  Recent work on ultracold polar molecules, governed by a generalization of the
t-J Hamiltonian, suggests that molecules may be better suited than atoms for
studying d-wave superfluidity due to stronger interactions and larger
tunability of the system. We compute the phase diagram for polar molecules in a
checkerboard lattice consisting of weakly coupled square plaquettes. In the
simplest experimentally realizable case where there is only tunneling and an
XX-type spin-spin interaction, we identify the parameter regime where d-wave
superfluidity occurs. We also find that the inclusion of a density-density
interaction destroys the superfluid phase and that the inclusion of a
spin-density or an Ising-type spin-spin interaction can enhance the superfluid
phase. We also propose schemes for experimentally realizing the perturbative
calculations exhibiting enhanced d-wave superfluidity.
