  Fundamental properties of superfluids with d-wave pairing symmetry are
investigated theoretically. We consider neutral atomic Fermi gases in a
harmonic trap, the Cooper pairing being produced by a Feshbach resonance via a
d-wave interaction channel. A Ginzburg-Landau (GL) functional is constructed
which is symmetry constrained for five component order parameters (OPs). We
find stable OP textures and vortices for all the three phases which are known
to be the energy minimum of the GL functional; the ferromagnetic, polar and
cyclic phases both at rest and under rotation. In particular, we touch upon the
stability conditions for a non-Abelian fractional 1/3-vortex in the cyclic
phase under rotation. It is proposed how to create the intriguing 1/3-vortex
experimentally in atomic gases via optical means.
