Linear Response of Correlated Electrons Across Temperature Regimes
• Influence of the electron spill-out and nonlocality on gap-plasmons in the limit of vanishing gaps