Annihilation dynamics of topological monopoles on a fiber in nematic liquid crystals

Abstract

We use the laser tweezers to create isolated pairs of topological point defects in a form of radial and hyperbolic hedgehogs, located close and attracted to a thin fiber with perpendicular surface orientation of nematic liquid crystal molecules in a thin planar nematic cell. We study the time evolution of the interaction between the two monopoles by monitoring their movement and reconstructing their trajectories and velocities. We find that there is a crossover in the pair interaction force between the radial and hyperbolic hedgehog. At small separation d, the elastic force between the opposite monopoles results in an increase of the attractive force with respect to the far field, and their relative velocity v scales as a v(d)∝d^{-2±0.2} power law. At large separations, the two oppositely charged monopoles can either attract or repel with constant interaction force. We explain this strange far-field behavior by the experimental inaccuracy in setting the fiber exactly perpendicular to the cell director.

Creation and topological charge switching of defect loops on a long fibre in the nematic liquid crystal

“…1 (c) and (d) by using the λ wave-plate (the second panels) and illustrated by the schematic drawings (the third panels). The effect of this small offset of the orientation of the fibre with respect to far field director was also observed in our previous work on the annihilation dynamics of the monopoles on topological soliton [45].…”

“…Namely, additional pairs of defects can always be created as long as their total topological charge is kept to zero. This was first demonstrated in a series of experiments with long fibers inserted in the NLC [26,[44][45][46]. Using the laser tweezers one is able to create pairs of oppositely charged topological defects, cut them into smaller entities, merge them into larger entities etc... Long fibre included in nematic nematic liquid crystals has emerged as a perfect setting to prove and observe the basic laws of topology in two dimensions.…”

“…In different experiments the stability of the soliton obtained by electric field [50], colloidal particles [44], film thickness gradient and the surface anchoring was studied [51,52]. We have recently reported on the creation of a linear topological soliton on a long, micrometer-diameter glass fibre in a NLC film in which the fibre was set perpendicular to the bulk orientation of the NLC [45]. The focus of that study was the creation of hedgehogs of opposite topological charge on the fibre and their annihilation dynamics, which demonstrated a Coulomb-like elastic attraction between the hedgehogs at short separation.…”

Creation of a Dirac monopole-antimonopole pair in a spin-1 Bose-Einstein condensate

“…To achieve a sufficiently strong gradient, we choose the parameters of the magnetic coils in Eqs. (8) and (9) to be R 1 = R 2 = 4 cm, A 1 = −A 2 = 1 cm, I = 400 A, and N = 500. Two technical challenges arise immediately.…”

“…While monopoles in the natural magnetic field remain elusive to experimental observation, a great deal of effort has been put into the search for corresponding configurations in experimentally more tractable systems. Analogs of magnetic monopoles have been found in a number of classical systems such as exotic spin ices [6,7] and nematic liquid crystals [8]. Creation of a Dirac monopole in a ferromagnetic Bose-Einstein condensate (BEC) was recently achieved experimentally, providing the first known realization of Dirac's monopole theory [9][10][11].…”