Enantiomorphic kagome bands in a two-dimensional covalent organic framework with non-trivial magnetic and topological properties.

The kagome lattice is one of the most intriguing topics to study. It has a frustrated flat band touching a set of Dirac bands and can possess various promising properties, such as ferromagnetism, superconductivity, and a non-trivial topology. Covalent organic frameworks (COFs) are a rare type of inorganic material, however, they can provide a platform for generating certain required lattices. Based on first-principles density functional theory calculations, we show that a newly synthesized two-dimensional COF named COF-SH has novel enantiomorphic kagome bands, which include two sets of flat bands touching the Dirac bands around the Fermi level. The Bloch wave of the flat-valence band at the K-point shows the kagome nature of the phase interference. Under charge doping, the COF-SH exhibits a ferromagnetic ground state. Moreover, when COF-SH is doped with iodine atoms, a sizable gap in the system is opened between the flat bands and the Dirac bands due to the spin-orbit coupling (SOC) effect. Meanwhile, the spin degeneracy is lifted since the organic layer loses electrons due to the oxidizing property of iodine. In addition, our tight-binding analysis with the SOC effect shows that the flat valence band separates from the Dirac bands and holds a nonzero Chern number. Consequently, this I-doped COF can give rise to a quantum anomalous Hall effect.