  The coupling between a quantum particle's intrinsic angular momentum and its
center-of-mass motion gives rise to the so-called helicity states that are
characterized by the projection of the spin onto the direction of momentum. In
this paper, by unfolding the superfluid-density tensor into its intra-helicity
and inter-helicity components, we reveal that the latter contribution is
directly linked with the total quantum metric of the helicity bands. We
consider both Rashba and Weyl spin-orbit couplings across the BCS-BEC
crossover, and show that the geometrical inter-helicity contribution is
responsible for up to a quarter of the total superfluid density. We believe
this is one of those elusive effects that may be measured within the
highly-tunable realm of cold Fermi gases.
