An energetically competitive $\tau_3$ $B_{1g}$ pairing in a $t-J_{1}-J_{2}$ model with orbital differentiated exchange couplings: implications for superconductivity in alkaline iron selenides

The pairing state in the alkaline iron selenides remains a challenge to our understanding. We address this issue in the incipient Mott picture based on the bad-metal behavior [1] of these materials. In conjunction with this picture, the multi-orbital effect is amplified, with two studied possibilities being the orbital-selective Mott transition [2] and the orbital-dependent pairing [3]. Here we carry out calculations in a five-orbital $t-J_{1}-J_{2}$ model, in which the orbital-dependent correlations are directly encoded in the exchange couplings. Specifically, we consider intra-orbital exchange couplings for $d_{xz}$, $d_{yz}$, and $d_{xy}$ but allow varying the ratio $r_o=J_{xz,xz}/J_{xy,xy}$. For $r_o<1$, we find a regime in the phase diagram where the leading pairing channel is an unusual $\tau_3$ $s_{x^2y^2}^{B_{1g}}$. This state has a full gap on the Fermi surfaces at both the zone boundary and center, with the pairing function changing sign between the two electron pockets. We propose this pairing state as a viable candidate for superconducting alkaline iron selenides. [1] R. Yu et al.,Nat. Commun. 4:2783 doi:10.1038/ncomms3783 (2013). [2] R.Yu and Q.Si, Phys. Rev. Lett. 110, 146402 (2013). [3] R. Yu, J.-X. Zhu, and Q. Si, Phys. Rev. B 89, 024509 (2014).