Wake effect in interactions of fast ions with supported two-dimensional electron gas

We study the interactions of fast charged particles with a two-dimensional electron gas supported by an insulating substrate, describing its high-frequency plasmon excitations by a two-fluid hydrodynamic model with the parameters characteristic of graphene. The induced number density per unit area of electrons in the two-dimensional electron gas and the total electric potential in its plane are derived as functions of the projectile velocity and the particle position. We show that, when the speed of the particle moving parallel to the two-dimensional electron gas exceeds a threshold value for the collective excitations of σ and π electrons, the oscillatory wake effect develops both in the induced number density and in the total electric potential trailing the particle. When the particle speed matches the phase velocity of the quasiacoustic π plasmon, the induced number density shows usual wake oscillations, in contrast to the single-walled carbon nanotubes where oscillations precede the position of the particle.