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 Î-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=12 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 Néel ordered magnetic insulator.