Nematic shells: new insights in topology- and curvature-induced effects

Orientable materials, such as magnetic materials or liquid crystals, are known to give rise to several special textures, whose complexity is as beautiful as it is interesting to explore and understand their nature. Their confinement in curved layers gives rise to new geometry-induced effects that are not usually observed in flat layers. In this paper we draw a parallel between ferromagnetic and nematic shells, both of which are characterized by local interaction and anchoring potentials. We show that, the different nature of the order parameter, a vector in ferromagnets and a tensor in nematics, although leading to similar curvature-induced effects (such as anisotropy and chirality), yields different textures on genus zero surfaces. Thus, on a sphere, the textures of ferromagnets are characterised by integer charge vortices, while the textures of nematics also admit half-integer charge vortices.