Abstract
Skyrmions are swirl-like topological entities that have been shown to emerge in various condensed matter systems. Their identification has been carried out in different ways including scattering techniques and real-space observations. Here we show that Kossel diagrams can identify the formation of a hexagonal lattice of half-Skyrmions in a thin film of a chiral liquid crystal, in which case Kossel lines appear as hexagonally arranged circular arcs. Our experimental observations on a hexagonal lattice of half-Skyrmions and other defect structures resembling that of a bulk cholesteric blue phase are perfectly accounted for by numerical calculations and a theoretical argument attributing strong reflections yielding Kossel lines to guided mode resonances in the thin liquid crystal film. Our study demonstrates that a liquid crystal is a model system allowing the investigation of topological entities by various optical means, and also that Kossel techniques are applicable to the investigation of thin systems with non-trivial photonic band structures including topologically protected optical surface states.
Highlights
Skyrmions are not real particles with distinct physical properties, but coreless solitonic field excitations that behave like a particle
We demonstrated the formation of a hexagonal lattice of half-Skyrmions in a thin region, and a structure resembling a thin slice of the cubic lattice of BP I (“Region 2” neighbouring Region 1, with thickness between 250–260 nm and 430 nm)
The six-fold symmetry of the Kossel diagram is consistent with the hexagonal symmetry of the half-Skyrmion lattice we identified earlier[16]
Summary
Skyrmions are not real particles with distinct physical properties, but coreless solitonic field excitations that behave like a particle. The subject of our study, and magnetic ones have many commonalities Both are described phenomenologically by a vector order parameter (in magnetic systems the vector magnetisation m, and in liquid crystals the director n, a unit vector without head-tail distinction, that allows the existence of additional topologically distinct structures). The chirality in both systems manifests itself in the Lifshitz invariant of the form n⋅∇ × n (and the same with m for magnetic systems) in the free energy that stabilises Skyrmions[17,18]. The identification of Skyrmions as many different ways as possible can corroborate their formation in a more convincing manner, and enables the investigation of various aspects of their structural and dynamical properties
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