Defect generation and deconfinement on corrugated topographies

Abstract

We investigate topography-driven generation of defects in liquid crystals films coating frozen surfaces of spatially varying Gaussian curvature whose topology does not automatically require defects in the ground state. We study in particular disclination-unbinding transitions with increasing aspect ratio for a surface shaped as a Gaussian bump with an hexatic phase draped over it. The instability of a smooth ground state texture to the generation of a single defect is also discussed. Free boundary conditions for a single bump are considered as well as periodic arrays of bumps. Finally, we argue that defects on a bump encircled by an aligning wall undergo sharp deconfinement transitions as the aspect ratio of the surface is lowered.

24 pages

References in corpus (6)

• Grain Boundary Scars and Spherical Crystallography
• The Geometry of Soft Materials: A Primer
• Interacting Topological Defects on Frozen Topographies
• Curvature-Induced Defect Unbinding in Toroidal Geometries
• Topological Defects on Fluctuating Surfaces: General Properties and the Kosterlitz-Thouless Transition
• Hexatic Undulations in Curved Geometries

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• Bubble Raft Model for a Paraboloidal Crystal
• Frustrated order on extrinsic geometries
• Ground state of a large number of particles on a frozen topography
• Curvature-induced frustration in the $XY$ model on hyperbolic surfaces
• Dynamics and Instabilities of Defects in Two-Dimensional Crystals on Curved Backgrounds
• Defect Spirograph: Dynamical Behavior of Defects in Spatially Patterned Active Nematics
• Crystalline Particle Packings on Constant Mean Curvature (Delaunay) Surfaces
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• Topological Defects in Gravitational Lensing Shear Fields
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• Simulating defect textures on coalescing nematic shells
• A simple, general criterion for onset of disclination disorder on curved surfaces
• Curvature-driven stability of defects in nematic textures over spherical disks
• Thermal Properties of Vortices on Curved Surfaces
• Continuous Transition of Defect Configuration in a Deformed Liquid Crystal Film