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Motivated by the recent discovery of superconductivity in the iron-basedladder compound BaFe$_2$S$_3$ under high pressure, we derive low-energyeffective Hamiltonians from first principles. We show that the complex bandstructure around the Fermi level is represented only by the Fe 3$d_{xz}$ (mixedwith 3$d_{xy}$) and 3$d_{x^2-y^2}$ orbitals. The characteristic band degeneracyallows us to construct a four-band model with the band unfolding approach. Wealso estimate the interaction parameters and show that the system is morecorrelated than the 1111 family of iron-based superconductors. Provided thesuperconductivity is mediated by spin fluctuations, the $3d_{xz}$-like bandplays an essential role, and the gap function changes its sign between theFermi surface around the $\Gamma$ point and that around the Brillouin-zoneboundary.

Ab initio downfolding study of the iron-based ladder superconductor BaFe$_2$S$_3$