The wealth of complex polar topologies^1–10 recently found in nanoscale ferroelectrics results from a delicate balance between the intrinsic tendency of the materials to develop a homogeneous polarization and the electric and mechanical boundary conditions imposed on them. Ferroelectric–dielectric interfaces are model systems in which polarization curling originates from open circuit-like electric boundary conditions, to avoid the build-up of polarization charges through the formation of flux-closure^11–14 domains that evolve into vortex-like structures at the nanoscale^15–17 level. Although ferroelectricity is known to couple strongly with strain (both homogeneous¹⁸ and inhomogeneous^19,20), the effect of mechanical constraints²¹ on thin-film nanoscale ferroelectrics has been comparatively less explored because of the relative paucity of strain patterns that can be implemented experimentally. Here we show that the stacking of freestanding ferroelectric perovskite layers with controlled twist angles provides an opportunity to tailor these topological nanostructures in a way determined by the lateral strain modulation associated with the twisting. Furthermore, we find that a peculiar pattern of polarization vortices and antivortices emerges from the flexoelectric coupling of polarization to strain gradients. This finding provides opportunities to create two-dimensional high-density vortex crystals that would enable us to explore previously unknown physical effects and functionalities.

In scanning transmission electron microscopy (STEM), single atoms can be imaged by detecting electrons scattered through high angles using post-specimen, annular-type detectors. Recently, it has been shown that the atomic-scale electric field of both the positive atomic nuclei and the surrounding negative electrons within crystalline materials can be probed by atomic-resolution differential phase contrast STEM. Here we demonstrate the real-space imaging of the (projected) atomic electric field distribution inside single Au atoms, using sub-Å spatial resolution STEM combined with a high-speed segmented detector. We directly visualize that the electric field distribution (blurred by the sub-Å size electron probe) drastically changes within the single Au atom in a shape that relates to the spatial variation of total charge density within the atom. Atomic-resolution electric field mapping with single-atom sensitivity enables us to examine their detailed internal and boundary structures.

At interfaces between conventional materials, band bending and alignment are classically controlled by differences in electrochemical potential. Applying this concept to oxides in which interfaces can be polar and cations may adopt a mixed valence has led to the discovery of novel two-dimensional states between simple band insulators such as LaAlO₃ and SrTiO₃. However, many oxides have a more complex electronic structure, with charge, orbital and/or spin orders arising from strong Coulomb interactions at and between transition metal and oxygen ions. Such electronic correlations offer a rich playground to engineer functional interfaces but their compatibility with the classical band alignment picture remains an open question. Here we show that beyond differences in electron affinities and polar effects, a key parameter determining charge transfer at correlated oxide interfaces is the energy required to alter the covalence of the metal–oxygen bond. Using the perovskite nickelate (RNiO₃) family as a template, we probe charge reconstruction at interfaces with gadolinium titanate GdTiO₃. X-ray absorption spectroscopy shows that the charge transfer is thwarted by hybridization effects tuned by the rare-earth (R) size. Charge transfer results in an induced ferromagnetic-like state in the nickelate, exemplifying the potential of correlated interfaces to design novel phases. Further, our work clarifies strategies to engineer two-dimensional systems through the control of both doping and covalence.

Material properties are sensitive to atomistic structure defects such as vacancies or impurities, and it is therefore important to determine not only the local atomic configuration but also their chemical bonding state. Annular dark-field scanning transmission electron microscopy (STEM) combined with electron energy-loss spectroscopy has been utilized to investigate the local electronic structures of such defects down to the level of single atoms. However, it is still challenging to two-dimensionally map the local bonding states, because the electronic fine-structure signal from a single atom is extremely weak. Here, we show that atomic-resolution differential phase-contrast STEM imaging can directly visualize the anisotropy of single Si atomic electric fields in monolayer graphene. We also visualize the atomic electric fields of Stone–Wales defects and nanopores in graphene. Our results open the way to directly examine the local chemistry of the defective structures in materials at atomistic dimensions.