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

Flat band systems and strong electronic correlations promise to be a playground for unconventional phases of matter, such as high-temperature superconductivity and other strongly correlated phenomena. Understanding superconductivity in strongly correlated electron systems is one of the grand challenges of modern physics. There has recently been large interest in flat bands with the discovery of superconductivity in twisted bilayer graphene but designing materials with flat bands is difficult.



Metal organic frameworks (MOFs) are materials whose underlying lattice is easily designed and tuned because of the unprecedented control over the metallic centers and the ligand linkers. They are often insulating, which is thought to be due to strong electronic correlations. It was recently reported that Cu-BHT has unconventional superconductivity and exhibits strong electronic correlations. Many MOFs, like Cu-BHT, form a kagome lattice of the metals which have large covalency with ligands lying along the bonds.



We introduce the tight-binding model of the kagome-Lieb lattice as a minimal model. We find five flat bands, with three partially filled at half-filling with a large energy gap to other bands. Including longer-ranged hopping beyond nearest-neighbor introduces a finite bandwidth to the three flat bands, but they remain flatter and more isolated than those in twisted bilayer graphene. Thus, framework materials are ideal for exploring flat band physics in bulk materials at higher electronic densities.