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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 $U&#39;$, increase with $U=U&#39;$, both the local spin and orbital susceptibilities, $χ_{s}$ and $χ_{o}$, increase with $χ_{s}=χ_{o}$ because of the spin-orbital symmetry. Due to the Hund&#39;s rule coupling $J$, $χ_{s}$ is enhanced and dominates over $χ_{o}$ resulting in the repulsive local pairing interaction $V_{\rm loc}>0$, while due to the electron-phonon coupling $g$, $χ_{o}$ is enhanced and dominates over $χ_{s}$ 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.