  We consider a generic two-dimensional system of fermionic particles with
attractive interactions and no disorder. If time-reversal symmetry is absent,
it is possible to obtain incompressible insulating states in addition to the
superfluid at zero temperature. The superfluid-insulator phase transition is
found to be second order in type-II systems using a perturbative analysis of
Cooper pairing instability in quantum Hall states of unpaired fermions. We
obtain the pairing phase diagram as a function of chemical potential (density)
and temperature. However, a more careful analysis presented here reveals that
the pairing quantum phase transition is always preempted by another transition
into a strongly correlated normal state which retains Cooper pairing and cannot
be smoothly connected to the quantum Hall state of unpaired fermions. Such a
normal phase can be qualitatively viewed as a liquid of vortices, although it
may acquire conventional broken symmetries. Even if it did not survive at
finite temperatures its influence would be felt through strong quantum
fluctuations below a crossover temperature scale. These conclusions directly
apply to fermionic ultra-cold atom systems near unitarity, but are likely
relevant for the properties of other strongly correlated superfluids as well,
including high temperature superconductors.
