Theory of chiral smectic AA liquid crystalline membranes

This work is intended to be a brief introduction to smectic AA and chiral smectic AA liquid crystals and current research topics focusing on chiral smectic AA liquid crystalline membranes. We derive the elastic free energies of smectic AA and chiral smectic AA phases, as well as the surface energies of smooth membranes. Furthermore, we explain how twist and bend deformations can penetrate into smectic layers despite geometrical constraints, either by external deformations or due to a tendency of tilting of chiral molecular packing, in analogy with the magnetic field penetration into bulk superconductors.