Collective variable model for the dynamics of liquid crystal skyrmions

Liquid crystal skyrmions are topologically protected spatially-localized distortions of the director field which exhibit particle-like properties including translational motion in oscillating electric fields. Here, we develop a collective variable model of the skyrmion dynamics, extending the approach of Long and Selinger proposed earlier for one dimensional systems. The model relates the skyrmion motion to a complex dynamics of the width of the twist wall around the skyrmion core. The width evolves in a non-reciprocal way, quantifying squirming deformations of the high twist region within on and off states of the field. We analyze in details the average skyrmion velocity as a function of the frequency and strength of the field as well as its duty cycle. The model predictions agrees qualitatively with experiments and results of numerical minimization of the Frank-Oseen model. Our results provide insights into the conditions necessary to observe velocity reversal as a function of the field parameters.