  We study the zero temperature phase diagram of an imbalanced bilayer of
dipolar fermions. We consider perpendicularly aligned identical dipoles in two
layers and investigate the effect of population imbalance on the ground state
phase at different layer spacings and average densities. The attractive part of
the interlayer interaction could lead to the BEC-BCS crossover and the Fermi
surface mismatch between two layers results in interesting uniform and
nonuniform superfluid phases, which we have investigated here using the BCS
mean-field theory together with the superfluid-mass density criterion. The
density imbalance reduces the pairing gap. At low densities, where the system
is on the BEC side of the crossover, this reduction is quite smooth while a
dense system rapidly becomes normal at intermediate density polarizations.
Stable homogeneous superfluidity is predicted to appear on the phase diagram
when the dipolar length exceeds both the layer spacing and the average
intralayer distance between dipoles, a regime which should be readily
accessible experimentally. This homogeneous superfluid phase becomes unstable
at intermediate densities and layer spacings. We have also examined that these
uniform and inhomogeneous superfluid phases survive when the effects of
intralayer screenings are also incorporated in the formalism.
