  We study fermions in a lattice, with on-site and nearest neighbor attractive
interactions between two spin species. We consider two geometries: both spins
in a triangular lattice, and a mixed geometry with up-spins in honeycomb and
down-spins in triangular lattices. We focus on the interplay between
spin-population imbalance, on-site and valence bond pairing, and order
parameter symmetry. The mixed geometry leads to a rich phase diagram of
topologically non-trivial phases. In both geometries, we predict order
parameters with simultaneous time-reversal and translational symmetry breaking.
