Mapping Nanoscale Electrostatic Field Fluctuations around Graphene Dislocation Cores Using Four-Dimensional Scanning Transmission Electron Microscopy (4D-STEM).

Defects in crystalline lattices cause modulation of the atomic density, and this leads to variations in the associated electrostatics at the nanoscale. Mapping these spatially varying charge fluctuations using transmission electron microscopy has typically been challenging due to complicated contrast transfer inherent to conventional phase contrast imaging. To overcome this, we used four-dimensional scanning transmission electron microscopy (4D-STEM) to measure electrostatic fields near point dislocations in a monolayer. The asymmetry of the atomic density in a (1,0) edge dislocation core in graphene yields a local enhancement of the electric field in part of the dislocation core. Through experiment and simulation, the increased electric field magnitude is shown to arise from "long-range" interactions from beyond the nearest atomic neighbor. These results provide insights into the use of 4D-STEM to quantify electrostatics in thin materials and map out the lateral potential variations that are important for molecular and atomic bonding through Coulombic interactions.