# The Coulomb problem in iron based superconductors

## TL;DR

This paper investigates how iron-based superconductors maintain high transition temperatures despite strong Coulomb repulsion, proposing a flexible pairing mechanism that adapts to Coulomb constraints through orbital and momentum space adjustments.

## Contribution

It introduces the orbital and k-space flexibility (OKF) mechanism as a way for FeSCs to circumvent Coulomb repulsion, supported by Landau theory and microscopic calculations.

## Key findings

- OKF requires large condensate degeneracy
- On-site Coulomb repulsion enforces certain condensate components to vanish
- Reconsideration of triplet pairing as a potential solution

## Abstract

We discuss the role of strong Coulomb interactions in iron-based superconductors (FeSCs). The presumed $s^{\pm}$ character of these superconductors means that the condensate is not symmetry protected against Coulomb repulsion. Remarkably, the transition temperatures and the excitation gap are quite robust across the large family of iron based superconductors, despite drastic changes in Fermi surface geometry. The Coulomb problem is to understand how these superconductors avoid the strong onsite Coulomb interaction at the iron atoms, while maintaining a robust transition temperature. Within the dominant space of $t_{2g}$ orbitals, on-site repulsion in the FeSCs enforces two linearly independent components of the condensate to vanish. This raises the possibility that iron-based superconductors might adapt their condensate to the Coulomb constraints by rotating the pairing state within the large manifold of entangled, extended s-wave gap functions with different orbital and momentum space structure. We examine this "orbital and k-space flexibility" (OKF) mechanism using both Landau theory and microscopic calculations within a multi-orbital t-J model. Based on our results, we conclude that OKF necessitates a large condensate degeneracy. One interesting possibility raised by our results, is that a resolution to the Coulomb problem in FeSC might require a reconsideration of triplet pairing.