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We model a system of ultracold fermionic dipolar molecules on atwo-dimensional square lattice. Assuming that the molecules are in theirnondegenerate hyperfine ground state, and that the dipole moment is polarizedperpendicular to the plane (as in the recent experiments on 40K-87Rbmolecules), we approximate these molecules as spinless fermions with long rangerepulsive dipolar interactions. We use mean field theory to obtain therestricted phase diagram as a function of the filling, the strength ofinteraction and the temperature. We find a number of ordered density wavephases in the system, as well as phase separation between these phases. A MonteCarlo analysis shows that the higher-period phases are usually suppressed inthe exact solution.

Density wave patterns for fermionic dipolar molecules on a square optical lattice: Mean-field-theory analysis