Using functional renormalization group we investigated possible superconductivity in doped Sr$_2$IrO$_4$. In the electron doped case, a $d^*_{x^2-y^2}$-wave superconducting phase is found in a narrow doping region. The pairing is driven by spin fluct
uations within the single conduction band. In contrast, for hole doping an $s^*_{pm}$-wave phase is established, triggered by spin fluctuations within and across the two conduction bands. In all cases there are comparable singlet and triplet components in the pairing function. The Hunds rule coupling reduces (enhances) superconductivity for electron (hole) doping. Our results imply that hole doping is more promising to achieve a higher transition temperature. Experimental perspectives are discussed.
In conventional and high transition temperature copper oxide and iron pnictide superconductors, the Cooper pairs all have even parity. As a rare exception, Sr$_2$RuO$_4$ is the first prime candidate for topological chiral p-wave superconductivity, wh
ich has time-reversal breaking odd-parity Cooper pairs known to exist before only in the neutral superfluid $^3$He. However, there are several key unresolved issues hampering the microscopic description of the unconventional superconductivity. Spin fluctuations at both large and small wavevectors are present in experiments, but how they arise and drive superconductivity is not yet clear. Spontaneous edge current is expected but not observed conclusively. Specific experiments point to highly band- and/or momentum-dependent energy gaps for quasiparticle excitations in the superconducting state. Here, by comprehensive functional renormalization group calculations with all relevant bands, we disentangle the various competing possibilities. In particular we show the small wavevector spin fluctuations, driven by a single two-dimensional band, trigger p-wave superconductivity with quasi-nodal energy gaps.
In iron selenide superconductors only electron-like Fermi pockets survive, challenging the $S^{pm}$ pairing based on the quasi-nesting between the electron and hole Fermi pockets (as in iron arsenides). By functional renormalization group study we sh
ow that an in-phase $S$-wave pairing on the electron pockets ($S^{++}_{ee}$) is realized. The pairing mechanism involves two competing driving forces: The strong C-type spin fluctuations cause attractive pair scattering between and within electron pockets via Cooperon excitations on the virtual hole pockets, while the G-type spin fluctuations cause repulsive pair scattering. The latter effect is however weakened by the hybridization splitting of the electron pockets. The resulting $S^{++}_{ee}$-wave pairing symmetry is consistent with experiments. We further propose that the quasiparticle interference pattern in scanning tunneling microscopy and the Andreev reflection in out-of-plane contact tunneling are efficient probes of in-phase versus anti-phase $S$-wave pairing on the electron pockets.
