Constraints Imposed by Symmetry on Pairing Operators for the Pnictides

TL;DR

This paper explores how symmetry constraints in pnictides influence pairing operators, revealing that interband pairing is inevitable in multiorbital models and that purely intraband pairing requires fine-tuning, challenging previous assumptions.

Contribution

It demonstrates that symmetry considerations naturally lead to interband pairing in pnictides and clarifies the form and implications of intraband pairing operators in multiorbital systems.

Findings

Interband pairing is unavoidable in symmetry-respecting models.

Purely intraband pairing operators have a specific form with limited gap variation.

Interband pairing tendencies may be more relevant than previously thought.

Abstract

Considering model Hamiltonians that respect the symmetry properties of the pnictides, it is argued that pairing interactions that couple electrons at 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 $\Delta^+(k)=f(k) \sum_{\alpha} d^+_{k,\alpha,\uparrow}d^+_{-k, \alpha,\downarrow}$ 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.