  We consider a Fermi gas that is loaded onto a square optical lattice and
subjected to a perpendicular artificial magnetic field, and determine its
superfluid transition boundary by adopting a BCS-like mean-field approach in
momentum space. The multi-band structure of the single-particle Hofstadter
spectrum is taken explicitly into account while deriving a generalized pairing
equation. We present the numerical solutions as functions of the artificial
magnetic flux, interaction strength, Zeeman field, chemical potential, and
temperature, with a special emphasis on the roles played by the density of
single-particle states and center-of-mass momentum of Cooper pairs.
