Interaction of tilted liquid crystal skyrmions

Skyrmions are topologically protected defect structures which also exhibit particle-like behaviors. Cholesteric liquid crystals (LC) confined between parallel substrates can host such LC skyrmions as well as other static solitons. There, a background alignment provided by external electric field or surface anchoring stabilizes the barrel-shaped skyrmions against shrinking or expansion. When the alignment is perpendicular to the plane of the LC cell, skyrmions are axisymmetric and upright and the interaction between two nearby skyrmions is that of soft-disk repulsion. However, when the background alignment is tilted, the directors also get tilted and the skyrmion takes a radially anisotropic form. The tilted skyrmion is topologically equivalent to the upright one but the interaction between two skyrmions is quite different. In this work we investigate this interaction in a variety of cases.