Decisive proofs of the $s_\pm \to s_{++}$ transition in the temperature dependence of the magnetic penetration depth

Abstract

One of the features of the unconventional s ± 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 ± state. Here we study the temperature dependence of the London magnetic penetration depth within the two-band model for the s ± 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 ± → s ++ transition: (1) sharp change in the behavior of the penetration depth λ L as a function of the impurity scattering rate at low temperatures; (2) before the transition, the slope of ∆λ L (T ) = λ L (T ) − λ 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, λ −2 L (Γa), 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 ).