The recent discovery of polar vortex in PbTiO3/SrTiO3 (PTO/STO) superlattices opens up exciting opportunities to explore the structure and dynamics of complex topological states of ferroelectric dipoles and potentially leads to novel electronic functionalities. To obtain deep insights into the vortex formation mechanisms, we applied machine learning analysis to the atomically resolved microscopy images of PTO/STO, revealing the ground-truth vortex fine structure which suggests the contribution of flexoelectricity. Phase-field modeling was performed to systematically survey the flexocoupling effect on the system. We matched the experiment and modeling results and thereby quantified the flexocoupling coefficients of PTO and STO. On the other hand, ultrafast electric field in the form of THz laser pulses can couple with the vortices via coherent dipole interaction, providing a well-defined, easy-to-model external control knob for probing the ultrafast structural dynamics of this system. We performed a THz pulse pump, ultrafast X-ray scattering probe study of PTO/STO based on the hard X-ray free-electron laser at the Linac Coherent Light Source. We observed a set of subterahertz collective excitations of the polar vortices stemming from the lattice dipoles, and further identified a unique soft vortex mode with marked strain and electric-field tunabilities. These observations were well corroborated by multiscale simulations combining the newly developed dynamical phase-field modeling and atomistic modeling.
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