# Peculiar Rotation of Electron Vortex Beams

## TL;DR

This paper investigates the complex rotational behaviors of electron vortex beams, revealing a combination of Larmor, cyclotron, and Gouy rotations, supported by a new model and experimental data.

## Contribution

It introduces a comprehensive model explaining the diverse rotational dynamics of electron vortex beams, including Landau states and multiple rotation regimes.

## Key findings

- Electron vortex beams exhibit various rotation types including no, cyclotron, Larmor, and Gouy rotations.
- The developed model links Landau states to the transition between different rotational regimes.
- Experimental data confirms the coexistence of multiple rotation behaviors in a single beam.

## Abstract

Standard electron optics predicts Larmor image rotation in the magnetic lens field of a TEM. Introducing the possibility to produce electron vortex beams with quantized orbital angular momentum brought up the question of their rotational dynamics in the presence of a magnetic field. Recently, it has been shown that electron vortex beams can be prepared as free electron Landau states showing peculiar rotational dynamics, including no and cyclotron (double-Larmor) rotation. Additionally very fast Gouy rotation of electron vortex beams has been observed. In this work a model is developed which reveals that the rotational dynamics of electron vortices are a combination of slow Larmor and fast Gouy rotations and that the Landau states naturally occur in the transition region in between the two regimes. This more general picture is confirmed by experimental data showing an extended set of peculiar rotations, including no, cyclotron, Larmor and rapid Gouy rotations all present in one single convergent electron vortex beam.