Prediction of large gap flat Chern band in a two-dimensional metal-organic framework

Systems with a flat Chern band have been extensively studied for their potential to realize high-temperature fractional quantum Hall states. To experimentally observe the quantum transport properties, a sizable topological gap is highly necessary. Here, taking advantage of the high tunability of two-dimensional (2D) metal-organic frameworks (MOFs), whose crystal structures can be easily tuned using different metal atoms and molecular ligands, we propose a design of a 2D MOF [Tl₂(C₆H₄)₃, Tl₂Ph₃] showing nontrivial topological states with an extremely large gap in both the nearly flat Chern band and the Dirac bands. By coordinating π-conjugated thallium ions and benzene rings, crystalline Tl₂Ph₃ can be formed with Tl and Ph constructing honeycomb and kagome lattices, respectively. The p_x,y orbitals of Tl on the honeycomb lattice form ideal p_xy four-bands, through which a flat Chern band with a spin-orbit coupling (SOC) gap around 140 meV evolves below the Fermi level. This is the largest SOC gap among all the theoretically proposed organic topological insulators so far.