$d$-wave pairing from spin fluctuations in the ${\mathrm{K}}_x$Fe${}_{2-y}$Se${}_2$ superconductors

Angle-resolved photoemission spectroscopy measurements on the recently discovered superconductors in the KFe${}_2$Se${}_2$ family with critical temperatures up to $~33$ K suggest that no Fermi pockets of hole character centered on the $\Gamma$ point of the Brillouin zone are present, in contrast to all other known ferropnictide and ferrochalcogenide superconductors. Using a fluctuation exchange approximation and a five-orbital tight-binding description of the band structure, we calculate the effective pairing interaction. We find that the pairing state in this system is most likely to have $d$-wave symmetry due to pair scattering between the remaining electron Fermi pockets at wave vector $\mathbf{q}~(\pi ,\pi )$, but without any symmetry-imposed nodes for the given Fermi surface. We propose experimental tests of this result, including the form of the resonance spectrum probed by inelastic neutron scattering.