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

## TL;DR

This study uses renormalization group analysis to explore the phase diagram of a two-leg, two-orbital ladder model for BaFe$_2$S$_3$, revealing conditions for superconductivity and Mott insulating phases based on electron filling and Hund's coupling.

## Contribution

It provides a detailed RG analysis of a realistic ladder model for BaFe$_2$S$_3$, incorporating ab-initio parameters and identifying phases relevant to superconductivity and Mott insulators.

## Key findings

- A fully gapped superconductor is stabilized at large Hund's coupling.
- Different phases emerge depending on electron filling, including superconducting and Mott insulating states.
- The phase diagram depends on the ratio J/U and electron filling, with specific phase characteristics at incommensurate and half fillings.

## Abstract

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 $0 \leq J/U <1$. 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.