  We study a system of ultra-cold fermionic polar molecules in a
two-dimensional square lattice interacting via both the long-ranged
dipole-dipole interaction and a short-ranged on-site attractive interaction.
Singlet superfluid, charge density wave, and supersolid phases are found to
exist in the system. We map out the zero temperature phase diagram and find
that the supersolid phase is considerably stabilized by the dipole-dipole
interaction and thus can exist over a large region of filling factors. We study
the melting of the supersolid phase with increasing temperature, map out a
finite temperature phase diagram of the system at fixed filling, and determine
the parameter region where the supersolid phase can possibly be observed in
experiments.
