Effect of electron-phonon interactions on orbital fluctuations in iron-based superconductors

To investigate the possibility whether electron-phonon coupling can enhance orbital fluctuations in iron-based superconductors, we develop an ab initio method to construct the effective low-energy models including the phonon-related terms. With the derived effective electron-phonon interactions and phonon frequencies, we estimate the static part (\omega=0) of the phonon-mediated effective on-site intra- or inter-orbital electron-electron attractions as ~ -0.4 eV and exchange or pair-hopping terms as ~ -0.02 eV. We analyze the model with the derived interactions together with the electronic repulsions within the random phase approximation. We find that the enhancement of the orbital fluctuations due to the electron-phonon interactions is small, making the spin fluctuations dominant. As a result, the superconducting state with the sign reversal in gap functions ($s_\pm$-wave) is realized.