Slope of the upper critical field at Tc in two-band superconductors with nonmagnetic disorder: s++ superconductivity in Ba1−xKxFe2As2

A recent theory of the disorder-dependent slope of the upper critical field at the superconducting transition temperature T_c, defined as S ≡ |dH_c2/dT|_{T→T_c}, is extended to multiband superconductors aimed at iron-based superconductors, considering two constant gaps of different magnitudes and, potentially, different signs. Here, we show that the slope S decreases with increasing nonmagnetic scattering rate P in the s_± pairing state and increases in the s₊₊ superconductor for a reasonable range of parameters. The experiment shows that in a typical iron-based superconductor, Ba_1–xK_xFe₂As₂ (BaK122), the nonmagnetic disorder induced by electron irradiation leads to an increasing S(P) across the superconducting “dome,” at different x. This implies that Ba_1–xK_xFe₂As₂ is likely an s₊₊ superconductor with two effective gaps of different magnitudes, at least at moderate doping levels, x< 0.6. This work reopens a decade-long discussion about the nature of the superconducting order parameter in iron pnictides.