Cutoff parameter of the field distribution in the mixed state of iron pnictides with $s_{\pm }$ and $s_{++}$ pairing symmetries

The effects of the pairing symmetries ($s_{\pm }$ and $s_{++}$) on the cutoff parameter of field distribution, ${\xi }_h$, in stoichiometric (like LiFeAs) and nonstoichiometric (like doped ${\mathrm{BaFe}}_2{\mathrm{As}}_2$) iron pnictides have been investigated using Eilenberger quasiclassical equations. Magnetic field, temperature, and impurity scattering dependencies of ${\xi }_h$ have been calculated. Two opposite behaviors have been discovered. The ${\xi }_h/{\xi }_{c2}$ ratio is less in $s_{\pm }$ symmetry when the intraband impurity scattering (${\Gamma }_0$) is much larger than 1 and is much larger than the interband impurity scattering (${\Gamma }_{\pi }$), i.e., in nonstoichiometric iron pnictides. In contrast, the value ${\xi }_h/{\xi }_{c2}$ is higher in the $s_{\pm }$ case and the field-dependent curve is shifted upward from the “clean” case (${\Gamma }_0={\Gamma }_{\pi }=0$) for stoichiometric iron pnictides (${\Gamma }_0={\Gamma }_{\pi }\ll 1$). Results can be tested in muon spin rotation measurements.

Figure 1

(a) The magnetic field dependence of ${\xi }_h/{\xi }_{c2}$ for superconductors with impurity scattering. Solid lines represent our solution of Eilenberger equations at $T/T_{c0}=0.5$ for the “clean” case (${\Gamma }_0={\Gamma }_{\pi }=0$) and $s_{\pm }$ model (${\Gamma }_0=0.5$, ${\Gamma }_{\pi }=0.03$ and ${\Gamma }_0=3$, ${\Gamma }_{\pi }=0.02$). Dotted lines show results for the $s_{++}$ model (${\Gamma }^{*}=0.5$ and ${\Gamma }^{*}=3$). The dashed line demonstrates the result of the AGL theory for ${\xi }_v$ from Eq. (8). The inset shows magnetic field dependence of mean square deviation of the $h_{\mathrm{EGL}}$ distribution from the Eilenberger distribution normalized by the variance of the Eilenberger distribution, $\varepsilon$, for $T/T_{c0}=0.5$ at ${\Gamma }_0={\Gamma }_{\pi }=0$ (clean); ${\Gamma }_0=3$, ${\Gamma }_{\pi }=0.02$ and ${\Gamma }_0=0.5$, ${\Gamma }_{\pi }=0.03$. (b) The interband scattering ${\Gamma }_{\pi }$ dependence of ${\xi }_h/{\xi }_{c2}$ at different temperatures $T/T_{c0}$ (intraband scattering ${\Gamma }_0=0.5$ and $B=5$) for the $s_{\pm }$ pairing.

Figure 2

The magnetic field dependence of cutoff parameter ${\xi }_h/{\xi }_{c2}$ with different temperatures ($T/T_{c0}=0.2,0.3,0.4,0.5$) for $s_{\pm }$ pairing with ${\Gamma }_0=3$, ${\Gamma }_{\pi }=0.04$. The inset shows the magnetic field dependence of ${\xi }_h/{\xi }_{c2}$ for the $s_{\pm }$ model (${\Gamma }_0=3$, ${\Gamma }_{\pi }=0.04$, solid line) and the $s_{++}$ model (${\Gamma }^{*}=3$, dotted line) at $T/T_{c0}=0.5$.

Figure 3

The magnetic field dependence of the cutoff parameter at $T/T_{c0}=0.5$ with the same values of intraband ${\Gamma }_0$ and interband ${\Gamma }_{\pi }$ scattering $\Gamma$ ($\Gamma =0$ for the clean case and $\Gamma =0.01,0.035$ for the $s_{\pm }$ pairing). The dotted line shows result for the $s_{++}$ model (${\Gamma }^{*}=0.25$).