Topological and magnetic phases with strong spin-orbit coupling on the hyperhoneycomb lattice

We study the general phase diagram of correlated electrons for iridium-based (Ir) compounds on the hyperhoneycomb lattice, a crystal structure where the Ir⁴⁺ ions form a three-dimensional network with threefold coordination recently realized in the β-Li₂IrO₃ compound. Using a combination of microscopic derivations, symmetry analysis, and density functional calculations, we determine the general model for the electrons occupying the jeff=1/2 orbitals at the Ir⁴⁺ 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 q=0 magnetic order reveals a phase diagram with continuous phase transition between a topological band insulator and a N\'eel ordered magnetic insulator.