Forming a cube from a sphere with tetratic order

TL;DR

This paper analytically demonstrates that tetratic order on a sphere leads to eight +1/4-disclinations positioned at cube vertices, causing the sphere to deform into a superspheroid with cubic symmetry.

Contribution

It provides an analytical framework for understanding defect arrangements in tetratic phases on curved surfaces, revealing a cube-like defect configuration on spheres.

Findings

Eight +1/4-disclinations favor cube vertices on a sphere.

Sphere deforms into a superspheroid with cubic symmetry.

Analytical solution for defect positions in tetratic order.

Abstract

Composed of square particles, the tetratic phase is characterised by a four-fold symmetry with quasi-long-range orientational order but no translational order. We construct the elastic free energy for tetratics and find a closed form solution for 1/4-disclinations in planar geometry. Applying the same covariant formalism to a sphere we show analytically that within the one elastic constant approximation eight +1/4-disclinations favor positions defining the vertices of a cube. The interplay between defect-defect interactions and bending energy results in a flattening of the sphere towards superspheroids with the symmetry of a cube.