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The superconducting metal-organic framework Cu-BHT forms a kagome latticewith metals at the vertices and ligands along the bonds. We show that atight-binding model with metal and ligand sites on this lattice yields fiveflat topological bands (FTBs), three of which are partially occupied athalf-filling, with large gaps between them and all other bands. Long-rangehopping induces curvature in the FTBs but leaves them flatter and more isolatedthan those in twisted bilayer graphene. Thus, framework materials are idealmaterials for exploring flat band physics at high electronic densities.

Robust, gapped, flat bands at half-filling in the minimal model of the superconducting metal-organic framework, Cu-BHT