Strong electronic correlations and Fermi surface reconstruction in the quasi-one-dimensional iron superconductor ${\mathrm{BaFe}}_2{\mathrm{S}}_3$

${\mathrm{BaFe}}_2{\mathrm{S}}_3$ is a special iron superconductor with a two-leg ladder structure, which can help to unravel the role played by the electronic correlations in high-$T_c$ superconductivity. At zero pressure, it is insulating with stripe antiferromagnetic (AF) order and it has been claimed to be a Mott insulator. Superconductivity emerges under pressure. To analyze the strength of the local correlations in ${\mathrm{BaFe}}_2{\mathrm{S}}_3$, we apply the slave-spin technique to a model, which includes the five Fe $d$ orbitals. We find that at zero pressure, ${\mathrm{BaFe}}_2{\mathrm{S}}_3$ is strongly correlated. The correlations are particularly severe for the two orbitals with the largest weight at the Fermi level, which show mass enhancements $m^{*}\sim 12–15$. Such strong correlations invalidate nesting as the mechanism for AF. We find that the system is not a Mott insulator at zero temperature. Nevertheless these two orbitals will become incoherent at higher temperatures. At the pressure at which the superconductivity appears, the electronic correlations in ${\mathrm{BaFe}}_2{\mathrm{S}}_3$ are strongly reduced and similar to the ones measured in other iron superconductors. Different from what happens in other iron superconductors, at both pressures, the Fermi surface is reconstructed by the electronic correlations.

Figure 1

Crystal structure of ${\mathrm{BaFe}}_2{\mathrm{S}}_3$ with planes containing iron two-leg ladders. The iron-sulfur plane structure is equivalent to the one in iron superconductors except that one of each three iron rows is missing. The position of the missing row shifts between consecutive planes.

Figure 2

(a) Orbital dependent quasiparticle weight $Z_{\gamma }$ (main figure) and filling $n_{\gamma }$ (inset) at zero pressure vs the intraorbital interaction $U$. At the Hund's metal crossover, $U^{*}\sim 2.1$ eV, the system becomes strongly correlated due to the formation of local spins and a sharp drop of $Z_{\gamma }$ is observed. The dotted line marks the interaction value $U_{P=0}=2.9$ eV suitable for ${\mathrm{BaFe}}_2{\mathrm{S}}_3$, see text. At this interaction, the orbitals $w_{yz}$ and $w_{zx}$ with have the largest weight the bands close to the Fermi level are near half-filling and have a very small quasiparticle weight $Z_{\gamma }$ which corresponds to an enhanced mass $m^{*}\sim 15$. (b) Same as in main figure in (a) for $P=12.4$ GPa, pressure at which superconductivity is found. With pressure the Hund's metal crossover shifts to larger interactions due to larger bandwidth and the interaction is reduced to $U_{P=12.4}\sim 2.75$ eV. At this interaction, the strength of the correlations, as measured by $Z_{\gamma }$, becomes similar to the one found in other iron superconductors.

Figure 3

Band structure for $P=0$ and 12.4 GPa with and without including the electronic correlations. The band structure in (a) and (c) for $P=0$ and 12.4 GPa is calculated using the tight-binding model from [18] and mimics the one obtained in ab initio calculations, see text. The bandwidth is approximately 4 and 5 eV, respectively, for $P=0$ and 12.4 GPa. As shown in (c) and (d), the electronic correlations reduce these bandwidth below 2 and 3.5 eV, respectively. Band narrowing, is more evident close to the Fermi level.

Figure 4

Zoom of the band structure near the Fermi level for $P=0$ and 12.4 GPa with and without including the electronic correlations. Close to the Fermi level the bands are dominated by ${\mathrm{w}}_{yz}$ (red) and ${\mathrm{w}}_{zx}$ (green) orbitals. The electronic correlations modify the band structure and reconstruct the Fermi surface, characterized by very shallow pockets.

Figure 5

Fermi surface at $P=0$ and 12.4 GPa with and without including the electronic correlations: (a.1)–(d.1) 3D Fermi surface plotted in one fourth of the Brillouin zone. The Fermi surface is symmetric with respect to the $\left(k_x,k_y,0\right)$, the $\left(k,k,k_z\right)$, and the $\left(k,-k,k_z\right)$ planes. (a.2)–(d.2) Fermi surface cuts along $k_z-k_x=k_y$ reciprocal to the Fe-ladder plane. (a.3)–(d.3) Same as (a.2)–(d.2) but along $k_z-k_x=k_y$ plane, reciprocal to the plane perpendicular to the Fe-ladder plane. On spite of the quasi-one-dimensional lattice the Fermi surface has three-dimensional character. At both pressures, the Fermi surface is reconstructed due to electronic correlations. Enhanced scattering is expected at $\mathbf{Q}\sim (\mathbf{0},\mathbf{0},\mathbf{2}\pi )({\mathbf{Q}}^{*}\sim (\mathbf{0},\mathbf{0},\pi )$ if the Brillouin zone is unfolded along $k_z)$ between hole pockets along $(k_x,-k_x,\pm \pi )$ specially in the Fermi surface reconstructed by correlations.