  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 atoms, 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 Ir4+. The transport
measurements showed that Na3Ir3O8 is in fact a semi-metal. The electronic
structure calculation demonstrated that the strong spin-orbit coupling of Ir
yields the semi-metallic state out of an otherwise band insulating state, which
may harbor exotic topological effects embedded in the hyper-kagome lattice.
