Defect absorption and emission for p-atic liquid crystals on cones

Area of Science:

• Soft Matter Physics
• Materials Science
• Geometry and Topology

Background:

• Understanding the behavior of liquid crystals on curved surfaces is crucial for advanced materials and devices.
• The influence of intrinsic geometry on the elastic and topological properties of two-dimensional (2D) liquid crystals is not fully understood.

Purpose of the Study:

• To investigate the ground-state configurations of 2D liquid crystals with p-fold rotational symmetry (p-atics) on fixed curved surfaces.
• To analyze the role of intrinsic geometry, specifically focusing on cones, in determining defect behavior and stability.

Main Methods:

• Utilized isothermal coordinates to simplify the elastic potential by explicitly encoding geometric contributions.
• Developed an analytical framework to describe the effective topological charge of cone apexes and their interaction with topological defects.
• Performed numerical simulations to validate analytical predictions for defect configurations on cones with varying angles.

Main Results:

• Identified an effective topological charge at the cone apex, dependent on the cone's deficit angle, which dictates defect absorption and emission.
• For a disk, ground states feature p defects of charge +1/p arranged in a ring.
• On cones, three distinct ground-state configurations emerge based on the cone angle: complete defect absorption at the apex, partial absorption with ring formation, or all defects forming a ring on the flank.

Conclusions:

• The intrinsic geometry of curved surfaces significantly dictates the ground-state configurations and defect dynamics of 2D liquid crystals.
• Cone apexes act as tunable elements for defect management, enabling absorption or emission based on geometric parameters.
• The findings provide a comprehensive analytical and numerical understanding of topological defect behavior in curved liquid crystal systems.