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

TL;DR

This paper models the formation of plasmonic wakes in graphene using a hydrodynamic approach, revealing a transition from Mach to Kelvin wakes and proposing a new plasmon source based on a graphene drum.

Contribution

It introduces a hydrodynamic model for graphene plasmon wakes, derives analytical expressions for wake angles, and proposes a novel plasmon source using a graphene drum.

Findings

Identified transition from Mach to Kelvin wakes controlled by Froude number.

Derived simple expressions for electrostatic potential and wake angles.

Proposed a graphene drum as a tunable plasmon source.

Abstract

Using the hydrodynamic model in the electrostatic approximation, we describe the formation of graphene surface plasmons when a charge is in motion either perpendicular or parallel to a graphene sheet. In the first case, the electron-energy loss (EEL) spectrum of the electron is computed, showing that the resonances in the spectrum are linked to the frequency of the graphene surface plasmons. In the second case, we discuss the formation of plasmonic wakes due to the dragging of the surface plasmons induced by the motion of the charge. This effect is similar to Coulomb drag between two electron gases at a distance from each other. We derive simple expressions for the electrostatic potential induced by the moving charge on graphene. We find an analytical expression 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 a Kelvin-type wake at low ones and identify the Froude number for plasmonic wakes. We show that the Froude number can be controlled externally tunning both the Fermi energy in graphene and the dielectric function of the environment, a situation with no parallel in ship wakes. Using EEL we propose a source of graphene plasmons, based on a graphene drum built in a metallic waveguide and activated by an electron beam created by the tip of an electronic microscope. We also introduce the notion of a plasmonic billiard.