n-atic Order and Continuous Shape Changes of Deformable Surfaces of Genus Zero

Abstract

We consider in mean-field theory the continuous development below a second-order phase transition of $n$-atic tangent plane order on a deformable surface of genus zero with order parameter $\psi =⟨e^{in\theta }⟩$. Tangent plane order expels Gaussian curvature. In addition, the total vorticity of orientational order on a surface of genus zero is two. Thus, the ordered phase of an $n$-atic on such a surface will have $2n$ vortices of strength $1/n$, $2n$ zeros in its order parameter, and a nonspherical equilibrium shape. Our calculations are based on a phenomenological model with a gauge-like coupling between $\psi$ and curvature, and our analysis follows closely the Abrikosov treatment of a type II superconductor just below $H_{c2}$.

REVTEX, 12 pages

Cited by in corpus (24)

• The Geometry of Soft Materials: A Primer
• Two-Dimensional Matter: Order, Curvature and Defects
• Interacting Topological Defects on Frozen Topographies
• Mesoscale computational studies of membrane bilayer remodeling by curvature-inducing proteins
• Coarse-Grained Modeling of a Deformable Nematic Vesicle
• Active morphogenesis of patterned epithelial shells
• Bijels Containing Magnetic Particles: A Simulation Study
• Role of disclinations in determining the morphology of deformable fluid interfaces
• Liquid Crystals on Deformable Surfaces
• Modeling anisotropic elasticity of fluid membranes
• Investigation on the Ground States of a Model Thin-Film Superconductor on a Sphere
• Hexatic Undulations in Curved Geometries
• Chiral $p\pm ip$ superfluid on a sphere
• Liquid crystal director fields in three-dimensional non-Euclidean geometries
• Breaking the Rules for Topological Defects: Smectic Order on Conical Substrates
• Tuneable defect-curvature coupling and topological transitions in active shells
• Theoretical Study of Fluid Membranes of Spherical Topology with Internal Degrees of Freedom
• Forming a cube from a sphere with tetratic order
• Hexatic Order and Surface Ripples in Spherical Geometries
• Shapes and singularities in triatic liquid crystal vesicles
• Orientational order on curved surfaces - the high temperature region
• Effects of orientational order on modulated cylindrical interfaces
• Phase separation and folding in swelled nematoelastic films
• Stability of topological wall defects on spheres with n-atic order