Electronic friction for a slow impurity in an inhomogeneous metallic system

TL;DR

This paper derives an exact method to calculate the electronic friction coefficient for a slow impurity in an inhomogeneous metallic system using a static Kohn-Sham approach, emphasizing local system characteristics.

Contribution

It extends the Shifted Fermi Surface method to inhomogeneous systems, providing a local-characteristics-based exact calculation of the friction coefficient.

Findings

Friction coefficient varies linearly with impurity velocity.

The coefficient is determined solely by local system properties.

Non-local contributions can introduce errors, as shown in a 1D model.

Abstract

The stopping power of a metal for a slow structureless impurity varies linearly with projectile velocity. We show that the coefficient of this linear behavior (friction coefficient) is determined exactly in a static ensemble Kohn-Sham scheme, by extension of the Shifted Fermi Surface procedure originally derived for an homogeneous jellium. We prove that the friction coefficient is determined only by local characteristics of the system. The error incurred when adding a spurious non-local contribution is illustrated for a simple 1D model.