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We investigate a two-orbital model for iron-based superconductors toelucidate the effect of interplay between electron correlation and Jahn-Tellerelectron-phonon coupling by using the dynamical mean-field theory combined withthe exact diagonalization method. When the intra- and inter-orbital Coulombinteractions, $U$ and $U'$, increase with $U=U'$, both the local spin andorbital susceptibilities, $\chi_{s}$ and $\chi_{o}$, increase with$\chi_{s}=\chi_{o}$ in the absence of the Hund's rule coupling $J$ and theelectron-phonon coupling $g$. In the presence of $J$ and $g$, there aredistinct two regimes: for $J \stackrel{>}{_\sim} 2g^2/\omega_0$ with the phononfrequency $\omega_0$, $\chi_{s}$ is enhanced relative to $\chi_{o}$ and shows adivergence at $J=J_c$ above which the system becomes Mott insulator, while for$J \stackrel{<}{_\sim} 2g^2/\omega_0$, $\chi_{o}$ is enhanced relative to$\chi_{s}$ and shows a divergence at $g=g_c$ above which the system becomesbipolaronic insulator. In the former regime, the superconductivity is mediatedby antiferromagnetic fluctuations enhanced due to Fermi-surface nesting and isfound to be largely dependent on carrier doping. On the other hand, in thelatter regime, the superconductivity is mediated by ferro-orbital fluctuationsand is observed for wide doping region including heavily doped case without theFermi-surface nesting.

Metal-insulator transition and superconductivity in the two-orbital Hubbard-Holstein model for iron-based superconductors