On the role of the energy loss function in the image force on a charge moving over supported graphene

Abstract

We use a dielectric response theory to describe electrodynamic forces on a charged particle moving parallel to a supported two-dimensional layer. Using a Kramers–Kronig relation, we show that the image force on the particle can be expressed in terms of the energy loss function of the target materials. This enables us to analyze the stopping and the image forces on the particle on equal footing in the frequency–momentum domain encompassing all the energy loss channels in the target. Using the example of a graphene layer on a silicon carbide substrate, we show that both the image and stopping forces can be decomposed into contributions coming from two modes arising from hybridization of the sheet plasmon in doped graphene and a transverse optical phonon in the substrate.

Quantum view of Li-ion high mobility at carbon-coated cathode interfaces

“… 39 A carbon/LCO ohmic contact is formed, in this case the positive charge/ion inside the crystal forms a negative image charge at the carbon coating layer that in turn attracts the positrons, as predicted by Rivas et al. 40 In fact, Shi et al. 41 , 42 have shown that “positrons” are a highly sensitive probe at the coating/semiconductor quantum dots interface.…”

Launching Plasmons in a Two-Dimensional Material Traversed by a Fast Charged Particle

“…While this assumption is necessary to validate the neglect of the magnetic fields due to the moving particle, a fully relativistic formulation of the problem showed that the magnetic field due to the induced current in a conducting sheet may only be neglected if one additionally assumes that , see Equation ( 6 ) in [ 17 ]. This inequality is automatically satisfied by assuming for a particle moving parallel to the sheet because of the resonance condition [ 28 , 29 ], but for the perpendicular trajectory in Figure 1 , a strong hybridization of the plasmon dispersion with the light line can affect the launching of plasmons with long wavelengths, even when . The proximity of the region , which was shown to give rise to a sizeable radiative energy loss in doped graphene in the THz-MIR frequency range [ 22 , 23 , 24 ], renders the issue of the nonrelativistic approximation rather nontrivial in the present context.…”

“…Even before we commit to the study of a particular conductivity model, we can make a number of theoretical developments assuming that the 2D sheet is isotropic, so that its conductivity depends on the norm and is also an arbitrary complex function of frequency that must satisfy certain general properties [ 22 , 28 ]. The quantity of primary interest in this section is the integral which is related to the expression for the induced potential in the -domain by as can be seen from our convention ( 2 ) for the Fourier transform.…”

“…This model gives rise to the characteristic square-root dispersion of the plasmon frequency in 2D materials, , for small values. However, it is also necessary to take into account a correction to the in-plane conductivity in the THz–MIR range, which comes from high-energy interband electron transitions in those materials [ 27 , 28 , 29 ]. It was shown that this correction gives rise to a saturation of the plasmon dispersion as the wavenumber k increases, resulting in slowing down of such plasmons [ 25 , 28 , 29 ].…”

“…However, it is also necessary to take into account a correction to the in-plane conductivity in the THz–MIR range, which comes from high-energy interband electron transitions in those materials [ 27 , 28 , 29 ]. It was shown that this correction gives rise to a saturation of the plasmon dispersion as the wavenumber k increases, resulting in slowing down of such plasmons [ 25 , 28 , 29 ]. Hence, it is worthwhile to explore the effects of this slowing down in the dynamics of launching such sheet plasmons by an impact of the incident charged particle.…”