Electron Ptychography Reveals Correlated Lattice Vibrations at Atomic Resolution

TL;DR

This paper introduces CAVIAR, a novel electron ptychography framework that visualizes atomic-scale correlated lattice vibrations, enabling insights into phonon dynamics and atomic motion with sub-Angstrom resolution.

Contribution

The paper presents a new ptychography method, CAVIAR, capable of imaging correlated atomic vibrations and phonon frequencies at the atomic scale from small volumes.

Findings

Reconstructed atomic displacements at 10-20 pm range.

Measured phonon frequencies consistent with neutron scattering.

Demonstrated imaging of atomic correlations in silicon and boron nitride.

Abstract

In this paper we introduce an electron ptychography reconstruction framework, CAVIAR -- Correlated Atomic Vibration Imaging with sub-Angstrom Resolution -- that reveals an entirely new channel of information: spatial correlations in atomic displacements at the atomic scale. We show reconstructions of a symmetric $\Sigma$9 grain boundary in silicon from realistically simulated data and experimental data for hexagonal boron nitride. By reconstructing the object as an ensemble of multiple states we are able to observe correlations between movements of atoms in the range of 10-20 pm at room temperature in agreement with the expectation. Moreover, using only the masses of the atomic species and the temperature as input, we obtain average frequencies of $10.8\pm0.1$, $13.6\pm0.6$, $18.0\pm0.2$, $25.5\pm1.5$ THz for the longitudinal and transversal acoustic and optic phonons, respectively, in agreement with inelastic neutron scattering, albeit from just a few nm$^3$ volume. This ability to spatially resolve correlated atomic motion makes CAVIAR a unique tool to explore atom dynamics at the finest scale with the potential to be instrumental in the development of phononic devices, in studying phonon-based decoherence in quantum systems, or other emerging phonon-based applications.