Quantum discretization of Landau damping

Abstract

We derive and analyze analytical expressions for the quantum electron current density and electromagnetic field distribution inside a metallic nanoslab. Besides, we obtain general explicit expressions for the surface impedances of both metal slab boundaries. We found that the phenomenon of Landau damping manifests itself in the frequency dependence of the surface impedances as resonances associated with the discretization of the electromagnetic and electron wave numbers inside the metal nanoslab. In particular, the quantum nonlocal resonances of the surface impedances are clearly discernible at slab thicknesses smaller than the electromagnetic skin depth. The predictions for the surface impedances in the quantum regime turn out to be radically different from those of the quantum local approach, the semiclassical Boltzmann kinetic equation formalism and the classical Drude-Lorentz local model. The analytical study completely agrees with the respective numerical calculations.