Decisive proofs of the s(+/-) -> s(++) transition in the temperature dependence of the magnetic penetration depth

Shestakov, V. A.; Korshunov, M. M.; Togushova, Yu N.; Dolgov, O., V Superconductor Science & Technology.

One of the features of the unconventional $s_\pm$ state in iron-based superconductors is possibility to transform to the s++ state with the increase of the nonmagnetic disorder. Detection of such a transition would prove the existence of the $s_\pm$ state. Here we study the temperature dependence of the London magnetic penetration depth within the two-band model for the $s_\pm$ and s++ superconductors. By solving Eliashberg equations accounting for the spin-fluctuation mediated pairing and nonmagnetic impurities in the T-matrix approximation, we have derived a set of specific signatures of the $s_\pm \to s_{++}$ transition: (1) sharp change in the behavior of the penetration depth λL as a function of the impurity scattering rate at low temperatures; (2) before the transition, the slope of $\Delta \lambda_{L}(T) = \lambda_{L}(T)-\lambda_{L}(0)$ increases as a function of temperature, and after the transition this value decreases; (3) the sharp jump in the inverse square of the penetration depth as a function of the impurity scattering rate, $\lambda_{L}^{-2}(\Gamma_a)$, at the transition; (4) change from the single-gap behavior in the vicinity of the transition to the two-gap behavior upon increase of the impurity scattering rate in the superfluid density ρs(T).