Polar vortices in twisted BaTiO₃ layers

Complex correlated oxides are a class of quantum materials characterized by unscreened d-electrons that interact across competing energy scales, giving rise to a diverse range of functionalities that can be modulated by a variety of external stimuli. However, their cube-on-cube epitaxial structure constrains their growth to single-crystalline substrates, thereby limiting the crystallographic orientations and interfacial phenomena available in sequential layer growth. Recent advances in the manipulation of complex oxides have enabled their isolation from parent substrates, characterization of their properties at the few unit cell limit (2D), and probing as a function of external strains.

Here we demonstrate that twisted BaTiO₃ layers produce unconventional strain configurations that results in the formation of ferroelectric topological structures. We analyze the formation of such non-trivial structures as a function of the twisted angle and the thickness of the different layers by means of aberration-corrected scanning transmission electron microscopy in combination with density-functional theory calculations. These results show the possibility to create non-trivial strain patterns through unique moiré assemblies with deep consequences in the ground-state and responses of complex correlated oxides.