Interactions of charged particle beams with double-layered two-dimensional quantum electron gases

• An oscillatory wake potential exists in the induced potential behind the proton.
• Two peaks for potential appear in two electron gases planes.
• The gap of two sheets has strong influence on the stopping and image forces.
• Double peaks existed in the stopping and image forces due to plasmon hybridization.
• The period of the wake oscillations is decreased by the existence of a substrate.

We investigate the interactions of external charged particles with a double-layered two-dimensional quantum electron gas (2DQEG), describing its collective or plasmon excitations by using the linearized quantum hydrodynamic (QHD) model. General expressions are derived for electron densities in the two layers, the induced potential, and the stopping and image forces on an external charged particle. Our calculations indicate that an oscillatory wake effect arises in the induced potential for a particle moving parallel the 2DQEG layers. In addition, double peaks are found in the stopping and image forces due to plasmon hybridization between the two 2DQEG layers. Finally, the induced number density in the double-layered 2DQEG is compared with the case of a single-layer 2DQEG supported by an insulating substrate.