Spin-orbit coupling induced semi-metallic state in the 1/3 hole-doped hyper-kagome Na3Ir3O8.

The complex iridium oxide Na3Ir3O8 with a B-site ordered spinel structure was synthesized in single crystalline form, where the chiral hyper-kagome lattice of Ir ions, as observed in the spin-liquid candidate Na4Ir3O8, was identified. The average valence of Ir is 4.33+ and, therefore, Na3Ir3O8 can be viewed as a doped analogue of the hyper-kagome spin liquid with Ir(4+). The transport measurements, combined with the electronic structure calculations, indicate that the ground state of Na3Ir3O8 is a low carrier density semi-metal. We argue that the semi-metallic state is produced by a competition of the molecular orbital splitting of t2g orbitals on Ir3 triangles with strong spin-orbit coupling inherent to heavy Ir ions.