Thermodynamics of fermions in flat band systems

In the pursuit of observing highly correlated fermionic many-body states such as superconductivity in ultracold neutral atom systems, one hurdle is that the temperatures at which these phases are realized are below what one could typically achieve. One idea is to use a part of the system with high entropy capacity as a reservoir to cool the region of interest in optical lattices. This cooling scheme has been demonstrated recently using a digital micromirror device (DMD) to create spatially separated region of heat reservoir and system of interest. We propose that for lattice structures with flat bands, due to the large number of energetically accessible states (in the non-interacting case), a region with filling factor within the flat band can act as an efficient entropy reservoir for a system loaded to the dispersive part of the band structure. We discuss how this can be implemented in the kagome optical lattice experiment at University of California, Berkeley.