Review: Topology of solitons and singular defects in chiral liquid crystals

TL;DR

This review explores how chiral liquid crystals serve as accessible systems to study complex topological solitons and defects, revealing insights relevant across physics disciplines.

Contribution

It provides a comprehensive overview of topological structures in chiral nematic liquid crystals and compares them with similar configurations in other condensed matter systems.

Findings

Detailed descriptions of skyrmions, dislocations, and defect lines in liquid crystals.

Analogies between liquid crystal topologies and magnetic systems.

Insights into knotted and localized structures like hopfions and torons.

Abstract

Widely known for their uses in displays and electro-optics, liquid crystals are more than just technological marvels. They vividly reveal the topology and structure of various solitonic and singular field configurations, often markedly resembling the ones arising in many field theories and in the areas ranging from particle physics to optics, hard condensed matter and cosmology. In this review, we focus on chiral nematic liquid crystals to show how these experimentally highly accessible systems provide valuable insights into the structure and behavior of fractional, full, and multi-integer two-dimensional skyrmions, dislocations and both abelian and non-abelian defect lines, as well as various three-dimensionally localized, often knotted structures that include hopfions, heliknotons, torons and twistions. We provide comparisons of some of these field configurations with their topological counterparts in chiral magnets, discussing close analogies between these two condensed matter systems.