Flat bands and unconventional superconductivity in a simple model of metal-organic frameworks

The superconducting metal-organic framework Cu-BHT forms a kagome lattice with metals at the vertices and ligands along the bonds. This bipartite motif is common in reticular materials. We show that a tight-binding model on this lattice yields partially occupied interference-induced flat bands at half-filling with large gaps between them and all other bands. Long-range hopping induces curvature in the bands but leaves them flatter and more isolated than those in twisted bilayer graphene. The slave boson theory of the t-J model on this lattice shows highly unconventional superconductivity including an f -wave singlet phase. Thus, framework materials provide an ideal lattice-driven approach to strongly correlated phenomena in flat bands at high electronic densities.