Slope of the upper critical field at $T_{c}$ in two-band superconductors with non-magnetic disorder: $s_{++}$ superconductivity in $\textrm{Ba}_{1-x}\textrm{K}_{x}\textrm{Fe}_{2}\textrm{As}_{2}$

TL;DR

This paper extends a theory of how non-magnetic disorder affects the slope of the upper critical field at $T_c$ in multiband superconductors, providing evidence that $ extrm{Ba}_{1-x} extrm{K}_{x} extrm{Fe}_{2} extrm{As}_{2}$ is likely an $s_{++}$ superconductor.

Contribution

The work applies an extended disorder-dependent slope theory to iron-based superconductors, suggesting an $s_{++}$ pairing state based on experimental irradiation data.

Findings

Non-magnetic disorder increases the $H_{c2}$ slope in BaK122.

Most of the phase space favors an $s_{++}$ pairing state.

The results support the $s_{++}$ pairing symmetry in iron pnictides.

Abstract

A recent theory of the disorder-dependent slope of the upper critical field, $H_{c2}$, at the superconducting transition temperature, $T_{c}$, is extended to multiband superconductors aiming at iron-based superconductors, considering two constant gaps of different magnitude and, potentially, different signs. The result shows that there is only a narrow domain inside the $s_{\pm}$ pairing state where the slope increases with the increase of transport (non-magnetic) scattering rate, $P$. In most phase space, the slope should decrease in an $s_{\pm}$ state and increase in the $s_{++}$ pairing state. The experiment shows that in an archetypal iron-based superconductor, $\textrm{Ba}_{1-x}\textrm{K}_{x}\textrm{Fe}_{2}\textrm{As}_{2}$ (BaK122), non-magnetic disorder induced by electron irradiation increases the slope $S$ across the superconducting ``dome,'' at different $x$. This implies that $\textrm{Ba}_{1-x}\textrm{K}_{x}\textrm{Fe}_{2}\textrm{As}_{2}$ is likely an $s_{++}$ superconductor with two (or more) gaps of different magnitudes. This work reopens a decade-long discussion of the nature of the superconducting order parameter in iron pnictides.