Superfluid density and penetration depth in the iron pnictides

We consider the superfluid density ${\rho }_s\left(T\right)$ in a two-band superconductor with sign-changing extended $s$-wave symmetry $\left(s^{+}\right)$ in the presence of nonmagnetic impurities and apply the results to Fe-pnictides. We show that the behavior of the superfluid density is essentially the same as in an ordinary $s$-wave superconductor with magnetic impurities. We show that, for moderate to strong interband impurity scattering, ${\rho }_s\left(T\right)$ behaves as a power law $T^n$ with $n\approx 1.6÷2$ over a wide range of $T$. We argue that the power-law behavior is consistent with recent experiments on the penetration depth $\lambda \left(T\right)$ in doped ${\text{BaFe}}_2{\text{As}}_2$ but disagrees quantitatively with the data on LaFePO.

Figure 1

(Color online) (a) Suppression of $T_c$ by interband scattering in a two-band $\left(\Delta ,-\Delta \right)$ model; (b) superfluid stiffness ${\rho }_s\left(T\right)$ in a dirty $s^{+}$ superconductor for fixed intraband impurity scattering ${\Gamma }_0/2\pi T_{c0}=3$ and various interband scatterings $\zeta ={\Gamma }_{\pi }/2\pi T_{c0}$; and (c) low-$T$ plot of ${\rho }_s$ vs $T^2$ showing near $n=2$ power law around onset of gapless regime.

Figure 2

(Color online) The fits to experimental data for ${\text{BaFe}}_2{\text{As}}_2$ (Ref. 15). We use only low-$T$ data as at higher $T$ the experimental $\lambda \left(T\right)$ may be influenced by sample geometry and fluctuations. (a) The data for electron-doped ${\text{BaFe}}_2{\text{As}}_2$ for optimally doped $\left(x=7.4\%\right)$ and overdoped $\left(x=10\%\right)$ samples can be fitted reasonably well using $\left(\Delta ,-\Delta \right)$-model; (b) the fit of data for two Co-doped $\left(x=7.3\%,10\%\right)$ and one K-doped samples with a phenomenological extension of the presented two-band model to the case of four gaps. We set gaps to be $\left(\Delta ,-\Delta ;\Delta ,-{\Delta }_h\right)$ with ${\Delta }_h=\Delta /3$, $\Delta /2$. In this case the pairbreaking parameter does not need to be large. The fitting values of $T=0$ penetration length are large, but for $x=7.4\%$ sample we show a fit with inclusion of Fermi-liquid effects that reduces this parameter to ${\lambda }_{\text{FL}}\left(0\right)\equiv {\lambda }_0\sim 190\text{nm}$ in agreement with experimental values.