Momentum dependence and nodes of the superconducting gap in the iron pnictides

Using general symmetry arguments and model calculations we analyze the superconducting gap in materials with multiple Fermi-surface pockets, with applications to iron pnictides. We show that the gap in the pnictides has an extended $s$-wave symmetry but is either nodeless or has nodes, depending on the interplay between intraband and interband interactions. We argue that the nodes in the gap emerge without a phase transition as the tendency toward a spin-density-wave order gets weaker. These findings provide a way to reconcile seemingly conflicting results of numerical and experimental studies of the pnictides.

Figure 1

(Color online) (a) Hole (center) and electron (edges) FSs in the unfolded BZ and interactions $u_4$ (intraband repulsion), $u_3$ (pair hopping between hole and electron bands) and $v_e$ (pair hopping between electron bands). The $s^{\pm }$ SC gap may have nodes along the dashed lines near the electron FS. (b) The folded BZ. Each corner now hosts two electron FSs with gaps ${\Delta }_{e1,2}\left(\tilde{\varphi }\right)$. (c) Schematic RG flow for $u_4$ and the momentum-independent part of $u_3\left(\mathit{q}-{\mathit{q}}^{\prime }\right)$ up to energies $\sim E_F$ (for $v_e=0$). If renormalized $u_3>u_4$ (line B), the pairing occurs even if $u_3\left(\mathit{q}-{\mathit{q}}^{\prime }\right)=\text{const}$, while for $u_3<u_4$ (line A) the pairing is induced by the momentum-dependent part of $u_3\left(\mathit{q}-{\mathit{q}}^{\prime }\right)$, and ${\Delta }_e\left(\phi \right)$ has nodes.

Figure 2

(Color online). The phase diagram in dimensionless variables $\gamma =u_4/u_3$ and $\delta ={\tilde{u}}_3/u_3$ (we set $v_e=0$). The nodeless $s^{\pm }$ state exists in the lower left corner below the line ${\delta }_{cr}\left(\gamma \right)$, when intraband repulsion $u_4$ and momentum-dependent interband hopping ${\tilde{u}}_3$ are small. Dashed lines show the contours of fixed ratio ${\tilde{\Delta }}_e/{\Delta }_e=\sqrt{2},2,3,4,5$. The narrow solid line shows the position of a minimum of ${\tilde{\Delta }}_e/{\Delta }_e$ in the region where the gap has nodes. Below this line, the gap develops nodes primarily to reduce the effect of intrapocket repulsion.