Superfluid density in the $s_{\pm}$-wave state of clean iron-based superconductors

Based on a phenomenological model and the Kubo formula, we investigate the superfluid density $ρ_s(T)$ and then the penetration depth $λ(T)$ of the iron-based superconductors in the coexistence region of the spin-density-wave(SDW) and superconductivity, and also in the over-doped region. Our calculations show a dramatic increase of $λ(0)$ with the decrease of the doping concentration $x$ below $x=0.1$. This result is consistent with the experimental observations. At low temperatures, $ρ(T)$ shows an exponential-law behavior, while at higher temperatures, the linear-in-$T$ behavior is dominant before it trends to vanish. The evolution of $Δλ(T)$ can be roughly fitted by a exponential function at overdoped levels while in other doping range it is a power-law function with the exponent depending on the doping concentration. We show that the Uemura relation holds for the iron-based superconductors only at very low doping levels.

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