Electronic and topological properties of 2D metal-organic frameworks*

We present a theoretical investigation of electronic and topological properties of several proposed and experimentally realized 2D hexagonal metal-organic frameworks (MOFs) through ab initio and tight-binding calculations. The band structures of these materials near the Fermi level are composed by a combination of flat and dispersive bands, with the dispersive bands possessing Dirac cones at the corners of the Brillouin zone. We show that the band structures of several of the investigated materials are strongly affected by the partial inclusion of exact exchange terms on the exchange-correlation potential, primarily for those materials with a strong contribution of d electrons on the bands near the Fermi level. We also show that the presence of metal atoms on the structures of the MOFs lead to spin-orbit coupling induced band gaps, and that the magnitude of these gaps can be enlarged by more than 5 times with appropriate choices of the metal centers. Finally, we show that the band structure of bilayer systems constructed by the stacking of the MOFs M₃C₁₂S₁₂ is a realization of the Kane and Mele model for topological insulating graphene with a large spin-orbit gap.