Flatband magnetism of trapped Fermi gases in Lieb lattices

Abstract

We investigate the density profile of harmonically trapped Fermi gases in optical Lieb lattices by employing the real-space variant of the cellular dynamical mean-field theory. With repulsive on-site interaction, we find that there exists a three-shell structure where an incompressible domain with a ferrimagnetic order is found at the trap center while the trap edge is unpolarized and metallic, and those are separated by the intermediate area showing a mixed phase with highly inhomogeneous spin-density fluctuations. This suggests that the chemical-potential-driven transition in a corresponding translational-invariant system is not of a simple first-order type but goes through a region of a short-range magnetic order possibly with high degeneracy.