3D mapping of defects and moiré corrugations via electron ptychography atomic coordinate retrieval

Defects and reconstructions in two-dimensional (2D) moiré materials cause out-of-plane deformations that strongly modify their electronic properties but are difficult to experimentally access. Here, we solve the 3D atomic coordinates of twisted bilayer WSe₂ with picometer-scale accuracy using multislice electron ptychography (MEP) acquired from a single orientation. The resulting atomic models individually visualize each of the six atomic planes, revealing the curvature of each WSe₂ layer, variations in the interlayer spacing, and the 3D locations of individual vacancies, which lie exclusively in the outer Se planes. We also observe an unexpected type of structural disorder consisting of mixed bending- and breathing-type moiré-induced corrugations that should strongly affect the emergent electronic properties. Broadly, our methods generate 3D atom-by-atom models of a 2D heterointerface from data acquired in about 30 seconds, methods that should unlock routine access to 3D atomic information in 2D systems and catalyze design methods to control out-of-plane deformations.