Ab Initio Evidence for Strong Correlation Associated with Mott Proximity in Iron-Based Superconductors

We predict that iron-based superconductors discovered near $d^6$ configuration (5 Fe $3d$ orbitals filled by 6 electrons) is located on the foot of an unexpectedly large dome of correlated electron matter centered at the Mott insulator at $d^5$ (namely, half filling). This is based on the many-variable variational Monte Carlo results for ab initio low-energy models derived by the downfolding. The $d^5$ Mott proximity extends to subsequent emergence of incoherent metals, orbital differentiations due to the Mott physics, and Hund’s rule coupling, followed by antiferromagnetic quantum criticality, in quantitative accordance with available experiments.

Figure 1

(a) Magnetic ordered moment $m(q_{\mathrm{peak}})$ at the Bragg wave number $q_{\mathrm{peak}}$ (for the pattern, see right) calculated by MVMC simulations (red circles). The result at $\lambda =1$ represents that of the ab initio model for LaFeAsO while the $\lambda$ dependence illustrates the results of the models obtained by uniformly scaling the interaction strengths by $\lambda$. The black-framed yellow diamonds indicate the results of the ab initio models, where they are plotted at the corresponding $\lambda$. The plotted results are those in the thermodynamic limit after the size extrapolation. Experimentally observed values [5, 6, 7, 8] are also plotted at corresponding $\lambda$ by asterisks, where FeTe shows double-stripe and others show stripe orders in agreement with our ab initio results. (b) Magnetic ordered moment in the plane of $\lambda$ and doping concentration $\delta$. The data are plotted in the cross sections for $\lambda =1$ as well as for $\delta =0$. It shows a peak at $d^5$ ($\delta =-1.0$) and decreases monotonically over $d^6$ ($\delta =0$), which forms a large half-dome structure peaked at $d^5$. The MVMC results of the ab initio models are shown by black-framed yellow diamonds. The green and blue shaded regions represent the $G$-type and stripe-type AF orders, respectively, as is illustrated in the right panel of Fig. 1a. There exist two first-order transitions (black dashed lines), one indicated by the jumps in the ordered moment around $\delta \sim 0.17$ and the other at the transition between the $G$-type and stripe around $\delta \sim -0.22$, which signals large charge fluctuations under phase-separation effects. In the present short-ranged-interaction model, the phase separation indeed occurs in the gray shaded regions.

Figure 2

Filling dependence of orbital-resolved momentum distribution $n_{\nu }(k)\equiv ⟨c_{\nu ,k}^{†}{c}_{\nu ,k}⟩$ plotted for the “unfolded” Brillouin zone (BZ), where the creation and annihilation operators of an electron at the orbital $\nu$ and the wave number $k$ are denoted by $c_{\nu ,k}^{†}$ and $c_{\nu ,k}$, respectively. In the bottom left, the unfolded BZ (with the coordinates $k_x$ and $k_y$) and folded BZ (with $k_X$ and $k_Y$) are depicted by the red and black lines, respectively. In the bottom right, the Fermi surfaces of the local density approximation band structures are shown by the red curve, which can be identified in the corresponding sharp changes in $n_{\nu }(k)$ for $\nu =d_{YZ/ZX}$ and $d_{X^2-Y^2}$ on the top panels. Note that the orbitals are represented according to the folded BZ. Fade out of sharp boundaries in $n_{\nu }(k)$, representing the Fermi pockets, are seen especially for $d_{YZ/ZX}$ and $d_{X^2-Y^2}$ together with $d_{Z^2}$, which signals strong renormalizations of quasiparticles with bad metallic behavior when $\delta$ decreases progressively to negative.

Figure 3

(a) Magnetic ordered moments in the plane of ${\lambda }_U$ and ${\lambda }_J$ for system size $N_s=6\times 6$, which is expected to be close to the thermodynamic limit. Here, ${\lambda }_J$ (${\lambda }_U$) scales exchange (Coulomb) interactions from the ab initio model for LaFeAsO at ${\lambda }_U={\lambda }_J=1$. The sharp change in the ordered magnetic moment is triggered by a synergy effect of the direct Coulomb (${\lambda }_U$) and the exchange (${\lambda }_J$) interactions and the two interactions comparably contribute. (b) Orbital-resolved double occupation $D_{\nu }$ defined by probability of simultaneous occupation of up and down spin electrons on the $\nu$ orbital at the same site. (c) Orbital occupation $n_{\nu }$ defined by the averaged density of electrons on the orbital $\nu$ as a function of $\lambda$ at filling $\delta =0(d^6)$. Antiferromagnetic phase is represented as shaded region. System sizes $8\times 8$ for (b) and (c) are sufficient to well represent these quantities in the thermodynamic limit. Near the realistic parameter $\lambda =1$, strong correlation of the $d_{X^2-Y^2}$ orbital synergetically starts involving the $d_{Z^2}$ orbital through the Hund’s rule coupling, which drives the $d_{Z^2}$ into the state close to half filling $n=1$ with reduced $D$.