The response of an electron in the image potential on the external steady fields

TL;DR

This paper derives exact wave functions for an electron in an image potential under a perpendicular magnetic field, calculates energy corrections due to an external electric field, and discusses potential experimental measurements of local electric fields.

Contribution

It provides exact solutions for electron states in combined image potential and magnetic field, and analyzes energy shifts due to external electric fields.

Findings

Exact wave functions for electron in image potential and magnetic field

First-order energy correction due to external electric field

Potential for measuring local electric fields via level shifts

Abstract

The exact wave functions, which describe the states of an electron, bound in the image potential, and the magnetic field, which is perpendicular to surface of a metal, are obtained. The correction terms to the energy of an electron in the first order of the perturbation theory with respect to the interaction with the external electric field are calculated. The possibility of experimental measurement of a local electric field by the level shift is analyzed.