Interactions of fast charged particles with supported two-dimensional electron gas: One-fluid model

We investigate the interactions of fast charged particles with a two-dimensional (2D) electron gas (2DEG) supported by an insulating substrate, describing its collective or plasmon excitations by a one-fluid hydrodynamic model with the parameters characteristic of graphene. By linearizing the hydrodynamic equations, we derive general expressions for the induced potential, stopping force and the image force on a particle moving parallel to the 2DEG, as well as for the induced number density per unit area of electrons in the 2DEG. Numerical results are obtained showing the effects of variation in size of the gap between the 2DEG and the SiO2 substrate on these quantities. It is also found that, when the particle speed exceeds a threshold value for the collective excitations, the oscillatory wake effect develops in the induced number density trailing the particle.