Robust $s_{\pm}$-wave superconductivity against multi-impurity in iron-based superconductors

Effects of disorder on electron-doped iron pnictides are investigated systematically based on self-consistent Bogoliubov-de Gennes equations. Multiply impurities with same scattering potential (SP) are randomly distributed in a square lattice. Probability distribution functions of normalized order parameters for different impurity concentrations $\delta_{imp}$, different electron doping concentrations $\delta$ are investigated for given SPs. Samples are found to be very robust against weak SP, in which order parameters do not have qualitative change even at very large $\delta_{imp}$. While strong SP is able to easily break down the order parameters. For moderate SP, variations of order parameters on and around impurities strongly depend on $\delta$, however the distribution functions of normalized order parameters have similar behavior as $\delta_{imp}$ increases. Compared with superconducting (SC) order, the magnetic order is more sensitive to multi-impurity effect. The spatial spin density wave pattern has already been destroyed before the system loses its superconductivity. Dependence of SC order on temperature is similar to that of impurity-free case, with the critical temperature being remarkably suppressed for high $\delta_{imp}$.