Model for the Magnetic Order and Pairing Channels in Fe Pnictide Superconductors

A two-orbital model for Fe-pnictide superconductors is investigated using computational techniques on two-dimensional square clusters. The hopping amplitudes are derived from orbital overlap integrals, or by band structure fits, and the spin frustrating effect of the plaquette-diagonal Fe-Fe hopping is remarked. A spin striped state is stable in a broad range of couplings in the undoped regime, in agreement with neutron scattering. Adding two electrons to the undoped ground state of a small cluster, the dominant pairing operators are found. Depending on the parameters, two pairing operators were identified: they involve inter-$xz\mathrm{\text{−}}yz$ orbital combinations forming spin singlets or triplets, transforming according to the $B_{2g}$ and $A_{2g}$ representations of the $D_{4h}$ group, respectively.

Figure 1

(a) Geometry of the FeAs layer. As atoms are located above (open circles) or below (filled circle at the origin) the Fe plane (remaining filled circles). (b) The Fe-Fe NN path. (c) The Fe-Fe NNN path. (d) Fermi surface of $H_{\mathrm{FeAs}}$ for $pd\pi /pd\sigma =-0.2$ in the $U=J=0$ limit. (e) Same as (d) but for the parameters of Ref. 11. In (d), the half-filled chemical potential is at $-0.03$. (f) The tilted 8-site cluster used here.

Figure 2

(a) $S(q)$ vs $q$ for the $\sqrt{8}\times \sqrt{8}$ cluster at the $U$’s indicated, with $J=U/4$ and $pd\pi /pd\sigma =-0.2$. The momenta allowed in this cluster are (0, 0), ($\pm \pi /2$, $\pm \pi /2$), (0, $\pi$), ($\pi$, 0), and ($\pi$, $\pi$) [30]. (b) VCA grand potential [in energy units $(pd\sigma {)}^2/{\Delta }_{pd}$] vs staggered magnetic fields $h_{\mathrm{stagg}}$ for $\mathbf{q}=(\pi ,\pi )$ and (0, $\pi$), and $pd\pi /pd\sigma =-0.2$, $U=1$, $J=0.25$, The minimum for (0, $\pi$) at $h_{\mathrm{stagg}}\ne 0$ indicates symmetry breaking. (c) $m_{\mathrm{stagg}}$ vs $U$, with $U/J=4$. The small $U$ region at $pd\pi /pd\sigma =-0.2$ was numerically unstable.

Figure 3

One-particle VCA spectral function $A(\mathbf{k},\omega )$ of $H_{\mathrm{FeAs}}$ for (a) $U=0.5$, $J=0.125$, and $pd\pi /pd\sigma =-0.2$, and (b) $U=1$, $J=0.25$, $pd\pi /pd\sigma =-0.5$ in the symmetry broken phase with (0, $\pi$) magnetic ordering at half-filling. A broadening 0.05 was used. (c) Density of states obtained by $\mathbf{k}$-integrating the spectral functions, at the $U$’s indicated, with $U/J=4$ and $pd\pi /pd\sigma =-0.2$. (d) FS corresponding to case (a). The FS has been symmetrized under rotations.

Figure 4

(a) $\sqrt{8}\times \sqrt{8}$ cluster results with 2 more electrons than half-filling, at $U/J=4$. Shown are regions with singlet and triplet pairing (see text). (b, c) Schematic representation of the singlet and triplet pairs (see text). Black arrows represent the magnetically ordered background. White arrows are the added electrons. $x$, $y$ are the orbitals.