Programmable Higher-Order Topological Phases in Open-Shell Metal-Organic Frameworks

Metal-organic frameworks (MOFs) offer remarkable structural and functional tunability across chemistry, physics and materials science, yet most MOFs built from closed-shell ligands remain wide-gap insulators, limiting their electronic functionality. Here we introduce a general strategy for imparting programmable topology to MOFs by leveraging open-shell ligands. Integrating radical nanographene linkers─featuring singly occupied molecular orbitals─into cobalt-coordination networks via on-surface synthesis, we create MOFs on Au(111) with emergent electronic states spanning the Fermi level. As a proof of concept, we synthesize Sierpiński-triangle fractal MOFs and directly observe topologically protected corner modes─the hallmarks of higher-order topological phases─using low-temperature scanning tunneling microscopy/spectroscopy. Through precise, molecule-by-molecule tip-induced assembly, we systematically tune the fractal hierarchy and monitor the evolution of topological states, supported by tight-binding simulations that align with experimental data. Our work establishes open-shell ligand chemistry as a versatile route to topological MOFs, paving the way for designer molecular quantum materials with programmable electronic and quantum properties.