Topological Inclusions in 2D Smectic-C Films

TL;DR

This paper models topological inclusions in 2D smectic-C liquid crystal films as dipoles, analyzing their interactions, fluctuations, and the effects of thermal dynamics within a simplified theoretical framework.

Contribution

It introduces a topological dipole model for inclusions and defects in smectic-C films, incorporating thermal fluctuations and charge neutrality constraints.

Findings

Dipoles acquire logarithmic charge when deviating from preferred orientation.

Thermal fluctuations of dipole directions scale logarithmically with system size.

Dipole interactions are influenced by global charge neutrality constraints.

Abstract

In thin films of smectic-C liquid crystals, localized regions containing additional smectic layers form circular inclusions that carry a topological charge. Such inclusions nucleate a companion topological defect. These inclusion-defect pairs are modeled as topological dipoles within the context of a one-coupling constant approximation to the 2D Frank free energy. Deviations of the dipole direction from a preferred orientation cause the dipoles to acquire a logarithmic charge. Thermal fluctuations of the dipole direction are calculated and found to be large, scaling as the logarithm of the system size. In addition to dipole-dipole interactions arising from the topological charges, we also find that the thermal fluctuations of the dipole directions are coupled through a preference for global charge neutrality of the logarithmic charges.