Dynamics of flowing 2D skyrmions

Area of Science:

• Soft Matter Physics
• Liquid Crystal Dynamics
• Nonlinear Field Theory

Background:

• Liquid crystal (LC) skyrmions are topological defects with potential applications in data storage and display technologies.
• Understanding their behavior under external stimuli, such as material flow, is crucial for practical applications.
• Previous studies have explored static properties, but dynamic responses to flow are less understood.

Purpose of the Study:

• To numerically investigate the impact of externally imposed material flows on the structure and evolution of 2D liquid crystal skyrmions.
• To characterize skyrmion shape changes as a function of flow velocity and the presence of other skyrmions.
• To identify and analyze the transition between different skyrmion deformation regimes.

Main Methods:

• Modeling the 2D skyrmion system using the Ericksen-Leslie theory, incorporating coupled equations for material flow and director fields.
• Employing a simplified approach with instantaneous velocity field relaxation due to disparate time scales.
• Utilizing a finite-differences method (artificial compressibility) for velocity field and a fourth-order Runge-Kutta method for the director field.

Main Results:

• Identified two distinct regimes of skyrmion deformation: stretching along flow streamlines in weak flows and perpendicular stretching above a critical velocity.
• Discovered an abrupt, first-order dynamical transition separating these two regimes, robust against LC elastic anisotropy.
• Observed that the presence of a second skyrmion influences the shape evolution compared to isolated skyrmions.

Conclusions:

• External material flow significantly alters LC skyrmion morphology, exhibiting distinct behaviors dependent on flow velocity.
• The critical velocity transition is a key phenomenon governing skyrmion dynamics under flow.
• Inter-skyrmion interactions play a role in their dynamic shape evolution.