A hydrodynamic model approach to the formation of plasmonic wakes in graphene

摘要

Using the hydrodynamic model in the electrostatic approximation, we describethe formation of graphene surface plasmons when a charge is in motion eitherperpendicular or parallel to a graphene sheet. In the first case, theelectron-energy loss (EEL) spectrum of the electron is computed, showing thatthe resonances in the spectrum are linked to the frequency of the graphenesurface plasmons. In the second case, we discuss the formation of plasmonicwakes due to the dragging of the surface plasmons induced by the motion of thecharge. This effect is similar to Coulomb drag between two electron gases at adistance from each other. We derive simple expressions for the electrostaticpotential induced by the moving charge on graphene. We find an analyticalexpression for the angle of the plasmonic wake valid in two opposite regimes.We show that there is a transition from a Mach-type wake at high speeds to aKelvin-type wake at low ones and identify the Froude number for plasmonicwakes. We show that the Froude number can be controlled externally tunning boththe Fermi energy in graphene and the dielectric function of the environment, asituation with no parallel in ship wakes. Using EEL we propose a source of graphene plasmons, based on a graphene drumbuilt in a metallic waveguide and activated by an electron beam created by thetip of an electronic microscope. We also introduce the notion of a plasmonic billiard.