Coarse-grained theory for motion of solitons and skyrmions in liquid crystals

TL;DR

This paper develops a coarse-grained theoretical framework to describe the motion of skyrmions and solitons in liquid crystals under electric fields, explaining their directionality and rectification behavior.

Contribution

It introduces a macroscopic approach to model skyrmion dynamics in liquid crystals, extending previous work on disclinations to 2D skyrmion motion.

Findings

Skyrmions move perpendicular to the induced tilt of the director.

Skyrmions exhibit rectified motion when the field is removed.

Theoretical predictions match observed directional behaviors.

Abstract

Recent experiments have found that applied electric fields can induce motion of skyrmions in chiral nematic liquid crystals. To understand the magnitude and direction of the induced motion, we develop a coarse-grained approach to describe dynamics of skyrmions, similar to our group's previous work on the dynamics of disclinations. In this approach, we represent a localized excitation in terms of a few macroscopic degrees of freedom, including the position of the excitation and the orientation of the background director. We then derive the Rayleigh dissipation function, and hence the equations of motion, in terms of these macroscopic variables. We demonstrate this theoretical approach for 1D motion of a sine-Gordon soliton, and then extend it to 2D motion of a skyrmion. Our results show that skyrmions move in a direction perpendicular to the induced tilt of the background director. When the applied field is removed, skyrmions move in the opposite direction but not with equal magnitude, and hence the overall motion may be rectified.