Flexoelectricity-driven toroidal polar topology in liquid-matter helielectrics

Magnetic and electric dipoles have similar symmetry and are therefore expected to exhibit many common structures. However, despite frequent reports of various spin textures composed of magnetic dipoles, investigations on long-range ordered electric dipoles have been scarce, until recently. Here we discover spontaneous toroidal polar topology in an emerging ferroelectric liquid state with polarization helices, dubbed ‘helielectric nematic’. The interplay between liquid-crystal elasticity and polar interactions results in a continuous in-plane rotation of the polarization, producing a periodic toroidal assembly. In partial analogy with magnetism, the neighbouring toroidal domains are separated by circularly shaped domain walls. The local polarization switching enables unique shrinkage and expansion dynamics of the toroidal domains. The discovery provides opportunities for developing designable and switchable ferroelectric-liquid-matter opto-electronics.