Kinetic Density Functional Theory for Plasmonic Nanostructures: Breaking of the Plasmon Peak in the Quantum Regime and Generation of Hot Electrons

We develop a quantum kinetic theory of the dynamic response of typical noble metals. Our approach is based on the density functional theory (DFT) and incorporates new important elements as compared to the conventional time-dependent DFT formalism. The kinetic DFT is derived starting from the master equation of motion for the density matrix, which involves both momentum and energy relaxation processes. Therefore, the quantum system is described by two relaxation parameters, unlike the conventional time-dependent DFT incorporating only one relaxation parameter. This allows us to describe both the absorption of light and the generation of hot plasmonic electrons. Using our kinetic DFT theory, we also observe the transition from the multiple peaks in small size-quantized systems to the intensive plasmonic resonance in large classical systems. Unlike the standard picture of collisional broadening of the plasmon peak in small systems, we observe a very different scenario: the formation of multiple plasmonic-like peaks in small quantized systems. These peaks are the result of a hybridization of the collective plasmon mode and the single-particle transitions in a quantized electron gas. There are a few experimental observations that seem to correlate with such a scenario of the plasmonic broadening in small systems. Our approach also incorporates the interband transitions, which are important for a qualitative description of gold and silver. Although this paper gives an application of our kinetic DFT only to the slab geometry, our theory can be applied to nanocrystals of arbitrary shape. The kinetic DFT formalism developed here can be employed to model and predict a variety of metal and hybrid nanostructures for applications in photocatalysis, sensors, photodetectors, metamaterials, etc.