  We analyze the phase structure of mass- and spin-imbalanced unitary Fermi
gases in harmonic traps. To this end, we employ Density Functional Theory in
the local density approximation. Depending on the values of the control
parameters measuring mass and spin imbalance, we observe that three regions
exist in the trap, namely: a superfluid region at the center, surrounded by a
mixed region of resonantly interacting spin-up and spin-down fermions, and
finally a fully polarized phase surrounding the previous two regions. We also
find regimes in the phase diagram where the existence of a superfluid region at
the center of the trap is not energetically favored. We point out the
limitations of our approach at the present stage, and call for more detailed
(ab initio) studies of the equation of state of uniform, mass-imbalanced
unitary Fermi gases.
