Manifold learning of four-dimensional scanning transmission electron microscopy

Four-dimensional scanning transmission electron microscopy (4D-STEM) of local atomic diffraction patterns is emerging as a powerful technique for probing intricate details of atomic structure and atomic electric fields. However, efficient processing and interpretation of large volumes of data remain challenging, especially for two-dimensional or light materials because the diffraction signal recorded on the pixelated arrays is weak. Here we employ data-driven manifold leaning approaches for straightforward visualization and exploration analysis of 4D-STEM datasets, distilling real-space neighboring effects on atomically resolved deflection patterns from single-layer graphene, with single dopant atoms, as recorded on a pixelated detector. These extracted patterns relate to both individual atom sites and sublattice structures, effectively discriminating single dopant anomalies via multimode views. We believe manifold learning analysis will accelerate physics discoveries coupled between data-rich imaging mechanisms and materials such as ferroelectric, topological spin, and van der Waals heterostructures.