Disordered Creutz lattice: The role of flat bands in superfluid behavior

Physical systems displaying flat or quasi-flat bands have been intensively investigated due to the enhanced effects that interactions may bring. This is for example, believed to be behind the manifestation of superconductivity in the twisted bilayer graphene, where by adjusting the twisting angles, one can induce the formation of (quasi-) flat bands close to the Fermi energy. On a typically non-interacting picture, a flat band would correspond to an infinite effective mass for the carriers, halting transport. In the case one possess attractive interactions, it has been recently shown that superfluid transport is robust and the associated superfluid weight bounded by topological invariants the bands may possess. Further, when comparing the robustness of the superfluid properties to the presence of quenched disorder, the constrast between topological and non-topological systems becomes extremely clear. In this presentation, we will show results for the disordered Hubbard model with attractive interactions in the presence of flat or dispersive bands, checking the influence topological properties may possess in stabilizing the superfluid behavior in this interacting system.