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

TL;DR

This study investigates how spin-orbit coupling influences the pairing mechanisms and gap structures in iron-based superconductors using a realistic multi-orbital model, revealing doping-dependent effects on pairing symmetry.

Contribution

It provides a comprehensive theoretical analysis of SOC effects on pairing in FeSCs across different doping levels and band structures, highlighting conditions where SOC alters pairing symmetry.

Findings

SOC has negligible effect on generic FeSCs band and s+- pairing remains dominant.

In hole-doped cases, SOC induces a transition from d-wave to helical triplet pairing.

In electron-doped cases, SOC favors s-wave pairing over d-wave.

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 $\Gamma$-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.