  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.
