Microscopic model realization of d-wave pseudospin current order in Sr_2IrO_4

The d-wave pseudospin current order (dPSCO) with staggered circulating pseudospin current has been proposed as the hidden electronic order to describe the unexpected breaking of spatial symmetries in stoichiometric Sr_2IrO_4 and the unconventional pseudogap phenomena in electron doped Sr_2IrO_4. However, a microscopic model for the emergence of dPSCO is still lacking. The nearest neighbor Coulomb repulsion V, which is expected to be significant in Sr_2IrO_4 due to the large spatial extension of the Ir 5d orbitals, is capable of driving dPSCO on the mean-field level, albeit the latter is energetically degenerate to the staggered flux phase with circulating charge current. We find the in-plane anisotropy Γ_2 in the effective superexchange interaction between J_eff=1 2 pseudospins, originating from the cooperative interplay between Hund's rule coupling and spin-orbit coupling of Ir 5d electrons, is able to lift the degeneracy and stabilize the pseudospin currents. The effective single-orbital model of J_eff=1 2 electrons, including onsite Coulomb repulsion U, nearest neighbor Coulomb repulsion V, and the in-plane anisotropy Γ_2, is then studied. We obtain the mean-field ground states, analyze their properties, and determine the phase diagram of stoichiometric Sr_2IrO_4 in the plane spanned by U and V at a fixed Γ_2. We demonstrate the realization of dPSCO, and its competition and coexistence with antiferromagnetism. Remarkably, we find the coexistence of dPSCO and antiferromagnetism naturally leads to spin bond nematicity, with the spin directions of these three orders forming nontrivial chirality. Furthermore, we show that the emergence of the coexistent state and its chirality can be tuned by carrier doping.