Twistronics has heavily relied on two-dimensional van der Waals materials. However, recent experiments have shown that twisting ferroelectric perovskite oxides could also result in novel features, such as the occurrence of an unusual shear strain morphology and the emergence of polar textures consisting of interconnected lattices of vortex and antivortex. Yet very little is known on the analytical formula of this strain pattern and of the finite-temperature stability and control or even annihilation of these polar textures in twisted ferroelectric oxide layers. We reveal here an analytical formula for the inhomogeneous shear strain imposed on a barium titanate layer by the twisting angle, and further develop a numerical scheme based on an effective Hamiltonian and resulting in Moiré lattices. We numerically confirm that the vortex-antivortex lattice emerges from the coupling of this inhomogeneous strain with local dipoles through the flexoelectric effects. We also predict that the vortex-antivortex lattice can be controlled and even annihilated by means of in-plane electric fields via striking phenomena, and that the shear strain (which is controlled by the twist angle) can revert the electric toroidal moment of the vortices, as well as a new order parameter characterizing polar antivortices, in the Moiré lattice.

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• Electric polarization
• Ferroelectricity
• Flexoelectricity