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Anomalous enhancement of Wilson ratio in a quantum spin liquid with strong spin-orbital entanglement: the case of Na4Ir3O8

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.