Topological zoo of free-standing knots in confined chiral nematic fluids

Abstract

Knotted fields are an emerging research topic relevant to different areas of physics where topology plays a crucial role. Recent realisation of knotted nematic disclinations stabilised by colloidal particles raised a challenge of free-standing knots. Here we demonstrate the creation of free-standing knotted and linked disclination loops in the cholesteric ordering fields, which are confined to spherical droplets with homeotropic surface anchoring. Our approach, using free energy minimisation and topological theory, leads to the stabilisation of knots via the interplay of the geometric frustration and intrinsic chirality. Selected configurations of the lowest complexity are characterised by knot or link types, disclination lengths, and self-linking numbers. When cholesteric pitch becomes short on the confinement scale, the knotted structures change to practically unperturbed cholesteric structures with disclinations expelled close to the surface. The drops with knots could be controlled by optical beams and may be used for photonic elements.