Quantum Anomalous Hall Effect in Metal-bis(dithiolene), Magnetic Properties, Doping and Interfacing Graphene

The realization of the Quantum anomalous Hall effect (QAHE) in two dimensional (2D) metal organic frameworks (MOFs), (MC4S4)3 with M = Mn, Fe, Co, Ru and Rh, has been investigated based on a combination of first-principles calculations and tight binding models. Our analysis of the magnetic anisotropy energy (MAE) reveals that the out-of-plane (in-plane) magnetization is favored for M = Mn, Fe, and Ru (Co, and Rh). Therefore, we predict that the structural symmetry of (MC4S4)3 yields the QAHE only for M = Mn, Fe and Ru. Such a quantum anomalous Hall phase has been confirmed through the calculation of the Chern number, and examining the formation of topologically protected (metallic) edge states. Furthermore, we show that viable electron (n-type) doping of the MOFs can be used to place the Fermi level within the non-trivial energy gap; where we find that in (RuC4S4)3, in addition to the up-shift of the Fermi level, the MAE energy increases by 40%. Finally, we show that in MOF/graphene (vdW) interfaces, the Fermi level tuning can be done with an external electric field, which controls the charge transfer at the MOF/graphene interface, giving rise to switchable topologically protected edge currents in the MOFs.