  The attractive Fermi-Hubbard Hamiltonian is solved via the Bogoliubov-de
Gennes formalism to analyze the ground state phases of population imbalanced
fermion mixtures in harmonically trapped two-dimensional optical lattices. In
the low density limit the superfluid order parameter modulates in the radial
direction towards the trap edges to accommodate the unpaired fermions that are
pushed away from the trap center with a single peak in their density. However
in the high density limit while the order parameter modulates in the radial
direction towards the trap center for low imbalance, it also modulates towards
the trap edges with increasing imbalance until the superfluid to normal phase
transition occurs beyond a critical imbalance. This leads to a single peak in
the density of unpaired fermions for low and high imbalance but leads to double
peaks for intermediate imbalance.
