Realization of Lieb lattice in covalent-organic frameworks with tunable topology and magnetism.

Lieb lattice has been predicted to host various exotic electronic properties due to its unusual Dirac-flat band structure. However, the realization of a Lieb lattice in a real material is still unachievable. Based on tight-binding modeling, we find that the lattice distortion can significantly determine the electronic and topological properties of a Lieb lattice. Importantly, based on first-principles calculations, we predict that the two existing covalent organic frameworks (COFs), i.e., spC-COF and spN-COF, are actually the first two material realizations of organic-ligand-based Lieb lattice. Interestingly, the spC-COF can experience the phase transitions from a paramagnetic state to a ferromagnetic one and then to a Néel antiferromagnetic one, as the carrier doping concentration increases. Our findings not only confirm the first material realization of Lieb lattice in COFs, but also offer a possible way to achieve tunable topology and magnetism in organic lattices.