  We present a theory for the metal-insulator transition (MIT) in the
quantum-spin-liquid candidate material Na4Ir3O8. We consider an extended
Hubbard model on the hyperkagome lattice, which incorporates atomic spin-orbit
coupling (SOC) and multi-orbital interactions of iridium 5d electrons. This
model is analyzed using the slave-rotor mean-field theory and thermodynamic
properties across the MIT are studied. The ground state in the insulating side
is a U(1) quantum spin liquid with spinon Fermi surfaces that consist of
multiple particle-like and hole-like pockets. It is shown that the Wilson ratio
in the quantum spin liquid phase is highly enhanced compared to the metallic
state. This originates from the fact that the magnetic susceptibility in the
quantum spin liquid phase acquires multiple enhancements due to the strong SOC,
reduced band-width and on-site spin-orbital exchange, while the heat capacity
does not change much across MIT. This explains the large Wilson ratio of the
insulating phase observed in the previous experiment on Na4Ir3O8. Possible
connections to other existing and future experiments, in particular on the
metallic phase, are discussed.
