Using electron vortex beams to determine chirality of crystals in transmission electron microscopy

TL;DR

This paper introduces a novel method using electron vortex beams in transmission electron microscopy to determine the chirality of crystals by analyzing diffraction pattern symmetries, applicable to very thin samples and verified through simulations and experiments.

Contribution

The paper develops a theoretical framework linking vortex beam properties to crystal chirality and proposes a new diffraction-based technique that does not rely on multiple scattering.

Findings

Method successfully distinguishes crystal handedness.

Simulations and experiments confirm the technique's effectiveness.

Applicable to ultra-thin chiral crystal samples.

Abstract

We investigate electron vortex beams elastically scattered on chiral crystals. After deriving a general expression for the scattering amplitude of a vortex electron, we study its diffraction on point scatterers arranged on a helix. We derive a relation between the handedness of the helix and the topological charge of the electron vortex on one hand, and the symmetry of the Higher Order Laue Zones in the diffraction pattern on the other for kinematically and dynamically scattered electrons. We then extend this to atoms arranged on a helix as found in crystals which belong to chiral space groups and propose a new method to determine the handedness of such crystals by looking at the symmetry of the diffraction pattern. Contrary to alternative methods, our technique does not require multiple scattering which makes it possible to also investigate extremely thin samples in which multiple scattering is suppressed. In order to verify the model, elastic scattering simulations are performed and an experimental demonstration on Mn$_2$Sb$_2$O$_7$ is given where we find the sample to belong to the right handed variant of its enantiomorphic pair. This demonstrates the usefulness of electron vortex beams to reveal the chirality of crystals in a transmission electron microscope and provides the required theoretical basis for further developments in this field.