Hydrodynamic approximation for the nonlinear response of a metal surface

TL;DR

This paper develops hydrodynamic models to analyze the nonlinear electronic response of a metal surface, deriving explicit expressions for the dynamic image potential and revealing significant nonlinear effects near the surface.

Contribution

It introduces semi-classical and quantized hydrodynamic models to compute the quadratic electronic response and dynamic image potential of a metal surface, including nonlinear corrections.

Findings

Nonlinear image potential is enhanced by up to 15% near the surface for aluminum.

Nonlinear effects are more significant inside the solid than outside.

Explicit expressions for the dynamic image potential up to third order are derived.

Abstract

We present semi-classical and quantized hydrodynamic models to obtain the quadratic electronic response of a plane-bounded electron gas. Explicit expressions for the dynamic image potential experienced by charged particles moving near a jellium surface are derived, up to third order in the projectile charge. These expressions are employed to compute the image potential at all distances outside the surface. Though nonlinear corrections are found to be more important far inside the solid than outside, our results indicate that the nonlinear image potential is enhanced with respect to the linear image potential by a factor that is for Al as large as $\sim 1.15$ near the surface in the case of a stationary particle ($v\to 0$) with positive unit charge $e$.