Equilibrium of fluid membranes with tangent-plane order (TPO), elasticity of smectics with TPO, and dispiration asymmetry in smectics-C*

TL;DR

This paper develops a theoretical framework for understanding the equilibrium shapes and topological defects of fluid membranes with tangent-plane order, extending to smectic liquid crystals with TPO and predicting observable effects in chiral smectics-C*.

Contribution

It introduces a spin-connection formulation for membrane energy that accounts for TPO and extends this to smectic liquid crystals, revealing new effects in chiral smectics-C*.

Findings

Derived equilibrium equations for membranes with TPO.

Extended the formulation to smectic liquid crystals with TPO.

Predicted experimentally verifiable consequences in chiral smectics-C*.

Abstract

Fluid membranes endowed with tangent-plane order (TPO) such as tilt- and hexatic order afford unique soft matter systems for investigating the interplay between elasticity, shape, topology, and thermal fluctuations. Using the spin-connection formulation of membrane energy we obtain equa- tions of equilibrium together with free boundary conditions for ground states of such membranes. We extend the spin-connection formulation to smectic liquid crystals with TPO and show that for chiral smectics-C* this generalization leads to experimentally verifiable consequences for dispirations having topological indices (helicities) of the same magnitude but opposite signs.