Fig. 5.

Second-principles calculations of electric polarization textures and their topological properties for n = 10. (A–C) Three different local minima, degenerate in energy. Each texture contains a pair of counterrotated cores yet has different chiral properties. Black arrows indicate the local dipoles, projected onto the (010)_χ plane. A large axial component of the polarization along ±[010]_χ, represented by the green and magenta domains, is observed. (D–F) Simplified cartoon with cylinders representing the cores and arrows that show their rotational and axial polarization components. A right-hand rule reveals the chirality of each cylinder. By curling one’s fingers in the direction of polar rotation around the core, the thumb points (anti-)parallel to the axial polarization for a (left-) right-handed core. (G–I) Maps of helicity. When the handedness of the two cores is the same, the system as a whole is chiral and the enantiomers can be distinguished by the sign of the integrated helicity (ℋ). Results obtained at temperature of 10 K.