Interorbital Pairing and its Physical Consequences in Iron Pnictide Superconductors

We study interorbital pairings of iron pnictide superconductors within a minimal two-orbital tight-binding model. We find that in real space, a set of self-consistently determined pairing order parameters forms two sublattices with a relative phase of $\pi$ and the pairing symmetry is $d_{x^{2}-y^{2}}\sim \cos k_{x}-\cos k_ {y}$. In momentum space, it corresponds to the $\eta$ pairing proposed by C. N. Yang [Phys. Rev. Lett. \textbf{63}, 2144 (1989)], with nonzero momenta of Cooper pairs. One physical consequence of this type of pairing is the existence of a significant amount of zero energy (gapless) states around the Fermi surface even in the absence of disorder, which contradicts current experiments thus excluding such a pairing in iron pnictide superconductors.