  We study a two-dimensional Fermi gas with an attractive interaction subjected
to synthetic magnetic fields assumed to be mutually antiparallel for two
different spin components. By employing the mean-field approximation, we find
that its phase diagram at zero temperature consists of pair superfluid and
quantum spin Hall insulator phases and closely resembles that of the
Bose-Hubbard model. The resulting two phases are separated by a second-order
quantum phase transition classified into the universality class of either the
dilute Bose gas or the XY model. We also show that the pairing gap can be
enhanced significantly by the antiparallel magnetic fields as a consequence of
magnetic catalysis, which may facilitate the realization of the pair superfluid
in two dimensions by ultracold atom experiments.
