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We investigate the magnetic shell structure of repulsively interacting two-component Fermi gases trapped in a two-dimensional harmonic potential and loaded on the optical Lieb lattices. We employ the real-space dynamical mean-field theory (R-DMFT) to explicitly consider the trap potential in a self-consistent way. Computing the profiles of particle density and local magnetization across the lattice sites in the trap, we find that the incompressible core with ferrimagnetic ordering appears with the density plateau at the trap center, which is surrounded by the shell of the normal metallic phase. We examine the incompressibility of the core by adding more particles and creating the higher spin-population imbalance. While the core area expands from the outer shell with added particles and increased polarization, the excess particles are prohibited from going inside the core, and thus the density plateau is unchanged at the half-filling with the same magnetic ordering. In addition, we find that the feature of the phase separation differs with the sublattices, where the interstitial sites causing the flat band dispersion shows the signature of the abrupt transition in the density and magnetization at the boundary between the core and surrounding shells.

Magnetic Shell Structure of 2D-Trapped Fermi Gases in the Flat-Band Lieb Lattices