Imbalanced Superfluid Fermi Gas on a Lieb Lattice

We study the Hubbard model with spin imbalance in multiband systems, particularly the Lieb lattice, which features a flat band. The flat band is known to enhance superfluidity due to a diverging density of states. We obtain a phase diagrams of this system using a BCS (mean field) theory, and we identify a variety of phases. Apart from the standard BCS and normal states, we observe the Fulde-Ferrell-Larkin-Ovchinnikov type phases with space-dependent pairing function. We also find a thermodynamically stable Sarma phase, where the imbalance coexists with a spatially uniform order parameter.