Probing Valence Electron Distributions at Subatomic Resolution in a Charge Density Wave Material

This is the authors' abstract. We don't add key points for this paper.

Probing the internal electronic structure of complex materials with atomic spatial resolution has remained an outstanding challenge in condensed-matter science. A promising approach is convergent-beam electron diffraction (CBED) in four-dimensional scanning transmission electron microscopy (4D-STEM). Here, we apply 4D-STEM CBED to the charge-density-wave (CDW) material 1T-TaS2. We demonstrate a qualitative breakdown of the conventional independent atom model (IAM) in reproducing the experimental CBED patterns. A robust low-angle intensity maximum is systematically absent in IAM-based simulations but is consistently reproduced in simulations that use electrostatic potentials derived from density functional theory. A comparison of CBED patterns with projected charge densities reveals a remarkable correspondence between the local real-space valence charge distribution and diffracted intensities, reflecting site-dependent charge density variations within the CDW structure. These results establish atomic-resolution CBED as an experimental probe of valence electron contributions to the scattering potential and open a route to resolving complex electronic ordering phenomena.