Tunable Electronic Honeycomb and (Breathing) Kagome Lattices Through Molecular Orbital Design in 2D Metal-Organic Frameworks

The pursuit of quantum materials with honeycomb and Kagome lattices hosting flat and Dirac bands has predominantly focused on inorganic crystals, where electronic tunability is constrained by the rigidity of atomic orbitals. Metal-organic frameworks (MOFs) offer an alternative paradigm, enabling band structure engineering through molecular orbital design, yet experimental realization remains elusive due to synthetic challenges. Here, we demonstrate the bottom-up fabrication of two-dimensional MOFs with precisely engineered frontier molecular orbitals (FMOs). By employing ligands with three-fold rotational symmetry, we construct electronic honeycomb, Kagome, and breathing Kagome lattices through an on-surface coordination chemistry approach, with the resulting structures directly resolved by scanning tunneling microscopy. Combined scanning tunneling spectroscopy (STS) and density functional theory (DFT) calculations reveal local density of states and projected-band features that are consistent with tunable Dirac-like and flat-band-like electronic states in the designed honeycomb and Kagome nanostructured lattices, establishing a solid-state platform for band-structure engineering. This work establishes MOFs as a versatile platform for exploring correlated quantum phases, bridging the gap between theoretical band engineering and experimental materials design.