Real-Time Electron-Electron Scattering Dynamics in Plasmonic Nanostructures

Electron-electron scattering is one of the most important hot carrier relaxation pathways in plasmonic nanoparticles. Understanding the dynamics of this scattering process and the effects of this on excited state dephasing and relaxation is therefore essential for the design of plasmonic nanostructures, including optical properties and the dynamics of electrons in plasmon-driven catalytic reactions. In this work, we have developed an approach that incorporates real-time time-dependent density functional tight-binding (DFTB) simulations with a Lindblad quantum Boltzmann equation (QBE) based on a screened electron-electron interaction that is determined by the random phase approximation. This approach enables a self-consistent description of electron-electron scattering effects that occur during and after plasmon excitation in clusters/nanoparticles with hundreds of atoms. With our RT-TDDFTB+QBE method, we investigate the quasiparticle lifetime as well as population and coherence dynamics in silver, gold and aluminum nanoclusters with sizes between 1.5 and 2.6 nm. Our results show that the quasiparticle lifetimes and relaxation dynamics are highly energy dependent, becoming much faster at higher energies. For clusters less than 2 nm, quantum effects associated with discrete energy levels can lead to the fluctuating lifetimes and deviation of the dynamics from the typical thermalization process, while for larger nanoparticles, the transition to bulk metallic behavior is found. Decoherence of the initially excited plasmon resonance is observed with a time scale of 10 fs, much faster than population relaxation. For gold, we find that the 5d-band can significantly slow down the relaxation of energetic electrons though Auger scattering, and interband transitions can lead to a secondary decoherence process longer than 50 fs. Our method provides a general framework for incorporating electron-electron scattering in the dynamics of metallic systems and demonstrates the capability of tight-binding methods to accurately describe electron dynamics for time scales up to ps for clusters/nanoparticles that transition from molecular to metallic properties.