Hydrodynamic model approach to the formation of plasmonic wakes in graphene

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.

Mesoscopic electrodynamics at metal surfaces

“…Depending on the level of doping and the ratio of optical energy ℏ𝜔 relative to the Fermi energy  F , quantum nonlocal effects can manifest in graphene nanostructures of a finite dimension [73,[348][349][350][351] or when the large-q ∥ response of graphene is probed, e.g. by singular metasurfaces [352], electron beams [353,354] or by in-elastic scattering processes [355]. In addition, the termination of the graphene lattice can also lead to electronic edge states at the Dirac point, e.g.…”

Wigner-Weyl description of massless Dirac plasmas

“…As one can readily observe by comparing Eqs. ( 40) and ( 46), a proportionality relation of the form relation p = mv does not hold for massless particles [42]. However, by allowing a space and time dependence on the mass, we are able to define an effective "mass tensor" as…”

Terahertz Frequency Comb in Graphene Field-Effect Transistors

“…The electronic flow in graphene is suitable to be modelled by in a hydrodynamic description neglecting viscosity, and assuming also that transport is restricted to occur only in on direction, x [10,11]. This motion is governed by the Euler equations ∂n ∂t + ∂ ∂x nv = 0 and ∂v ∂t…”

“…Moreover, throughout this work electrons are considered to be at degenerate Fermi liquid regime insofar that the Fermi level remains bellow the Van Hove singularities, such conditions in graphene at room temperature translate to 0.025 eV E F 3 eV. Yet, the fact that electrons in graphene behave as massless fermions pose a difficulty to the development of models with explicit dependency on the mass, in our case the nominal Drude mass m * = √ πn 0 /v F , where v F = 10 6 ms −1 is the Fermi velocity and n 0 the equilibrium carrier density, is used as an effective mass [10,12]. Then, the pressure term in (1) can be recast as P = v F √ πn 3 /3, resorting to the usual Fermi liquid pressure.…”