Dimensionality effects in time-dependent screening

The time dependent screening of a negative charge suddenly introduced in a two-dimensional free electron gas is studied. With time-dependent density functional theory, we show that the screening is built up over time scales similar to those of a three dimensional electron gas. However, and in marked contrast with the three dimensional system, collective oscillations are rapidly damped, and the system quickly reaches the stationary limit. This can be understood from the dispersion of the plasmon modes in the long wavelength limit. Scaling laws are outlined for the dynamics of screening in 2D electron gases with different densities.