Your hands are mirror images of each other, and among molecules this “handedness”—or chirality—is ubiquitous in both artificial and biological contexts. In chiral liquid crystals, the molecules twist about each other in accordance with a preferred handedness, but this simple picture belies a great diversity of macroscopic behaviors. The principles that facilitate or impede global chirality provide fundamental insights into the nature of condensed phases and material properties. Particular focus often falls on defects, for they reveal the material properties most keenly. Here, we describe the global chiral properties of spherical droplets of a type of chiral liquid crystal, and their defects, from experiments and by developing a mathematical framework. In a “cholesteric” liquid crystal, parallel rows of molecules arrange themselves in layers, with each layer twisted relative to its neighbors. Point defects disrupt the chiral order and reverse this sense of twisting. As a result, defects that are themselves chiral have a special structure, which we identify for those that have been observed experimentally. Defects within a droplet arrange themselves into geometric patterns reminiscent of atoms in small molecules, and we describe how the framework we introduce naturally captures such structures. We also show that spherical topology necessitates regions of the material with the “wrong” handedness—if the material is naturally right handed, some parts are nonetheless left handed—which represent a novel localized chiral structure. Our work provides a new framework for analyzing chiral materials and their defects. The blend of geometric structure with topology will offer guidance in the control and design of novel chiral materials.

• Publication: Joseph Pollard, Gregor Posnjak, Simon Copar, Igor Musevic, and Gareth P. Alexander, Phys. Rev. X 9, 021004 (2019)
• DOI: 10.1103/PhysRevX.9.021004