The Power of Poincaré: Elucidating the Hidden Symmetries in Focal Conic Domains

Abstract

Focal conic domains are typically the "smoking gun" by which smectic liquid crystalline phases are identified. The geometry of the equally-spaced smectic layers is highly generic but, at the same time, difficult to work with. In this Letter we develop an approach to the study of focal sets in smectics which exploits a hidden Poincaré symmetry revealed only by viewing the smectic layers as projections from one-higher dimension. We use this perspective to shed light upon several classic focal conic textures, including the concentric cyclides of Dupin, polygonal textures and tilt-grain boundaries.

4 pages, 3 included figures

References in corpus (2)

• Smectics: Symmetry Breaking, Singularities, and Surfaces
• Topology of Smectic Order on Compact Substrates

Cited by in corpus (7)

• Structural Landscapes in Geometrically Frustrated Smectics
• Geometry of Bend: Singular Lines and Defects in Twist-Bend Nematics
• Complex-tensor theory of simple smectics
• Smectic Layering: Landau theory for a complex-tensor order parameter
• A Bouquet for Apollonius: Focal Conics in Sessile Cholesteric Droplets
• Good Fibrations: Packing Rules for Diabolic Domains
• Compactness and sharp lower bound for a 2D smectics model