  Spin-orbital-angular-momentum (SOAM) coupling has been realized in recent
experiments of Bose-Einstein condensates [Chen et al., Phys. Rev. Lett. 121,
113204 (2018) and Zhang et al., Phys. Rev. Lett. 122, 110402 (2019)], where the
orbital angular momentum imprinted upon bosons leads to quantized vortices. For
fermions, such an exotic synthetic gauge field can provide fertile ground for
fascinating pairing schemes and rich superfluid phases, which are yet to be
explored. Here we demonstrate how SOAM coupling stabilizes vortices in Fermi
superfluids through a unique mechanism that can be viewed as the angular analog
to that of the spin-orbit-coupling-induced Fulde-Ferrell state under a Fermi
surface deformation. Remarkably, the vortex size is comparable with the beam
waist of Raman lasers generating the SOAM coupling, which is typically much
larger than previously observed vortices in Fermi superfluids. With tunable
size and core structure, these giant vortex states provide unprecedented
experimental access to topological defects in Fermi superfluids.
