Bogomol'nyi bound and screw dislocations in a mesoscopic smectic-A

TL;DR

This paper extends the Bogomol'nyi bound concept to anisotropic smectic-A liquid crystals, linking free energy to screw dislocations and anisotropy, and explores stability mechanisms in finite mesoscopic samples.

Contribution

It generalizes the Bogomol'nyi bound to anisotropic systems and derives a closed-form free energy expression relating screw dislocations to boundary effects.

Findings

Free energy depends only on dislocation number and anisotropy.

Boundary conditions enable stable screw dislocations in finite samples.

Relation between applied twist and screw dislocation count.

Abstract

The de Gennes free energy functional of an infinite smectic-A liquid crystal at the dual point is shown to be topological and to depend only on the number of screw dislocations and the anisotropy. This result generalizes the existence of a Bogomol'nyi bound to an anisotropic system. The role of the boundary of a finite mesoscopic smectic is to provide a mechanism for the existence of thermodynamically stable screw dislocations. We obtain a closed expression for the corresponding free energy and a relation between the applied twist and the number of screw dislocations.