  The structures of multiply quantized vortices (MQVs) of an equal-population
atomic Fermi superfluid in a rotating spherical bubble trap approximated as a
thin shell are analyzed by solving the Bogoliubov-de Gennes (BdG) equation
throughout the BCS-Bose Einstein condensation (BEC) crossover. Consistent with
the Poincare-Hopf theorem, a pair of vortices emerge at the poles of the
rotation axis in the presence of azimuthal symmetry, and the compact geometry
provides confinement for the MQVs. While the single-vorticity vortex structure
is similar to that in a planar geometry, higher-vorticity vortices exhibit
interesting phenomena at the vortex center, such as a density peak due to
accumulation of a normal Fermi gas and reversed circulation of current due to
in-gap states carrying angular momentum, in the BCS regime but not the BEC
regime because of the subtle relations between the order parameter and density.
The energy spectrum shows the number of the in-gap state branches corresponds
to the vorticity of a vortex, and an explanation based on a topological
correspondence is provided.
