We study the general phase diagram of correlated electrons for iridium-based (Ir) compounds on the hyperhoneycomb lattice, a crystal structure where the ${\mathrm{Ir}}^{4+}$ ions form a three-dimensional network with threefold coordination recently realized in the $\beta$-${\mathrm{Li}}_2\mathrm{Ir}{\mathrm{O}}_3$ compound. Using a combination of microscopic derivations, symmetry analysis, and density functional calculations, we determine the general model for the electrons occupying the $j_{\text{eff}}=\frac{1}{2}$ orbitals at the ${\mathrm{Ir}}^{4+}$ sites. In the noninteracting limit, we find that this model allows for both topological and trivial electronic band insulators along with metallic states. The effect of Hubbard-type electron-electron repulsion on the above electronic structure in stabilizing $\mathbf{q}=\mathbf{0}$ magnetic order reveals a phase diagram with continuous phase transition between a topological band insulator and a Néel ordered magnetic insulator.

• Received 18 March 2014

DOI:https://doi.org/10.1103/PhysRevB.89.205132