Slope of the upper critical field at $T_c$ in two-band superconductors with non-magnetic disorder: $s_{++}$ superconductivity in ${\text{Ba}}_{1-x}{\text{K}}_x{\text{Fe}}_2{\text{As}}_2$

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, ${\text{Ba}}_{1-x}{\text{K}}_x{\text{Fe}}_2{\text{As}}_2$ (BaK122), non-magnetic disorder induced by electron irradiation increases the slope $S$ across the superconducting ``dome,'' at different $x$. This implies that ${\text{Ba}}_{1-x}{\text{K}}_x{\text{Fe}}_2{\text{As}}_2$ 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.

v2 updated with the new data (Fig.10)

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