Smectic blue phases: layered systems with high intrinsic curvature

TL;DR

This paper introduces a construction method for smectic blue phases that combine layered order with three-dimensional crystalline structure, stabilized by saddle-splay energy and involving curvature and defect considerations.

Contribution

It presents a novel approach to constructing smectic blue phases using layers on minimal surfaces, highlighting the role of saddle-splay energy in their stability.

Findings

Structures fill space with layers on minimal surfaces.

Saddle-splay energy stabilizes these phases.

Curvature frustration influences structure stability.

Abstract

We report on a construction for smectic blue phases, which have quasi-long range smectic translational order as well as three dimensional crystalline order. Our proposed structures fill space by adding layers on top of a minimal surface, introducing either curvature or edge defects as necessary. We find that for the right range of material parameters, the favorable saddle-splay energy of these structures can stabilize them against uniform layered structures. We also consider the nature of curvature frustration between mean curvature and saddle-splay.