Flat-band ferromagnetism in the multilayer Lieb optical lattice

TL;DR

This paper investigates how the magnetic properties of multilayer Lieb optical lattices vary with the number of layers, revealing distinct behaviors for odd and even layers due to flat bands, using dynamical mean-field theory.

Contribution

It demonstrates the layer-dependent magnetic phenomena in multilayer Lieb lattices, highlighting the role of flat bands and providing insights into ferromagnetism in cold atom systems.

Findings

Odd layers exhibit finite magnetization with infinitesimal interaction.

Even layers develop magnetization from zero at finite interaction.

Layer magnetization can detect flat-band ferromagnetism without sublattice analysis.

Abstract

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-th layers in an odd-number-layer system, finite magnetization emerges even with an infinitesimal interaction. This is a striking feature of the flatband 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 behaviours 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.