Magnetic moment of an electron near a surface with dispersion

TL;DR

This paper derives a general formula for the magnetic moment correction of an electron near dispersive surfaces, revealing significant differences from idealized models and showing how material properties can tune the correction.

Contribution

It introduces a comprehensive method to calculate boundary-dependent magnetic moment corrections considering dispersion and evanescent modes.

Findings

Magnetic moment correction varies significantly with surface properties.

Dispersion and evanescent modes influence the correction more than perfect reflector models.

Material parameters can tune the magnitude and position of the magnetic moment peak.

Abstract

Boundary-dependent radiative corrections that modify the magnetic moment of an electron near a dielectric or conducting surface are investigated. Normal-mode quantization of the electromagnetic field and perturbation theory applied to the Dirac equation for a charged particle in a weak magnetic field yields a general formula for the magnetic moment correction in terms of any choice of electromagnetic mode functions. For two particular models, a non-dispersive dielectric and an undamped plasma, it is shown that, by using contour integration techniques over a complex wave vector, this can be simplified to a formula featuring just integrals over TE and TM reflection coefficients of the surface. Analysing the magnetic moment correction for several models of surfaces, we obtain markedly different results from the previously considered simplistic `perfect reflector' model, which is due to the inclusion of physically important features of the surface like evanescent field modes and dispersion in the material. Remarkably, for a general dispersive dielectric surface, the magnetic moment correction of an electron nearby has a peak whose position and height can be tuned by choice of material parameters.