# Nonuniform currents and spins of relativistic electron vortices in a magnetic field

## TL;DR

This paper provides a relativistic quantum mechanical analysis of electron vortex beams in magnetic fields, revealing complex current structures, conditions for zero spin-orbit mixing, and nonuniform spin polarization.

## Contribution

It introduces a detailed relativistic model of electron vortex beams, highlighting the conditions for zero spin-orbit mixing and analyzing spin polarization in magnetic fields.

## Key findings

- Electron vortex beams exhibit complex azimuthal current structures.
- Existence of vortex beams with zero spin-orbit mixing in relativistic regimes.
- Spin polarization varies across the beam, making spin and orbital degrees inseparable.

## Abstract

We present a relativistic description of electron vortex beams in a homogeneous magnetic field. Including spin from the beginning reveals that spin-polarized electron vortex beams have a complicated azimuthal current structure, containing small rings of counterrotating current between rings of stronger corotating current. Contrary to many other problems in relativistic quantum mechanics, there exists a set of vortex beams with exactly zero spin-orbit mixing in the highly relativistic and nonparaxial regime. The well defined phase structure of these beams is analogous to simpler scalar vortex beams, owing to the protection by the Zeeman effect. For states that do show spin-orbit mixing, the spin polarization across the beam is nonuniform rendering the spin and orbital degrees of freedom inherently inseparable.