Quantum anomalous Hall effect in metal-bis(dithiolene), magnetic properties, doping and interfacing graphene

Abstract: The realization of the Quantum anomalous Hall effect (QAHE) in two dimensional (2D) metal organic frameworks (MOFs), (MC$_4$S$_4$)$_3$ with M = Mn, Fe, Co, Ru and Rh, has been investigated based on a combination of first-principles calculations and tight binding models. Our results for the magnetic anisotropy energy (MAE) reveal that the out-of-plane (in-plane) magnetization is favored for M = Mn, Fe, and Ru (Co, and Rh). Given the structural symmetry of (MC$_4$S$_4$)$_3$, the QAHE takes place 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. Further electron ($n$-type) doping of the MOFs has been done in order to place the Fermi level within the non-trivial energy gap; where we find that in (RuC$_4$S$_4$)$_3$, 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 tunning 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 MOFs.