Motivated by novel 5d-electron systems such as Sr2IrO4 and Ba2IrO4, we study the ground state of a three-orbital Hubbard model with a spin-orbit coupling by using a variational Monte Carlo method. The obtained ground-state phase diagram reveals that an antiferromagnetic state, stable at around the electron density n = 5, is destabilized by carrier doping and that the ground state becomes superconducting. Similar to high-T c cuprates, a large asymmetry of the phase diagram between electron doping (n > 5) and hole doping (n <5) is also found, which can be understood as the band structure effect. Due to the large spin-orbit coupling which entangles spin and orbital degrees of freedom, the pseudospin becomes a good quantum number, and the superconductivity found here is characterized by the dx2-y2-wave "pseudospin singlet" pairing.
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