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Utilizing quantum effects in complex oxides, such as magnetism, multiferroicity and superconductivity, requires atomic-level control of the material's structure and composition. In contrast, the continuous conductivity changes that enable artificial oxide-based synapses and multiconfigurational devices are driven by redox reactions and domain reconfigurations, which entail long-range ionic migration and changes in stoichiometry or structure. Although both concepts hold great technological potential, combined applications seem difficult due to the mutually exclusive requirements. Here we demonstrate a route to overcome this limitation by controlling the conductivity in the functional oxide hexagonal Er(Mn,Ti)O 3 by using conductive atomic force microscopy to generate electric-field induced anti-Frenkel defects, that is, charge-neutral interstitial-vacancy pairs. These defects are generated with nanoscale spatial precision to locally enhance the electronic hopping conductivity by orders of magnitude without disturbing the ferroelectric order. We explain the non-volatile effects using density functional theory and discuss its universality, suggesting an alternative dimension to functional oxides and the development of multifunctional devices for next-generation nanotechnology.

Moiré superlattices in van der Waals heterostructures have given rise to a number of emergent electronic phenomena due to the interplay between atomic structure and electron correlations. Indeed, electrons in these structures have been recently found to exhibit a number of emergent properties that the individual layers themselves do not exhibit. This includes superconductivity 1,2 , magnetism 3 , topological edge states 4,5 , exciton trapping 6 and correlated insulator phases 7 . However, the lack of a straightforward technique to characterize the local structure of moiré superlattices has thus far impeded progress in the field. In this work we describe a simple, room-temperature, ambient method to visualize real-space moiré superlattices with sub-5-nm spatial resolution in a variety of twisted van der Waals heterostructures including, but not limited to, conducting graphene, insulating boron nitride and semiconducting transition metal dichalcogenides. Our method uses piezoresponse force microscopy, an atomic force microscope modality that locally measures electromechanical surface deformation. We find that all moiré superlattices, regardless of whether the constituent layers have inversion symmetry, exhibit a mechanical response to out-of-plane electric fields. This response is closely tied to flexoelectricity wherein electric polarization and electromechanical response is induced through strain gradients present within moiré superlattices. Therefore, moiré superlattices of two-dimensional materials manifest themselves as an interlinked network of polarized domain walls in a non-polar background matrix.

In the pursuit of ferroic-based (nano)electronics, it is essential to minutely control domain patterns and domain switching. The ability to control domain width, orientation and position is a prerequisite for circuitry based on fine domains. Here, we develop the underlying theory towards growth of ultra-fine domain patterns, substantiate the theory by numerical modelling of practical situations and implement the gained understanding using the most widely applied ferroelectric, Pb(Zr,Ti)O3, demonstrating controlled stripes of 10 nm wide domains that extend in one direction along tens of micrometres. The observed electrical conductivity along these thin domains embedded in the otherwise insulating film confirms their potential for electronic applications.