Figure 3
Topological analysis of director field textures.
(a), (b) Numerically obtained structures in vertical cross section with director marked with cylinders and defects shown as red isosurfaces. Similarly to experiments, both structures are found to be (meta)stable: (a) Toron-dressed particle with one point defect in bulk and one turn of the director on particle surface (indicated by an arrow) and (b) Hopfion-dressed structure without bulk defects with two opposite director turns on the particle surface. In-plane turns are found by marking the horizontal (quarter-turn) director with yellow (clockwise) or green (counterclockwise) line. (c–e) A theoretical model reveals that only the boojums contribute to the topological charge q of the whole, so the charge only depends on the arrow directions at the boojums (the director's arrow, marked also with colored tips, holds no physical significance for the nematic). Compare (a) to (d). The latitudes with horizontal director field are indicated by arrows. Note that (b) consists of two opposite turns and thus corresponds to the structure (c) instead of (e), although both have the same topological charge. The intrinsic pitch in simulations (a), (b) is 0.85 of the cell thickness.
