Dynamical Mean-Field Study of Local Pairing Interaction Mediated by Spin and Orbital Fluctuations in Iron Pnictide Superconductors

We investigate the two-orbital Hubbard model, which reproduces the electron and hole Fermi surfaces in the iron pnictide superconductors, in the presence of the Jahn-Teller electron-phonon coupling by using the dynamical mean-field theory. When the intra- and inter-orbital Coulomb interactions, $U$ and $U'$, increase with $U=U'$, both the local spin and orbital susceptibilities, $\chi_{s}$ and $\chi_{o}$, increase with $\chi_{s}=\chi_{o}$ because of the spin-orbital symmetry. Due to the Hund's rule coupling $J$, $\chi_{s}$ is enhanced and dominates over $\chi_{o}$ resulting in the repulsive local pairing interaction $V_{\rm loc}>0$, while due to the electron-phonon coupling $g$, $\chi_{o}$ is enhanced and dominates over $\chi_{s}$ resulting in the attractive one $V_{\rm loc}<0$ which induces the intra-orbital s-wave pairing. Remarkably, $V_{\rm loc}$ is weakly dependent on doping and can be attractive for heavily electron-doped regime where the superconductivity is observed without Fermi surface nesting.