Orbital Fluctuation Mediated Superconductivity in Iron Pnictides: Analysis of Five Orbital Hubbard-Holstein Model

In iron pnictides, we find that the moderate electron-phonon interaction due to the Fe-ion oscillation can induce the critical d-orbital fluctuations, without being prohibited by the Coulomb interaction. These fluctuations give rise to the strong pairing interaction for the s-wave superconducting (SC) state without sign reversal ($s_{++}$-wave state), which is consistent with experimentally observed robustness of superconductivity against impurities. When the magnetic fluctuations due to Coulomb interaction are also strong, the SC state shows a smooth crossover from the s-wave state with sign reversal ($s_{\pm }$-wave state) to the $s_{++}$-wave state as impurity concentration increases.