Dirac topological insulator in the d_(z²) manifold of a honeycomb oxide

We show by means of ab initio calculations and tight-binding modeling that an oxide system based on a honeycomb lattice can sustain topologically non-trivial states if a single orbital dominates the spectrum close to the Fermi level. In such situation, the low energy spectra is described by two Dirac equations that become non-trivially gapped when spin-orbit coupling (SOC) is switched on. We provide one specific example for this but the recipe is general. We discuss a realization of this starting from a conventional spin-a-half honeycomb antiferromagnet whose states close to the Fermi energy are d$_{z^2}$ orbitals. Switching off magnetism by atomic substitution and ensuring that the electronic structure becomes two-dimensional is sufficient for topologicality to arise in such a system. We show that the gap in such model scales linearly with SOC, opposed to other oxide-based topological insulators, where smaller gaps tend to appear by construction of the lattice. We also provide a study of the quantum Hall effect in such system, showing the close connections with the physics of graphene but in a d-electron system.