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

TL;DR

This paper demonstrates clear experimental signatures in the temperature dependence of magnetic penetration depth that indicate a transition from the $s_ ext{±}$ to $s_{++}$ pairing state in iron-based superconductors due to nonmagnetic disorder.

Contribution

The study provides the first detailed theoretical analysis of the $s_ ext{±} o s_{++}$ transition signatures in penetration depth, incorporating Eliashberg equations with impurity effects.

Findings

Sharp change in penetration depth behavior at transition

Decrease in slope of $ riangle \lambda_L(T)$ after transition

Jump in inverse square of penetration depth at transition

Abstract

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 $\lambda_{L}$ 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 $\rho_{s}(T)$.