  A superfluid atomic Fermi system may support a giant vortex if the trapping
potential is anharmonic. In such a potential, the single-particle spectrum has
a positive curvature as a function of angular momentum. A tractable model is
put up in which the lowest and next lowest Landau levels are occupied.
Different parameter regimes are identified and characterized. Due to the
dependence of the interaction on angular momentum quantum number, the Cooper
pairing is at its strongest not only close to the Fermi level, but also close
to the energy minimum. It is shown that the gas is superfluid in the interior
of the toroidal density distribution and normal in the outer regions.
Furthermore, the pairing may give rise to a localized density depression in
configuration space.
