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

We investigate a two-orbital model for iron-based superconductors to elucidate the effect of interplay between electron correlation and Jahn-Teller electron-phonon coupling by using the dynamical mean-field theory combined with the exact diagonalization method. When the intra- and inter-orbital Coulomb interactions, $U$ and $U'$, increase with $U=U'$, both the local spin and orbital susceptibilities, $χ_{s}$ and $χ_{o}$, increase with $χ_{s}=χ_{o}$ in the absence of the Hund's rule coupling $J$ and the electron-phonon coupling $g$. In the presence of $J$ and $g$, there are distinct two regimes: for $J \stackrel{>}{_\sim} 2g^2/ω_0$ with the phonon frequency $ω_0$, $χ_{s}$ is enhanced relative to $χ_{o}$ and shows a divergence at $J=J_c$ above which the system becomes Mott insulator, while for $J \stackrel{<}{_\sim} 2g^2/ω_0$, $χ_{o}$ is enhanced relative to $χ_{s}$ and shows a divergence at $g=g_c$ above which the system becomes bipolaronic insulator. In the former regime, the superconductivity is mediated by antiferromagnetic fluctuations enhanced due to Fermi-surface nesting and is found to be largely dependent on carrier doping. On the other hand, in the latter regime, the superconductivity is mediated by ferro-orbital fluctuations and is observed for wide doping region including heavily doped case without the Fermi-surface nesting.