Properties of a diagonal two-orbital ladder model of the iron pnictide superconductors

We study a diagonal two-orbital ladder model of the Fe-based superconductors using the density-matrix renormalization-group method. At half filling, we find a close competition between a “spin-striped” state and a noncollinear “spin-checkerboard” state, as well as significant nematic correlations. Upon finite hole or electron doping, the dominant pairing correlations are found to have ${\text{A}}_{1g}$ ($S$-wave) symmetry.

Figure 1

(Color online) (a) The diagonal ladder geometry. Each site has two orbitals, $d_{xz}$ and $d_{yz}$. Sites separated by $\left(2a,2a\right)$ (indicated by the arrow in the figure) are identified. (b) The Brillouin zone of the two-band model (Ref. 4) in the unfolded (one Fe/unit cell) scheme. The Fermi surfaces are shown, along with their orbital content. The diagonal lines show the $k$ states which can be accessed in the diagonal ladder.

Figure 2

(Color online) [(a) and (b)] Spin patterns in $4\sqrt{2}a\times \sqrt{2}a$ half-filled (two electrons per site) systems. The arrows are proportional to the local $⟨\mathbf{S}⟩$. The diagonal dashed lines show the actual boundaries of the system. Zeeman fields of strength $h=0.5$ were applied on (0,0) and (1,0) sites, in the directions indicated by the bold arrows. (c) A schematic phase diagram at half filling.

Figure 3

(Color online) Measurements of the nematic order parameters [see Eq. (3)] as a function of distance from the origin, in $4\sqrt{2}a\times \sqrt{2}a$ (16 site) systems. (The geometry is the same as in the clusters shown in Fig. 2.) (a) $U=4$ and (b) $U=8$. In these calculations, the hopping strengths of the bond from (0,0) to $\left(a,0\right)$ (at the upper left corner of the system) were 50% stronger than in the bulk.

Figure 4

(Color online) (a) Bond-pairing amplitudes for a $6\sqrt{2}a\times \sqrt{2}a$ (24 site) system with $U=4$, doped with six holes. Left: $d_{xz}\text{−}{d}_{xz}$ pairing and right: $d_{yz}\text{−}{d}_{yz}$ pairing. An external pairing field of strength $\Delta =0.5$ is applied to the upper left diagonal $d_{xy}\text{−}{d}_{xy}$ bond [see Eq. (4)], highlighted in the figure. The thickness of the bonds represents the amplitude of induced pair field on that bond. Solid (dashed) lines stand for positive (negative) amplitudes, respectively. (b) Detailed pair structure near the middle of the system. Upper left: $d_{xz}\text{−}{d}_{xz}$ amplitudes, upper right: $d_{yz}\text{−}{d}_{yz}$, and bottom: $d_{xz}\text{−}{d}_{yz}$ amplitudes.

Figure 5

(Color online) Induced pair amplitudes on diagonal bonds in three $4\sqrt{2}a\times \sqrt{2}a$ calculations, in which ${\text{A}}_{1g}$ (◻), ${\text{B}}_{1g}$ (○), and triplet (◇) pair fields are applied to the edge (see text). Solid (dashed) lines correspond to $d_{xz}\text{−}{d}_{xz}$ $\left(d_{yz}\text{−}{d}_{yz}\right)$ pairing, respectively.