  We study the phase diagram of a dipolar fermi gas at half-filling in a cubic
optical lattice with dipole moments aligned along the z-axis. The anisotropic
dipole-dipole interaction leads to the competition between pz-wave superfluid
and nematic charge-density-wave (CDW) orders at low temperatures. We find that
the superfluid phase survives with weak interactions and the CDW phase
dominates with strong interactions. In between, the supersolid phase appears as
a balance between superfluid and CDW orders. The superfluid density is
anisotropic in the supersolid and superfluid phases. In the CDW phase, there is
a semimetal to insulator transition with increase of the interaction strength.
Experimental implications are discussed.
