Andreev spectroscopy of iron-based superconductors: temperature dependence of the order parameters and scaling of the $\Delta_{L,S}$ with $T_C$

We studied iron-based superconductors of various families with critical temperatures covering almost all range $T_C = 9 - 53$ K. In natural arrays of contacts formed in these materials we observed intrinsic multiple Andreev reflections effect (IMARE). By using IMARE spectroscopy, we detected the two-gap superconductivity, determined the value of the large and the small superconducting gaps, and the corresponding BCS-ratios. The temperature dependencies of the large and the small gaps $\Delta_{L,S}(T)$ are similar for various families of the Fe-based superconductors and could be well-fitted in the framework of the two-band model by Moskalenko and Suhl. We concluded on the extended s-wave symmetry of the $\Delta_L$ order parameter (20-30 % anisotropy in k-space) and on the absence of nodes for $\Delta_S$. The BCS-ratio $2\Delta_L/k_BT_C \approx 5.2$ is nearly constant within the whole range of $T_C$ (this means that coupling rate is unchanged), reflecting the 20 % reduction of the $T_C^{local}$ in relation to the eigen $T_C^L$, and the large gap roughly corresponds to the energy of magnetic resonance $2\Delta_L \approx E_{res}$. This result requires a special theoretical consideration. Our estimation of the relative coupling constants and eigen parameters of each condensate (in a hypothetical case of a zero interband interaction) $2\Delta_L/k_BT_C^L = 4.2 - 4.8$ and $2\Delta_S/k_BT_C^S = 3.5 - 4.5$ leads to indirect conclusion that namely a strong electron-phonon interaction in each condensate described in the framework of the Eliashberg theory plays the key role in the superconductivity of iron-based oxypnictides. With it, the two condensates interact weakly with each other. The observed scaling of $\Delta_{L,S}$ with $T_C$, as was discussed above, is caused mainly by changing of the density of states $N_{L,S}$ in the bands, whereas Ln-O spacers act as charge reservoirs.