Dynamic polarization of graphene by moving external charges: random phase approximation

We evaluate the stopping and image forces on a charged particle moving parallel to a doped sheet of graphene by using the dielectric response formalism for graphene's $\pi$-electron bands in the random phase approximation (RPA). The forces are presented as functions of the particle speed and the particle distance for a broad range of charge-carrier densities in graphene. A detailed comparison with the results from a kinetic equation model reveal the importance of inter-band single-particle excitations in the RPA model for high particle speeds. We also consider the effects of a finite gap between graphene and a supporting substrate, as well as the effects of a finite damping rate that is included through the use of Mermin's procedure. The damping rate is estimated from a tentative comparison of the Mermin loss function with a HREELS experiment. In the limit of low particle speeds, several analytical results are obtained for the friction coefficient that show an intricate relationship between the charge-carrier density, the damping rate, and the particle distance, which may be relevant to surface processes and electrochemistry involving graphene.Comment: 14 pages, 10 figures, accepted for publication in Phys. Rev.

Invited Lecture INTERACTIONS OF IONS WITH CARBON NANO-STRUCTURES

Abstract. Investigation into the properties of carbon nano-structures, involving fullerene molecules, carbon nanotubes, and the most recently contrived graphene, has been growing at a relentless rate over the past decade or so owing to prospects of their applications in nanotechnology. While interactions with particle beams have been an important part of this research endeavor in the context of various spectroscopic techniques (TEM, EELS, ...), the use of energetic electron and ion beams has recently emerged as a novel engineering tool for modifications of atomic structure and electronic properties of carbon nano-structures In that context, the most widely studied themes in literature are concerned with changes in carbon nanotubes upon exposure to the ion-beam irradiation at energies ranging from several tens of eV to some MeV. On the other hand, the empty cylindrical space in individual carbon nanotubes, and a high degree of their ordering and alignment in structures called ropes or bundles, provide unique means for achieving the effect of ion channeling. Prospects of realization and a range of possible applications of ion channeling through carbon nanotubes at energies from keV to TeV have stimulated an active research area, which was recently reviewed After assessing some key experimental facts and the status of computer simulations of ion irradiation effects on carbon nanotubes, I shall discuss several problems arising in modeling of ion interactions with carbon nanotube