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A recent theory of the disorder-dependent slope of the upper critical field,$H_{c2}$, at the superconducting transition temperature, $T_{c}$, is extendedto multiband superconductors aiming at iron-based superconductors, consideringtwo constant gaps of different magnitude and, potentially, different signs. Theresult shows that there is only a narrow domain inside the $s_{\pm}$ pairingstate 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 experimentshows 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. Thiswork reopens a decade-long discussion of the nature of the superconductingorder parameter in iron pnictides.

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