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

TL;DR

This paper investigates the forces on a moving charge near doped graphene using RPA, highlighting the role of inter-band excitations, substrate effects, and damping, with analytical results relevant to surface processes.

Contribution

It provides a comprehensive RPA-based analysis of stopping and image forces on charges near graphene, including effects of substrate gaps and damping, with analytical expressions at low speeds.

Findings

Inter-band excitations are crucial at high particle speeds.

Finite damping and substrate gaps significantly influence the forces.

Analytical expressions for the friction coefficient at low speeds are derived.

Abstract

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.