Slope of the upper critical field at T_c in two-band superconductors with non-magnetic disorder: s_++ superconductivity in Ba_1-xK_xFe_2As_2

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_± 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_± state and increase in the s_++ pairing state. The experiment shows that in an archetypal iron-based superconductor, Ba_1-xK_xFe_2As_2 (BaK122), non-magnetic disorder induced by electron irradiation increases the slope S across the superconducting “dome,” at different x. This implies that Ba_1-xK_xFe_2As_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.