Orbital selectivity in Hund's metals: The iron chalcogenides

We show that electron correlations lead to a bad metallic state in chalcogenides FeSe and FeTe despite the intermediate value of the Hubbard repulsion $U$ and Hund's rule coupling $J$. The evolution of the quasiparticle weight $Z$ as a function of the interaction terms reveals a clear crossover at $U\simeq 2.5$ eV. In the weak coupling limit $Z$ decreases for all correlated $d$ orbitals as a function of $U$ and beyond the crossover coupling they become weakly dependent on $U$ while strongly dependent on $J$. A marked orbital dependence of the $Z$'s emerges even if in general the orbital-selective Mott transition only occurs for relatively large values of $U$. This two-stage reduction of the quasiparticle coherence due to the combined effect of Hubbard $U$ and the Hund's $J$ suggests that the iron-based superconductors can be referred to as Hund's correlated metals.

Figure 1

Quasiparticle weight in an $N_{\mathrm{orb}}$-fold degenerate Hubbard model with semicircular density of states as a function of $U/D$ for various Hund's coupling $J/U$, where $D$ is the half-bandwidth. Upper panel: $N_{\mathrm{orb}}=5$; lower panel: $N_{\mathrm{orb}}=3$. The panels show data for an average population of $N=N_{\mathrm{orb}}+1$ electrons and the insets for $N=N_{\mathrm{orb}}$.

Figure 2

Upper panel: quasiparticle weight in a Hubbard model with six electrons in five bands with semicircular densities with half-bandwidth $D$ split by a cubic crystal field in two manifolds of degeneracy 3 ($t_{2g}$ symmetry) and 2 ($e_g$ symmetry). Lower panel: populations of the two manifolds.

Figure 3

Results for FeSe (DFT+GA with $J/U=0.224$) as a function of $U$. From the top: (a) the quasiparticle weights for the different orbitals; (b) the expectation value of $S^2$; (c) the renormalized crystal-field splittings; (d) the population of each orbital; (e) the interorbital density correlations.

Figure 4

Results for FeSe and smaller $J/U=0.15$ (top panel) and for FeTe (bottom panel).