Liquid crystal skyrmions as elastic multipoles

Topological solitons in liquid crystals are spatially localised stable configurations of the director field, which exhibit emergent particle-like properties such as mutual interaction, translational motion and reconfigurable self-assembling behaviour in oscillating electric fields. Understanding solitons’ out-of-equilibrium interactions remains a significant challenge. In this paper, we discuss a minimalist model capable to address this challenge. The developed approach considers only relaxational dynamics of the director in two dimensions and neglects any material flows. For systems with negative dielectric anisotropy, we derive analytically elastic multipole potentials, which for symmetric skyrmions are exponentially screened. This corresponds, in an effective way, to the confinement-induced screening of toron interactions in three dimensions. We calculate skyrmion’s elastic multipole moments from the equilibrium director configurations obtained numerically. Incorporating time dependence of the soliton multipole moments in response to electric field oscillations, we carry out particle-based simulations that demonstrate the formation of soliton chains and two dimensional clusters by varying the amplitude and/or the frequency of the electric field, in agreement with experiments. The presented formalism may serve as a benchmark model for future theoretical developments incorporating, e.g., higher order elastic multipoles or/and many-body interactions. Liquid crystal skyrmions are quasiparticle structures whose interactions at large separations can be understood in terms of elastic multipoles. Here, the authors derive these multipole interactions analytically and show how they drive the formation of chains and clusters under oscillating electric fields.