Effects of spin-orbit coupling on spin-fluctuation induced pairing in iron-based superconductors

Abstract

We perform a theoretical study of the leading pairing instabilities and the associated superconducting gap functions within the spin-fluctuation mediated pairing scenario in the presence of spin-orbit coupling (SOC). Focussing on iron-based superconductors (FeSCs), our model Hamiltonian consists of a realistic density functional theory (DFT)-derived ten-band hopping term, spin-orbit coupling, and electron-electron interactions included via the multi-orbital Hubbard-Hund Hamiltonian. We perform an extensive parameter sweep and investigate different doping regimes including cases with only hole-or only electron Fermi pockets. In addition, we explore two different bandstructures: a rather generic band derived for LaFeAsO but known to represent standard DFT-obtained bands for iron-based superconductors, and a band specifically tailored for FeSe which exhibits a notably different Fermi surface compared to the generic case. It is found that for the generic FeSCs band, even rather large SOC has negligible effect on the resulting gap structure; the s+− (pseudo-)spin singlet pairing remains strongly favored and SOC does not lead to any SOC-characteristic gap oscillations along the various Fermi surfaces. By contrast in the strongly hole-doped case featuring only hole-pockets around the Γ-point, the leading solution is d-wave pseudo-spin singlet, but with a notable SOC-driven tendency towards helical pseudo-spin triplet pairing, which may even become the leading instability. In the heavily electron doped situation, featuring only electron pockets centered around the M -point, the leading superconducting instabilities are pseudo-spin singlets with SOC favoring the s-wave case as compared to d-wave pairing, which is the favored gap symmetry for vanishing SOC. We end with a discussion pertaining to the role of SOC on the gap structure relevant for FeSe from a weak-coupling point of view. As our formalism, described at length in the supplementary material, is rather general, our study is of relevance to other multiband superconductors as well.