  It has recently been proposed that Na4Ir3O8 is a weak Mott insulator at
ambient pressure, supporting a three-dimensional spin liquid phase with a
spinon Fermi surface. This proposal is consistent with recent experimental
findings that the material becomes a metal upon increasing pressure or doping.
In this work, we investigate the effect of the spin-orbit coupling arising from
5d Ir moments both in the metallic and spin liquid phases of Na4Ir3O8. The
effective Hubbard model in terms of pseudospin j=1/2 Ir states is derived and
its consequences to both metallic and spin liquid phases are studied. In
particular, the model leads to enhanced Wilson ratio and strong temperature
dependence of the Hall coefficient.
