  We study cholesteric order in liquid crystal shells with planar degenerate
anchoring. We observe that the bipolar and radial configurations intensively
reported for bulk droplets have a higher degree of complexity when the liquid
crystal is confined to a spherical shell. The bipolar configuration is replaced
by a structure where the boojums are linked to a stack of disclination rings
that spans the shell, while the radial configuration exhibits a double helix
structure where two disclinations wind around each other. Our results confirm
recent numerical simulations and highlight the complexity of the defect
structures arising when cholesteric liquid crystals are confined to spherical
geometries. We also show that the position of the boojums is only ruled by the
shell geometry, independently of the cholesteric pitch. To understand
quantitatively this behavior, we develop a simple yet insightful theoretical
framework which captures the essence of the observed phenomenology. We also
show that the transition between the two configurations is solely governed by
the confinement ratio c = h/p, where h is the average shell thickness and p is
the cholesteric pitch. Finally, we perform a dynamical study of this
transition, and report a fascinating defect waltz due to a chemical Lehmann
effect.
