Revealing the spatial distribution of quantum states in materials for quantum technologies: quantum crystallography of defects

Both electron and X-ray diffraction have been used to not only determine the positions of atoms in materials, but also to detect charge density changes due to bonding. This has become known as quantum crystallography. Diffraction methods can only be applied to perfect crystals.

This project aims to address a major challenge, the detection of charge redistribution at defects in crystals. Methods associated with 4D-STEM methods, such as ptychography, have been shown to have sensitivity to charge redistribution. The aim is to develop methods to detect charge redistribution at defects using a combination of 4D-STEM methods and DFT modelling.

The term, 4D-STEM, refers to the collection of a diffraction pattern (in two dimensions of reciprocal space) for each real-space position of a focused illumination electron beam which is scanned in two dimensions. Ptychography makes use of the 4D-STEM data set to unlock the phase problem so that the small phase shift experienced by an electron transmitted through a sample can be measured.

This phase shift is proportional to the project electrostatic potential in the sample. This potential will be dominated by nuclear scattering, but we have shown in previous work that small charge redistribution due to bonding can be detected in crystalline materials. The aim is to apply that approach to defects.

The approach will be to develop robust metrics, starting with an orthogonal multipolar basis set for non-round potentials, that can be compared with density functional theory (DFT) calculations. Specific steps include:

1. Building a portfolio of metrics to allow quantitative comparison of 4D-STEM data and DFT modelling, circular and spherical harmonics (multipoles). 2. Including the effects of dynamical scattering and thermal vibrations in the models. 3. Exploring the impact of a range of DFT functionals. 4. Recording experimental data to use in developed framework.

Initially, the project will work with defects in 2D materials such a transition metal dichalcogenides, but the longer goal is to develop methods for thicker crystals where the multiple scattering of electrons will become significant. This will allow us to look a crystals such as transition metal oxides and even battery cathode materials.

This project falls within the EPSRC research areas of analytical science; catalysis; electronic structure; energy storage; functional ceramics; graphene and carbon nanotechnology; materials for energy applications; quantum devices components and systems and the EPSRC theme of physical sciences.