Design of Chern insulating phases in honeycomb lattices

•Design of Chern insulating phases in honeycomb lattices.•We present a description of how our three groups, working on two different honeycomb lattice materials classes, learned and designed two examples of transition metal oxide nanolayers whose ground states are predicted to be Chern insulators (quantum anomalous Hall insulators). The main features or properties that guided our search are compared and contrasted between the two classes of materials. The search for robust examples of the magnetic version of topological insulators, referred to as quantum anomalous Hall insulators or simply Chern insulators, so far lacks success. Our groups have explored two distinct possibilities based on multiorbital 3d oxide honeycomb lattices. Each has a Chern insulating phase near the ground state, but materials parameters were not appropriate to produce a viable Chern insulator. Further exploration of one of these classes, by substituting open shell 3d with 4d and 5d counterparts, has led to realistic prediction of Chern insulating ground states. Here we recount the design process, discussing the many energy scales that are active in participating (or resisting) the desired Chern insulator phase.