Multiple excitation of Fuchs–Kliewer phonons by Ne⁺ions back-scattered by the LiF(100) surface at grazing incidence

Abstract

An analytic model is developed to describe the inelastic processes occurring when keV Ne(+) ions are scattered at grazing incidence by the (100) surface of LiF. The large energy losses (up to 30 eV) of the reflected Ne(+) particles reported by Borisov et al (1999 Phys. Rev. Lett. 83 5378) are shown to arise specifically from the long-range coupling between the projectiles and the so-called Fuchs-Kliewer (FK) optical phonons of LiF whose fields extend far outside the surface. The strength of the coupling is estimated, allowing one to compute the average number of excited FK phonon quanta (ħωS = 0.071 eV) and hence the mean energy losses. For emerging, neutralized Ne(0), a distinct energy loss mechanism is shown to occur, namely the excitation of FK phonons and other types of surface collective modes associated with the screening of the F(0) 'hole' left behind by the neutralization process. This mechanism contributes a large fraction of the loss, additional to that suffered by the incident Ne(+) ion. The model explains the experimental observations quantitatively (1999 Phys. Rev. Lett. 83 5378). The paper ends with a discussion of the large energy broadening of the observed loss peaks.

Probing the Plasmon-Phonon Hybridization in Supported Graphene by Externally Moving Charged Particles

“…Given that typical ion speeds used in the LEIGS technique [23][24][25][26] are precisely in the subthreshold velocity range, it appears that small variations in the doping density close to the neutrality point of graphene may cause dramatic changes in the mechanism of energy loss due to suppressing or enabling the plasmonphonon hybridization.…”

“…This technique was recently used to study collective modes in epitaxial graphene on a SiC substrate, revealing low-energy features in the REEL spectra [18,19] that were interpreted in terms of the plasmonphonon hybridization [19][20][21][22]. On the other hand, recent measurements of the energy loss spectra and the angular distributions of the Ne + ions with energies in the keV range, which are grazingly scattered with an angle of incidence of about 1°f rom a LiF(001) surface [23,24], showed strong promise as efficient probe for multiple excitations of the FK phonons on a polar insulating surface [25,26]. It is noteworthy that both REELS and the low-energy ion grazing scattering (LEIGS) [23][24][25][26] use charged particles that move at the speeds comparable to the Fermi speed v F ≈c/300 (where c is the speed of light in vacuum) of graphene's π electron bands in the Dirac cone approximation [2].…”

“…On the other hand, recent measurements of the energy loss spectra and the angular distributions of the Ne + ions with energies in the keV range, which are grazingly scattered with an angle of incidence of about 1°f rom a LiF(001) surface [23,24], showed strong promise as efficient probe for multiple excitations of the FK phonons on a polar insulating surface [25,26]. It is noteworthy that both REELS and the low-energy ion grazing scattering (LEIGS) [23][24][25][26] use charged particles that move at the speeds comparable to the Fermi speed v F ≈c/300 (where c is the speed of light in vacuum) of graphene's π electron bands in the Dirac cone approximation [2]. Since the LEIGS technique was never used to study plasmon-phonon hybridization on a surface, it is of interest to investigate dynamic polarization of a largearea monolayer graphene supported by a polar insulator due to external point charge particle that moves (almost) parallel to graphene.…”

“…Since the LEIGS technique was never used to study plasmon-phonon hybridization on a surface, it is of interest to investigate dynamic polarization of a largearea monolayer graphene supported by a polar insulator due to external point charge particle that moves (almost) parallel to graphene. In addition to the energy loss rate, or stopping power of that particle [23,25], the complexity of ion trajectories during skipping motion on the target surface in LEIGS also requires careful analysis of the dynamic image force [24,26].…”

“…We use the dielectric response formalism based on graphene's dielectric function within the random phase approximation (RPA) [34][35][36] to calculate the total electrostatic potential in the graphene plane, as well as the stopping and image forces on the incident charge in a setting of interest for the LEIGS technique [23][24][25][26].…”