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

Motivated by the recent discovery of superconductivity in the iron-based ladder compound BaFe$_2$S$_3$ under high pressure, we derive low-energy effective Hamiltonians from first principles. We show that the complex band structure around the Fermi level is represented only by the Fe 3$d_{xz}$ (mixed with 3$d_{xy}$) and 3$d_{x^2-y^2}$ orbitals. The characteristic band degeneracy allows us to construct a four-band model with the band unfolding approach. We also estimate the interaction parameters and show that the system is more correlated than the 1111 family of iron-based superconductors. Provided the superconductivity is mediated by spin fluctuations, the $3d_{xz}$-like band plays an essential role, and the gap function changes its sign between the Fermi surface around the $\Gamma$ point and that around the Brillouin-zone boundary.