Kohn-Sham theory of a rotating dipolar Fermi gas in two dimensions

A two-dimensional dipolar Fermi gas in a harmonic trap under rotation is studied by solving ab initio Kohn-Sham equations. The physical parameters used match those of an ultracold gas of fermionic Na-23 K-40 molecules, a prototypical system of strongly interacting dipolar quantum matter, which was created very recently. We find that, as the critical rotational frequency is approached and the system collapses into the lowest Landau level, an array of tightly packed quantum vortices develops, in spite of the nonsuperfluid character of the system. In this state the system loses axial symmetry and the fermionic cloud boundaries assume an almost perfect square shape. At higher values of the filling factor the vortex lattice disappears, while the system still exhibits square-shaped boundaries. At lower values of the filling factor the fermions become instead localized in a Wigner cluster structure.