Fermi-liquid, non-Fermi-liquid, and Mott phases in iron pnictides and cuprates

The role of Coulomb correlations in the iron pnictide LaFeAsO is studied by generalizing exact diagonalization dynamical mean-field theory to five orbitals. For rotationally invariant Hund’s rule coupling a transition from a paramagnetic Fermi-liquid phase to a non-Fermi-liquid metallic phase exhibiting frozen moments is found at moderate Coulomb energies. For Ising-like exchange, this transition occurs at a considerably lower critical Coulomb energy. The correlation-induced scattering rate as a function of doping relative to half filling, i.e., $\delta =n/5-1$, where $n=6$ for the undoped material, is shown to be qualitatively similar to the one in the two-dimensional single-band Hubbard model which is commonly used to study strong correlations in high-$T_c$ cuprates. In this scenario, the parent Mott insulator of LaFeAsO is the half-filled $n=5$ limit, while the undoped $n=6$ material corresponds to the critical doping region ${\delta }_c\approx 0.2$ in the cuprates, on the verge between the Fermi-liquid phase of the overdoped region and the non-Fermi-liquid pseudogap phase in the underdoped region.

Figure 1

(Color online) Density of states components of LaFeAsO for tight-binding band structure derived in Ref. 24. (a) $t_{2g}$ components ${\rho }_{xz,yz}$ and ${\rho }_{x^2-y^2}$, (b) $e_g$ components ${\rho }_{xy}$ and ${\rho }_{z^2}$.

Figure 2

(Color online) $\text{Fe}3d$ orbital occupancies (per spin) as functions of Coulomb interaction for $n=6$, with $J=U/4$ for $U\le 3\text{eV}$ and $J=0.75\text{eV}$ for $U>3\text{eV}$; Hund exchange.

Figure 3

(Color online) Imaginary part of self-energy components ${\Sigma }_m\left(i{\omega }_n\right)$ as function of Matsubara frequency for several Coulomb energies. (a) and (b): Hund coupling; (c) Ising exchange. The color coding is defined in panel (b).

Figure 4

(Color online) Quasiparticle weights $Z_m$ of $\text{Fe}3d$ orbitals as functions of Coulomb interaction for $n=6$; Hund exchange.

Figure 5

(Color online) Orbital-dependent low-frequency scattering rates ${\gamma }_m$ as functions of Coulomb interaction for Hund and Ising exchange.

Figure 6

(Color online) Variation of orbital dependent spin-spin correlation functions with imaginary time $\tau$ for three Coulomb energies and Hund coupling. (a) $U=1.75\text{eV}$, (b) $U=2.5\text{eV}$, and (c) $U=3.25\text{eV}$.

Figure 7

(Color online) Variation of orbital dependent spin-spin correlation functions with imaginary time $\tau$ for two Coulomb energies and Ising exchange. (a) $U=1.5\text{eV}$ and (b) $U=3.0\text{eV}$; $J=U/4$.

Figure 8

(Color online) Spectral distributions of $\text{Fe}3d$ subbands for (a) $U=1.75\text{eV}$ and (b) $U=3\text{eV}$; Hund coupling; (c) $U=2.5\text{eV}$: Ising exchange; with $J=U/4$ and 0.05 eV broadening.

Figure 9

(Color online) $\text{Fe}3d$ orbital occupancies as functions of chemical potential for $U=2.5\text{eV}$ with $J=0.625\text{eV}$ and Hund coupling. The arrows indicate the values of $\mu$ associated with integer total occupancies.

Figure 10

(Color online) Schematic phase diagram for doped LaFeAsO. Red solid curves: boundaries between Fermi-liquid and non-Fermi-liquid phases for Hund and Ising exchange. At half-filling $\left(n=5\right)$ a Mott insulating phase exists down to rather small $U$. The undoped material at $n=6$ with moderate $U\approx 2.5\text{eV}$ is a Fermi-liquid for Hund coupling, but an incoherent metal for Ising exchange. The $n=6$ Mott phase is located at $U>6\text{eV}$.

Figure 11

(Color online) (a) Orbital-dependent scattering rates ${\gamma }_m$ for LaFeAsO as functions of doping relative to half filling, $\delta =n/5-1$ (Hund exchange, $J=U/4$). (b) Cluster components of scattering rate for single-band two-dimensional Hubbard model as functions of hole doping (nearest and next-nearest-neighbor hopping $t=0.25\text{eV}$ and $t^{\prime }=-0.075\text{eV}$, respectively, $U=2.5\text{eV}$ and $T=0.01\text{eV}$) (Ref. 54). The vertical bars denote the approximate doping concentrations of the Fermi-liquid to non-Fermi-liquid transition.