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Perpendicular and parallel motion of a charged particle relatively to a graphene sheet: A hydrodynamic model approach in the electrostatic limit | | A.J. Chaves
; N.M.R. Peres
; G. Smirnov
; N. Asger Mortensen
; | | Date: |
14 Aug 2017 | | Abstract: | In this this paper we introduce the hydrodynamic model of graphene
considering for the hydrodynamic electronic mass graphene’s Drude mass
$m_{g}=hbar k_{F}/v_{F}$, where $k_{F}$ and $v_{F}$ are the Fermi wavenumber
and Fermi speed, respectively. 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 ship 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 ship
wake valid at high speeds of the moving charge. 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. | | Source: | arXiv, 1708.4274 | | Services: | Forum | Review | PDF | Favorites | |
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