Doping evolution of the gap structure and spin-fluctuation pairing in $Ba(Fe_{1-x}Co_{x})_{2}As_{2}$ superconductors

Doping dependence of the superconducting state structure and spin-fluctuation pairing mechanism in the $Ba(Fe_{1-x}Co_{x})_{2}As_{2}$ family is studied. BCS-like analysis of experimental data shows that in the overdoped regime, away from the AFM transition, the spin-fluctuation interaction between the electron and hole gaps is weak, and $Ba(Fe_{1-x}Co_{x})_{2}As_{2}$ is characterized by three essentially different gaps. In the three-gap state an anisotropic (nodeless) electron gap $\Delta_e (x, \phi)$ has an intermediate value between the dominant inner $\Delta_{2h}(x)$ and outer $\Delta_{1h}(x)$ hole gaps. Close to the AFM transition the electron gap $\Delta_e (x, \phi)$ increases sharply and becomes closer in magnitude to the dominant inner hole gap $\Delta_{2h}(x)$. The same two-gap state with close electron and inner hole gaps $\Delta_{2h}(x) \approx \Delta_e (x, \phi)$ is also preserved in the phase of coexisting antiferromagnetism and superconductivity. The doping dependence of the electron gap $\Delta_e (x, \phi)$ is associated with the strong doping dependence of the spin-fluctuation interaction in the AFM transition region. In contrast to the electron gap $\Delta_e (x, \phi)$, the doping dependence of the hole gaps $\Delta_{1,2h}(x)$ and the critical temperature $T_{c}(x)$, both before and after the AFM transition, are associated with a change of the density of states $\gamma_{nh}(x)$ and the intraband electron-phonon interaction in the hole bands. The non-phonon spin-fluctuation interaction in the hole bands in the entire Co concentration range is small compared with the intraband electron-phonon interaction and is not dominant in the $Ba(Fe_{1-x}Co_{x})_{2}As_{2}$ family.