Reversible transition between topologically equivalent states in a chiral liquid crystal with negative dielectric anisotropy

In a layer of a chiral liquid crystal with negative dielectric anisotropy and the thickness $d$ corresponding to the second Grandjean zone ($3p_0/4 < d < 5p_0/4$, where ${{p}_{0}}$ is the natural helical pitch) under the action of a planar electric field, an orientational transition occurs from the ground state twisted by the angle $2\pi $ to a topologically equivalent untwisted state ($0$ state). Although the $0$ state is metastable and long-lived, it can rapidly be transformed back to the $2\pi $ state by an electric field pulse of a comparatively small amplitude. The direct transition to the 0 state is induced by the interaction of the electric field with negative dielectric anisotropy, while the rapid reverse transition can be attributed to the flexoelectric interaction.