Switching and hopping of hopfions in chiral liquid crystals

Hopfions are 3D particle-like knotted field configurations. Realized in liquid crystals and predicted to exist in magnets, a hopfion is the higher dimensional analog of widely studied 2D skyrmions, stimulating fundamental and technological interest. Recently, a new type of particle-like lattice-forming 3D topological soliton, dubbed heliknoton [1], was realized in the helical background of chiral liquid crystals and was predicted to exist in chiral magnets [1,2]. We demonstrate how hopfions and heliknotons inter-transform smoothly between one another when the background field of the host medium is switched by an electric field between uniform and helical states, with myriads of different energetically stable embodiments of Hopf-fibration-like topology with and without applied electric fields. At intermediate field, Hopfions embedded in a heliconical background were also observed. Furthermore, under a modulating electric field, we find that the hopfions (heliknotons) oscillate between the two flavors and display activated hopping-like motion in a 3D bulk. This emergent behavior of topological solitons emerges from a periodic reorientation of the molecular alignment field that breaks the time reversal symmetry.

[1] Science 365, 1449 (2019).
[2] Phys. Rev. Lett. 125, 057201 (2020).