Unexpected impact of magnetic disorder on multiband superconductivity

We analyze how the magnetic disorder affects the properties of the two-band $s_{\pm }$ and $s_{++}$ models, which are the subject of discussions regarding iron-based superconductors and other multiband systems like ${\mathrm{MgB}}_2$. We show that there are several cases when the transition temperature $T_c$ is not fully suppressed by magnetic impurities in contrast to the Abrikosov-Gor'kov theory, but a saturation of $T_c$ takes place in the regime of strong disorder. These cases are: (1) the purely interband impurity scattering and (2) the unitary scattering limit. We show that in the former case the $s_{\pm }$ gap is preserved, while the $s_{++}$ state transforms into the $s_{\pm }$ state with increasing magnetic disorder. For case (2), the gap structure remains intact.

Figure 1

$T_c$ dependence on the scattering rate ${\Gamma }_a$ (a),(b) and frequency dependence of gaps $\mathrm{Re}{\Delta }_{\alpha }\left(\omega \right)$ (c),(d) for various values of ${\Gamma }_a$ for the $s_{\pm }$ (a),(c) and the $s_{++}$ (b),(d) superconductors. $N_b/N_a=2$ and coupling constants are $({\lambda }_{aa},{\lambda }_{ab},{\lambda }_{ba},{\lambda }_{bb})=(3,-0.2,-0.1,0.5)$ so that $\langle \lambda \rangle <0$ for the $s_{\pm }$ state and $(3,0.2,0.1,0.5)$ for the $s_{++}$ state.

Figure 2

Matsubara gap ${\Delta }_{\alpha n=1}$ dependence on the scattering rate ${\Gamma }_a$ for the $s_{\pm }$ (a),(b) and the $s_{++}$ (c),(d) superconductors with only interband scattering, $\mathcal{I}=0$ (a),(c), and with $\mathcal{I}=\mathcal{J}/2$ (b),(d). Parameters are the same as in Fig. 1.

Figure 3

Density of states $N$ as a function of frequency $\omega$ and interband magnetic impurities scattering rate ${\Gamma }_a$ (a) and inverse squared penetration depth $1/{\lambda }_L^2$ vs. ${\Gamma }_a$ and $T$ (b) for the $s_{\pm }$ superconductor with $\mathcal{I}=\mathcal{J}/2$, $\sigma =0.5$, and parameters as in Fig. 1.

Figure 4

Density of states $N$ as a function of frequency $\omega$ and ${\Gamma }_a$ (a) and inverse squared penetration depth $1/{\lambda }_L^2$ vs ${\Gamma }_a$ and $T$ (b) for the $s_{++}$ superconductor with $\mathcal{I}=\mathcal{J}/2$, $\sigma =0.5$, and parameters as in Fig. 1. Note the $s_{++}$ to $s_{\pm }$ transition at ${\Gamma }_a\sim 100{\mathrm{cm}}^{-1}$ and the gapless region right after that.