Singular stress field induced two-dimensional topological polar structures in SrTiO3: Topological number manipulation via loading modes

Topological structures in condensed matter attract much attention of the scientific community due to their unique and significant properties. In contrast to the well-explored topological spin structures such as meron, and skyrmion in ferromagnetic materials , ferroelectrics face challenges in forming topological polar structures due to the absence of a spontaneous driving force. Nevertheless, the coupling effect between polarization and strain (gradient), e.g. piezoelectricity and flexoelectricity , provides a mechanical approach to induce topological polar structures that reflect the intricate features of the strain (gradient) field. This study demonstrates the creation of a topological polar structure through a mode II crack-induced singular stress field in SrTiO 3 by using phase-field simulations. Furthermore, under mixed-mode loading of mode I and mode II, alterations in the mode ratio induce a variety of topological structures, including a novel structure (winding number n v = 4 ) that is absent under the single-mode loading. Our study demonstrates that topological strain field can be a general and effective tool to generate and control topological polar structures.