Theory of hybrid defects, with coupled orientational order parameters, on flat and curved surfaces

TL;DR

This paper develops a theoretical framework for understanding complex defect structures in systems with two coupled orientational orders on flat and curved surfaces, revealing how defect configurations evolve with coupling strength.

Contribution

It introduces a model for coupled m-atic and n-atic orders and analyzes defect structures on flat and spherical geometries, highlighting the effects of coupling strength.

Findings

Weak coupling leads to diffuse defect networks and domain structures.

Strong coupling causes defect merging and formation of stretched defect cores.

Defect configurations depend critically on the coupling strength and geometry.

Abstract

Many physical systems involve two types of orientational order, which are coupled together. For example, ferroelectric nematic liquid crystals have coupled polar and nematic order, and tilted hexatic phases have coupled polar and hexatic order. In these systems, defect structures can be quite complex. Here, we investigate phases with two types of two-dimensional orientational order, $m$-atic and $n$-atic, where $m$ and $n$ are two distinct integers. We simulate these phases in a flat disk with strong radial anchoring, and on a spherical surface, because both of these geometries require the presence of defects. If the coupling between the two types of order is weak, then the defects are connected by a network of diffuse walls, and the system forms a stable domain structure. As the coupling increases, the domain walls become sharper and shorter. For very strong coupling, the higher-order defects merge into the lower-order defects, forming stretched defect cores.