Mott transition between a spin-liquid insulator and a metal in three dimensions

We study a bandwidth controlled Mott metal-insulator transition (MIT) between a Fermi liquid metal and a quantum spin-liquid insulator at half-filling in three dimensions (3D). Using a slave rotor approach, and incorporating gauge field fluctuations, we find a continuous MIT and discuss the finite temperature crossovers around this critical point. We show that the specific heat $C \sim T \ln \ln (1/T)$ at the MIT and argue that the electrical transport on the metallic side near the transition should exhibit a `conductivity minimum' as a function of temperature. A possible candidate to test these predictions is the 3D spin liquid insulator Na$_4$Ir$_3$O$_8$ which exhibits a pressure-tuned transition into a metallic phase. We also present the electron spectral function of Na$_4$Ir$_3$O$_8$ at the transition.