Topological solitons in chiral liquid crystals

Abstract

ABSTRACT Topological solitons are quasi-particles of field deformations that are topologically nontrivial. Conceptualised by celebrated mathematicians and scientists including Carl Friedrich Gauss, Lord Kelvin, and Tony Skyrme, the ideas of knots, topology, and solitons have found a wealth of experimental embodiments in chiral liquid crystals in recent years. This is largely due to the exceptional capacity of the material for stabilising, characterising, and controlling topological solitons. In this review, I report the recent progress in realising and characterising topological solitons in chiral liquid crystals. Following the homotopy classification, I begin with the 1D twist walls and subsequently introduce 2D skyrmions and skyrmion bags, followed by 3D Hopf solitons including both hopfions and heliknotons. Physical properties of topological solitons are discussed, which include stability, soliton–soliton interaction, field-controlled transformation, field-activated dynamics, and crystalline self-assembly. Finally, the review ends by illustrating how liquid-crystal solitons can provide insights into topological solitons in other physical systems, and perspectives of future studies on the subject. The purpose of this review is to provide a fundamental overview of topological solitons in chiral liquid crystals.