Spin-triplet $p$-wave pairing in a three-orbital model for iron pnictide superconductors

We examine the possibility that the superconductivity in the newly discovered FeAs materials may be caused by the Coulomb interaction between $d$ electrons of the iron atoms. We find that when the Hund’s rule ferromagnetic interaction is strong enough, the leading pairing instability is in spin-triplet $p$-wave channel in the weak-coupling limit. The resulting superconducting gap has nodal points on the two-dimensional Fermi surfaces. The $\mathit{k}$ dependent hybridization of several orbitals around a Fermi pocket is the key for the appearance of the spin-triplet $p$-wave pairing.

Figure 1

(Color online) (a) The Fe-As plane and the $d$ orbitals of Fe. The filled dots are Fe atoms and the empty dots are As atoms. The plus and minus signs in the empty dots indicate if the As atom is above or below the Fe plane. The large square is the 2D unit cell. The dashed square is the reduced unit cell which contains only one Fe. The $d_{xz}$, $d_{yz}$, and $d_{xy}$ orbitals of the Fe atoms are described by the red, blue, and green curves, and marked by $xz$, $yz$, and $xy$ respectively. (b) The $y$ hopping between the $d_{xz}$ or $d_{yz}$ with $d_{xy}$ orbitals.

Figure 2

(Color online) (a) The Fermi surfaces of the $\text{Fe}d$ bands. The plus sign marks the hole pockets and the minus sign marks the electron pockets. The square is the Brillouin zone. (b) The extended Brillouin zone (dashed square) for the reduced unit cell and the positions of the Fermi pockets in the extended Brillouin zone. The $\tilde{\Gamma }$ point has $\left({\tilde{k}}_x,{\tilde{k}}_y\right)=\left(0,0\right)$. The folding of the extended Brillouin zone in (b) produces (a). After folding, the $\left(\tilde{\Gamma },\tilde{M}\right)$ and $\left(\tilde{X},\tilde{Y}\right)$ in the extended Brillouin-zone map into the $\Gamma$ and $M$ in the original Brillouin zone, respectively. The yellow shading marks the region where the $p$-wave pairing order parameter may have the same sign.

Figure 3

(Color online) (a) The zero energy contour of ${ϵ}_{xz}\left(\tilde{\mathit{k}}\right)$ (red) and ${ϵ}_{yz}\left(\tilde{\mathit{k}}\right)$ (dashed blue). The $\pm$ are signs of ${ϵ}_{xz}\left(\tilde{\mathit{k}}\right)$ and ${ϵ}_{yz}\left(\tilde{\mathit{k}}\right)$ in the region. The $\tilde{\Gamma }$ point has $\tilde{\mathit{k}}=0$. (b) The hybridization of the $d_{xz}$ and $d_{yz}$ bands. The curves are the zero energy contours of the hybridized bands. (c) The zero energy contour of ${ϵ}_{xy}\left(\tilde{\mathit{k}}\right)$. (d) The solid curves are the Fermi surfaces of the three-band tight-binding model as a result of the hybridization of (b) and (c).

Figure 4

(Color online) (a) The energy bands near $\tilde{Y}$ and $\tilde{\Gamma }$. The bands near $\tilde{Y}$ come from the $d_{xz}$ and $d_{xy}$ orbitals. The thickness of the curve indicates the weight in the $d_{xz}$ orbital. The bands near $\tilde{\Gamma }$ came from the $d_{xz}$ and $d_{yz}$ orbitals. (b) The contour plot of $\text{i}{u}_{\mathit{k}}{v}_{\mathit{k}}$ near $\tilde{Y}$. The dashed loop is the Fermi surface.