On the correlation between topological defects of polarization field and Euler characteristics of ferroelectric nanostructures

Abstract

Materials with spatial-reversal broken symmetry such as ferroelectrics rarely exhibit topological field patterns, in contrast to time-reversal broken symmetry materials. Recently, geometrical confinements at the nanoscale are demonstrated to play an important role in the stabilization of nontrivial topological polarization patterns in ferroelectrics; however, a direct correlation between them remains hidden. In the present study, we establish a correlation between the topology of finite nanostructures and the topology of polarization fields through phase-field simulations and topological theory of defects. The obtained results show that ferroelectric nanostructures can exhibit stable topological defects in their polar patterns that are composed of topological bulk and edge defects with an integer and fractional winding numbers, respectively. In addition, we demonstrate that topological characteristics of polarization patterns are conserved, regardless of the structure transformation and external electric and mechanical fields. Such conserved topological defects in polarization patterns consistently relate to the Euler characteristics of ferroelectric nanostructures. Furthermore, we propose and prove a concept for geometry-mediated trapping of local topological defects in ferroelectric nanostructures, where defects can be intentionally tailored through a geometrical design.