  We study the structure of pairing order parameter for spin-1/2 fermions with
attractive interactions in a square lattice under a uniform magnetic field.
Because the magnetic translation symmetry gives a unique degeneracy in the
single-particle spectrum, the wave function has both zero and finite momentum
components co-existing, and their relative phases are determined by a
self-consistent mean-field theory. We present a microscopic calculation that
can determine the vortex lattice structure in the superfluid phase for
different flux densities. Phase transition from a Hofstadter insulator to a
superfluid phase is also discussed.
