Time-dependent screening of a point charge at a metal surface

The space-time evolution of the dynamical screening charge density caused by a suddenly created point charge at the Cu(111) surface is investigated in the linear response approximation. Considering a thin slab as a model for the Cu(111) surface, we investigate the confinement effects on dynamical screening as well. The results have been obtained on the basis of self-consistent evaluation of the energy-momentum-dependent response function, taking into account the realistic surface band structure of Cu(111). At the initial stage, we observe fast long-range charge density oscillations due to excitation of the surface plasmon modes. Then we observe the propagation of the shock wave of the electron-hole excitations along the slab with velocity determined by the Fermi velocity of bulk Cu. At longer times, we have identified the propagation along the two slab surfaces of a much slower (with velocity similar to 0.3 au, close to the Fermi velocity of the Cu(111) surface state) charge disturbance due to acoustic surface plasmon. The role of the energy band gap in the direction perpendicular to the surface in establishing the screening is also addressed.