  There is considerable interest in understanding and controlling topological
defects in nematic liquid crystals (LCs). Confinement, in the form of droplets,
has been particularly effective in that regard. Here, we employ the Landau-de
Gennes method to explore the geometrical frustration of nematic order in shell
geometries, and focus on chiral materials. By varying the chirality and
thickness in uniform shells, we construct a phase diagram that includes
tetravalent structures, bipolar structures (BS), bent structures and radial
spherical structures (RSS). It is found that, in uniform shells, the BS-to-RSS
structural transition, in response to both chirality and shell geometry, is
accompanied by an abrupt change of defect positions, implying a potential use
for chiral nematic shells as sensors. Moreover, we investigate thickness
heterogeneity in shells and demonstrate that non-chiral and chiral nematic
shells exhibit distinct equilibrium positions of their inner core that are
governed by shell chirality c.
