Mott transition in multiorbital models for iron pnictides

The bad-metal behavior of the iron pnictides has motivated a theoretical description in terms of a proximity to Mott localization. Since the parent compounds of the iron pnictides contain an even number of 3d electrons per Fe, it is important to determine whether a Mott transition robustly exists and clarify the nature of the possible Mott insulating phases. We address these issues in a minimal two-orbital model and a more realistic four-orbital model for the parent iron pnictides using a slave-spin approach. In the two-orbital model with two electrons per Fe, we identify a single transition from a metal to a Mott insulator, showing that this transition must exist as a result of orbital degeneracy. Depending on the ratio between the inter- and intraorbital Coulomb repulsions, the insulating state can be either a high-spin Mott insulator or a low-spin orbital-Mott insulator. In the four-orbital model with four electrons per Fe, we find a rich phase diagram for the metal-to-insulator transition. At strong Hund's couplings, a localization transition to a high-spin Mott insulator always occurs. At zero and weak Hund's couplings, on the other hand, we find a transition to an intermediate-spin insulating state. This transition can be viewed as an orbitally selective metal-to-insulator transition: the transition to a Mott insulator in the $xz$ and $yz$ orbitals takes place at the same critical coupling as the transition to either a band insulator at zero Hund's coupling or an orbitally polarized insulator at weak but finite Hund's coupling in the $xy$ and $x^2-y^2$ orbitals. The implications of our model studies for the physics of iron pnictides and iron chalcogenides are discussed.

Figure 1

Evolution of the spectral weight $Z$ in the two-orbital model with (a) $J=0$, $U^{\prime }=U$ and (b) $J/U=0.2$, $U^{\prime }/U=0.6$. $D=12$ is the full bandwidth of the noninteracting band structure.

Figure 2

DOS in the two-orbital model at various $U$ values with the same model parameters as in Fig. 1.

Figure 3

Phase diagram in the $J$-$U$ plane of the two-orbital model at half filling. Here we have taken $U^{\prime }=U-2J$. The blue circles (red diamonds) give the phase boundary of the metal-to-Mott-insulator transition for the case of full (Ising-type) Hund's coupling.

Figure 4

Illustration of the high-spin Mott and low-spin orbital-Mott states in the two-orbital model at the atomic limit. In this model, the high-spin Mott state has $S=1$ and the ground-state energy has $U^{\prime }-J$; the low-spin orbital-Mott state has $S=0$ and the ground-state energy has $U-J$.

Figure 5

(a) The evolution of $Z$ at half filling with $J/U=0.2$ and different $U^{\prime }/U$ ratios showing the transition to different Mott states. (b)–(d): The evolution of $\langle n_{\uparrow }{n}_{\downarrow }\rangle$, $C_o^{1,2}$, and ${\mathbf{S}}^2$ (see text for the definitions of these quantities) for the same set of parameters.

Figure 6

Three candidate ground states in the atomic limit in the four-orbital model. The $S=2$ state is an analog of the high-spin Mott state in the two-orbital model.

Figure 7

SSMF results for the four-orbital model at $J=0$, showing evolution of (a) $Z$, (b) average electron filling per site per spin, (c) average of total spin, and (d) interorbital correlation between $xz$ and $yz$ orbitals.

Figure 8

SSMF results for the four-orbital model at $J/U=0.007$.

Figure 9

SSMF results for the four-orbital model at $J/U=1/4$.

Figure 10

The evolution of interorbital correlation between the $xy$ and $x^2-y^2$ orbitals, $C_O^{3,4}$, in the four-orbital model at $J=0$, $J/U=0.007$, and $J/U=1/4$, respectively.

Figure 11

Phase diagram in the $J$-$U$ plane of the four-orbital model. The thick solid (black) line shows the phase boundary between the metallic and insulating states. The blue dashed line at $J=0$ refers to the intermediate-spin insulating state IS1, and the thin solid (red) line refers to the low-spin to high-spin transition between the IS2 state and the high-spin Mott state. The dotted line at $U\approx 10$ eV separates the metallic phase into two regimes. To the left of this line, the Fermi surface topology is identical to the noninteracting case, while, in the regime between this dotted line and the thick solid line, the topology of the Fermi surface changes (see text). The inset shows a closer view of the lower-right corner of the phase diagram.