  Recent experimental realization of dipolar Fermi gases near or below quantum
degeneracy provides opportunity to engineer Hubbard-like models with long range
interactions. Motivated by these experiments, we chart out the theoretical
phase diagram of interacting dipolar fermions on the square lattice at zero
temperature and half filling. We show that in addition to p-wave superfluid and
charge density wave order, two new and exotic types of bond order emerge
generically in dipolar fermion systems. These phases feature homogeneous
density but periodic modulations of the kinetic hopping energy between nearest
or next-nearest neighbors. Similar, but manifestly different, phases of
two-dimensional correlated electrons have previously only been hypothesized and
termed "density waves of nonzero angular momentum". Our results suggest that
these phases can be constructed flexibly with dipolar fermions, using currently
available experimental techniques.
