Extended Data Fig. 2: Visualization of the role of the depolarization effect on field-induced dynamics of toroidal polar topology.

Comparisons between the simulation and experimental results on the polarization field reorientation behaviours under d.c. electric fields are shown. a,b, The directionalities of the applied d.c. electric field are shown by red arrows. The first rows of (a) and (b) show simulations of the time evolution of the polarization field under d.c. electric fields by considering the depolarization effect. The results are well consistent with the experimental observations. As a comparison, the second rows of (a) and (b) show the simulation by neglecting the depolarization effect. The results demonstrate complete deviation from the experiments. c,d, (c) and (d) are the corresponding equilibrium polarization fields under the electric fields reconstructed from the experimental FCPM images. Scale bar, 20 μm. The Methods and Supplementary Discussion 4 contain the parameters used in the simulations.