Pairing Symmetry in a Two-Orbital Exchange Coupling Model of Oxypnictides

We study the pairing symmetry of a two-orbital $J_1\mathrm{\text{−}}{J}_2$ model for FeAs layers in oxypnictides. We show that the mixture of an intraorbital unconventional $s_{x^2{y}^2}\sim \cos (k_x)\cos (k_y)$ pairing symmetry, which changes sign between the electron and hole Fermi surfaces, and a very small $d_{x^2-y^2}\sim \cos (k_x)-\cos (k_y)$ component is favored in a large part of the $J_1\mathrm{\text{−}}{J}_2$ phase diagram. A pure $s_{x^2{y}^2}$ pairing state is favored for $J_2>J_1$. The signs of the $d_{x^2-y^2}$ order parameters in the two different orbitals are opposite. While a small $d_{xy}\sim \sin (k_x)\sin (k_y)$ interorbital pairing coexists in the above phases, the intraorbital $d_{xy}$ pairing is not favored even for large $J_2$.

Figure 1

The superconducting phase diagram in the $J_1\mathrm{\text{−}}{J}_2$ plane at 18% electron doping obtained by solving the self-consistent Eqs. (3).

Figure 2

3D plot of the pairing weight $W_3-W_1$ as a function of ($k_x$, $k_y$) (electron doped) by setting ${\Delta }_1={\Delta }_2=1$ in Eq. (9).

Figure 3

(a) The pairing transition temperature as a function of the electron doping concentration at $J_1=0.25$ and $J_2=0.5$. The dotted line indicates the region where the spin-density wave competing phase takes over from the superconducting phase. (b) The intraorbital, $s_{x^2{y}^2}$, $d_{x^2-y^2}$ and the interorbital, $d_{xy}$, pairing order parameter, as a function of $J=J_1=J_2$ when the chemical potential is $\mu =1.8$.