Renormalization group analysis for the quasi-1D superconductor BaFe${}_2$S${}_3$

Motivated by the discovery of superconductivity in the two-leg, quasi-one dimensional ladder compound, BaFe${}_2$S${}_3$ we present a renormalization group study of electrons moving on a two leg, two orbital ladder, subjected to Hubbard repulsion $U$ and Hund’s coupling $J$. In our calculations, we adopt tightbinding parameters obtained from ab-initio studies on this material. At incommensurate filling, the long wavelength analysis displays four phases as a function of $0\le J\mathrm{/}U<1$. We show that a fully gapped superconductor is stabilized at sufficiently large Hund’s coupling, the relative phases at the three Fermi points are “+,-,-”. By contrast, when the system is tuned to half filling, Umklapp scattering gives rise to Mott insulating phases. We discuss the general implications of our study for the broad class of iron-based superconductors.