Flat-band ferromagnetism in the multilayer Lieb optical lattice

We theoretically study magnetic properties of two-component cold fermions in half-filled multilayer Lieb optical lattices, i.e., two, three, and several layers, using the dynamical mean-field theory. We clarify that the magnetic properties of this system become quite different depending on whether the number of layers is odd or even. In odd-number layers in an odd-number-layer system, finite magnetization emerges even with an infinitesimal interaction. This is a striking feature of the flat-band ferromagnetic state in multilayer systems as a consequence of the Lieb theorem. In contrast, in even-number layers, magnetization develops from zero on a finite interaction. These different magnetic behaviors are triggered by the flat bands in the local density of states and become identical in the limit of the infinite-layer (i.e., three-dimensional) system. We also address how interlayer hopping affects the magnetization process. Further, we point out that layer magnetization, which is a population imbalance between up and down atoms on a layer, can be employed to detect the emergence of the flat-band ferromagnetic state without addressing sublattice magnetization.