Quantum Vlasov theory of Mie oscillations in metal clusters : a self-consistent approach to quantum surface effects in nanoparticles

The electron dynamics in metal clusters is studied in the framework of the quantum Vlasov theory. The Vlasov theory describes equilibria and excitations in ideal plasmas by a self-consistent field approach. It is applied to the spherical jellium model of atomic clusters with an emphasis on quantum-size effects in nanometer sized clusters. A proper understanding of the spill-out-induced surface effects of the Mie plasmon is one of the major goals of this work. For this purpose, the Vlasov model is treated by theoretical and numerical methods both in the linear and nonlinear regime of free and laser-driven cluster excitations. Linear electrostatic cluster excitations are treated in a multistream-Vlasov and in a reduced single-state Vlasov model. In the framework of the single-state model, the damping of the Mie plasmon can be explained by a mode conversion process from surface to volume plasmons due to surface scattering. Increasing the number of representative states in the multistream approach, it is shown that the residual volume plasmons are damped by single-particle excitations (Landau damping).Reference calculations are performed for specific Na clusters with the multistream and the more common density-functional theory approach. The plasmon damping rate in the multistream model shows good quantitative agreement with the damping rate obtained by the single-state model, which indicates the importance of mode conversion for the plasmon decay. The damping rate shows a characteristic scaling with the inverse cluster radius. In addition, the resonance frequency is redshifted with respect to the Mie frequency especially for small clusters. By further including exchange-correlation corrections, close agreement of the damping rate coefficient with previous experimental and numerical results can be achieved. Linear electromagnetic cluster excitations are treated in the single-state model. Resonance absorption of clusters is investigated at the critical density where the light frequency equals the plasma frequency. In this framework, the well-known theory of resonance absorption is generalized from plane to spherical surfaces with variable angles of incidence and light polarizations along the surface. As a preparatory study for nonlinear electrostatic cluster excitations, the non resonant collision less absorption (Brunel mechanism) of thin foils is investigated. Brunel’s scaling can be confirmed for thick foils in the present quantum regime. However, the energy absorption shows a clear signature of quantum-size effects for thin foils due to the spill-out effect of the electron density. The main result is an increase of Brunel’s scaling exponent for thin foils. Nonlinear electrostatic cluster excitations are investigated for spherical Na clusters. The nonlinear Mie oscillation is studied based on an impulsive excitation of the cluster. For moderate perturbations, the resonance position of the Mieplasmon is blue shifted with respect to the linear result. In addition, the plasmon line width decreases. For sufficiently large perturbations, dynamical deformation effects are observed, which lead to a splitting of the Mie resonance. This splitting can be explained by a coupling of the cluster dipole moment to the quadrupole field induced by the electron cloud exterior to the cluster region. The residual excitations in the interior region of the cluster are characterized by local density fluctuations on the timescale of the plasma period. The interaction of clusters with femtosecond laser pulses is studied for peak intensities up to 1014W/cm2.Nonlinear plasma-wave generation at the cluster surface can be observed, which appears in the presence of strong laser-induced polarization fields. The acceleration of plasma waves through the cluster results in enhanced outer ionization close to the cluster poles. Recombinations of emitted electron wave packets result infast density oscillations on the attosecond scale