Superfluid density of the $\pm$s-wave state for the iron-based superconductors

TL;DR

This paper investigates how impurity scattering affects the superfluid density and penetration depth in the s-wave state of iron-based superconductors, revealing a continuous evolution consistent with experimental observations.

Contribution

It provides a detailed theoretical analysis of impurity effects on superfluid density and penetration depth in s-wave superconductors, explaining experimental trends across different doping levels.

Findings

Impurity scattering induces a self-energy with a specific form beyond a critical impurity concentration.

Superfluid density's temperature dependence evolves from exponential to T^3 to T^2 with increasing impurities.

The evolution of s-wave behavior aligns with measurements in various Fe pnictide superconductors.

Abstract

We study the superfluid density of the $\pm$s-wave state of the minimal two band model for the Fe-based superconductors and its evolution with impurity concentration. We show that the impurity scattering of the strong coupling limit induces the selfenergy of a generic form $Im \Sigma_{imp} (\omega) \approx i \gamma + i \beta \omega$ beyond a critical impurity concentration $\Gamma_{imp} > \Gamma_{crit}$. This form of $Im \Sigma_{imp} (\omega)$ causes the temperature dependence of the superfluid density $[\rho_{s}(T) - \rho_{s}(0)] \approx - \gamma T^2 -\beta T^3$. Combining with the full gap behavior of $\rho_{s}(T)$ for lower impurity concentration $\Gamma_{imp} < \Gamma_{crit}$, the $\pm$s-wave state produces a continuous evolution of $\Delta \lambda(T)$: exponentially flat $\to T^3 \to T^2$ with increasing impurity concentration that is consistent with the measurements of the Fe pnictide superconductors such as $M$-1111 ($M$=La,Nd,Sm,Pr) and Ba-122 with various dopings, except LaFePO which shows $\Delta \lambda(T) \propto T^{1.2}$ at low temperatures by recent experiment. Our results also demonstrate that the density of states (DOS) measured by thermodynamic properties and the DOS measured by transport properties can in general be different.