Particle-based model of liquid crystal skyrmion dynamics.

Motivated by recent experimental results that reveal rich collective dynamics of thousands-to-millions of active liquid crystal skyrmions, we have developed a coarse-grained, particle-based model of the dynamics of skyrmions in a dilute regime. The basic physical mechanism of skyrmion motion is related to squirming undulations of domains with high director twist within the skyrmion cores when the electric field is turned on and off. The motion is not related to mass flow and is caused only by the reorientation dynamics of the director field. Based on the results of the "fine-grained" Frank-Oseen continuum model, we have mapped these squirming director distortions onto an effective force that acts asymmetrically upon switching the electrical field on or off. The resulting model correctly reproduces the skyrmion dynamics, including velocity reversal as a function of the frequency of a pulse width modulated driving voltage. We have also obtained approximate analytical expressions for the phenomenological model parameters encoding their dependence upon the cholesteric pitch and the strength of the electric field. This has been achieved by fitting coarse-grained skyrmion trajectories to those determined in the framework of the Frank-Oseen model.

Motion-induced inertial effects and topological phase transitions in skyrmion transport.

When the skyrmion dynamics beyond the particle-like description is considered, this topological structure can deform due to a self-induced field. In this work, we perform Monte Carlo simulations to characterize the skyrmion deformation during its steady movement. In the low-velocity regime, the deformation in the skyrmion shape is quantified by an effective inertial mass, which is related to the dissipative force. When skyrmions move faster, the large self-induced deformation triggers topological transitions. These transitions are characterized by the proliferation of skyrmions and a different total topological charge, which is obtained as a function of the skyrmion velocity. Our findings provide an alternative way to describe the dynamics of a skyrmion that accounts for the deformations of its structure. Furthermore, such motion-induced topological phase transitions make it possible to control the number of ferromagnetic skyrmions through velocity effects.