Topology of ferroelectric nematic droplets: the case driven by flexoelectricity or depolarization field.

The recent discovery of ferroelectric nematics provides new opportunities for exploring polar topology in liquid matter. Here, we report numerous potential polarization topological states (, polar vortex-like and line disclination mediated structures) in confined ferroelectric nematics with similar free-energy levels. In the experiment, they appear according to the confinement size and surface anchoring conditions. Based on a minimal analytical approach, we reveal that the topological transformation is balanced among the nematic elasticity, the polarization gradient, the flexoelectric and the depolarization interactions.