Constraints imposed by symmetry on pairing operators for the iron pnictides

Considering model Hamiltonians that respect the symmetry properties of the pnictides, it is argued that pairing interactions that couple electrons in different orbitals with an orbital-dependent pairing strength inevitably lead to interband pairing matrix elements, at least in some regions of the Brillouin zone. Such interband pairing has not been considered of relevance in multiorbital systems in previous investigations. It is also observed that if, instead, a purely intraband pairing interaction is postulated, this requires that the pairing operator has the form Delta dagger(k) = f(k)Sigma(alpha)d(k,alpha dagger)(dagger)d(-k,alpha,down arrow)(dagger). where alpha labels the orbitals considered in the model and f(k) arises from the spatial location of the coupled electrons or holes. This means that the gaps at two different Fermi surfaces involving momenta k(F) and k'(F) can only differ by the ratio f(k(F))/f(k'(F)) and that electrons in different orbitals must be subject to the same pairing attraction, thus, requiring fine tuning. These results suggest that previously neglected interband pairing tendencies could actually be of relevance in a microscopic description of the pairing mechanism in the pnictides.