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

To investigate the possibility of 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 (ω=0) of the phonon-mediated effective on site intra- or interorbital 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 Coulomb repulsions within the random phase approximation. We find that the enhancement of the orbital fluctuations due to the electron-phonon interactions is small, and that the spin fluctuations enhanced by the Coulomb repulsions dominate. It leads to the superconducting state with the sign reversal in the gap functions (s± wave).