Topological metastability of textures in biaxial nematics

TL;DR

This paper explores the topological properties of textures in biaxial nematics confined between plates, revealing that for any given texture, a topologically equivalent minimum-energy texture exists.

Contribution

It introduces a topological analysis framework demonstrating the existence of energy-minimizing textures corresponding to any given texture in biaxial nematics.

Findings

Existence of topologically equivalent minimum-energy textures

Topological analysis applied to biaxial nematic textures

Textures can be paired with energetically equivalent counterparts

Abstract

We consider textures of biaxial nematics confined between two parallel plates. The boundary conformations at the bordering plates are supposed to be identical, the gradients of the order parameter being generally nonzero. We claim that for any texture (including stable uniform order parameter alignment) there exists its counterpart texture which is also a minimum of the gradient elastic energy. Our arguments are based on the topological analysis of the conformation of the order parameter.