Relativistic Electron Vortex Beams: Angular Momentum and Spin-Orbit Interaction

TL;DR

This paper constructs exact relativistic electron vortex beam solutions of the Dirac equation, revealing intrinsic spin-orbit coupling and Berry-phase effects, with observable spin-dependent distributions and corrected magnetic moments.

Contribution

It introduces exact Dirac equation solutions for electron vortex beams, incorporating relativistic, nonparaxial, and Berry-phase corrections, and predicts observable spin-orbit interactions.

Findings

Prediction of intrinsic spin-orbit coupling in free space

Calculation of magnetic moments with Berry-phase corrections

Observation of spin-dependent probability distributions

Abstract

Motivated by the recent discovery of electron vortex beams carrying orbital angular momentum (AM), we construct exact Bessel-beam solutions of the Dirac equation. They describe relativistic and nonparaxial corrections to the scalar electron beams. We describe the spin and orbital AM of the electron with Berry-phase corrections and predict the intrinsic spin-orbit coupling in free space. This can be observed as a spin-dependent probability distribution of the focused electron vortex beams. Moreover, the magnetic moment is calculated, which shows different $g$-factors for spin and orbital AM and also contains the Berry-phase correction.