Monte Carlo Study of an Unconventional Superconducting Phase in Iridium Oxide $J_{\mathrm{eff}}\mathbf{=}1/2$ Mott Insulators Induced by Carrier Doping

Based on a microscopic theoretical study, we show that novel superconductivity is induced by carrier doping in layered perovskite Ir oxides where a strong spin-orbit coupling causes an effective total angular momentum $J_{\mathrm{eff}}=1/2$ Mott insulator. Using a variational Monte Carlo method, we find an unconventional superconducting state in the ground state phase diagram of a $t_{2g}$ three-orbital Hubbard model on the square lattice. This superconducting state is characterized by a $d_{x^2\mathrm{\text{−}}{y}^2}$-wave “pseudospin singlet” formed by the $J_{\mathrm{eff}}=1/2$ Kramers doublet, which thus contains interorbital as well as both singlet and triplet components of $t_{2g}$ electrons. The superconducting state is found stable only by electron doping, but not by hole doping, for the case of carrier doped ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$. We also study an effective single-orbital Hubbard model to discuss the similarities to high-$T_c$ cuprate superconductors and the multiorbital effects.

Figure 1

(a) Fermi surface and (b) energy dispersions of the noninteracting tight-binding energy band for ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ with electron density $n=5$. Numbers in (b) denote the band index $m$, and $E_F$ is the Fermi energy. A set of tight-binding parameters used is $(t_2,t_3,t_4,t_5,{\mu }_{xy},\lambda )=(0.5,0.25,1.03,0.17,-1.0,1.39)t_1$.

Figure 2

The ground state phase diagram of the three-orbital Hubbard model on the 2D $20\times 20$ square lattice with $J=0$. PM-M, AFM-I, AFM-M, and SC denote paramagnetic metal, AFM insulator, AFM metal, and $d_{x^2\mathrm{\text{−}}{y}^2}$-wave “pseudospin singlet” SC, respectively.

Figure 3

The ground state phase diagram of the three-orbital Hubbard model on the 2D $20\times 20$ square lattice. The solid red and dotted blue lines represent the phase boundaries for $U/t_1=8$ and 10, respectively. PM-M, $x$-AFM-I, $x$-AFM-M, and SC denote paramagnetic metal, in-plane AFM insulator, in-plane AFM metal, and $d_{x^2\mathrm{\text{−}}{y}^2}$-wave “pseudospin singlet” SC, respectively.

Figure 4

Energy comparison of the effective single-orbital Hubbard model on the 2D $14\times 14$ square lattice with $U/t=13$, $t^{\prime }/t=0.26$, and $t^{\prime \prime }/t=-0.05$. The energies for different states are measured from the one for the paramagnetic state. The phase diagram is indicated in the upper part of the figure. Here $n=1$ corresponds to half filling. PM-M, AFM-I, AFM-M, and SC stand for paramagnetic metal, AFM insulator, AFM metal, and $d_{x^2\mathrm{\text{−}}{y}^2}$-wave SC, respectively.