Nonuniform localized distortions in generalized elasticity for liquid crystals

Skyrmion Tubes in achiral nematic liquid crystals

“…In the present paper, we generalize our previous work [17] with the addition of an external uniform magnetic field. We find Skyrmion-Tube-like nematic textures that form when a uniform magnetic field is applied along the axis of a heliconical state.…”

“…This represents the lowest order free-energy density that, for a suitable choice of the elastic constants, admits as global minimizer the so-called heliconical uniform distortion state [16,17], as opposed to the uniform state (8). By directly comparing (10) with (2) we get the following formal identification…”

“…which is the condition of positive definiteness of the quartic part of (10). In terms of n and its gradients ∇n, (10) can be written as follows [17]…”

“…In [17] we reviewed the theory presented in [16] and we found that, in the same region where N TB is preferred, localized stable excitations of the heliconical ground state are possible. In particular, we showed how axisymmetric structures, with a radial dependence of the conical angle and an additional twist around the heliconical axis, are stable minima of the generalized elastic theory, with energies falling in between those of the heliconical ground state and the nematic alignment.…”

“…However, theoretical studies such as [18,19] have been focused on its realization in ferromagnets, although its experimental attainment seems to be easier in liquid crystals [18]. In this context, [17] paved the way for a better theoretical understanding of Skyrmion Tubes in liquid crystals.…”