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Orbital Fluctuation Theory in Iron Pnictides: Effects of As-Fe-As Bond Angle, Isotope Substitution, and $Z^2$-Orbital Pocket on the Superconductivity

We study the pairing mechanism in iron pnictide superconductors based on the five-orbital Hubbard-Holstein model. Due to Fe-ion oscillations, the s-wave superconducting (SC) state without sign reversal (s_{++}-wave state) is induced by orbital fluctuations by using realistic model parameters. The virtue of the present theory is that the famous empirical relation between Tc and the As-Fe-As bond angle is automatically explained, since the electron-phonon (e-ph) coupling that creates the orbital fluctuations is the strongest when the As$_4$-tetrahedron is regular. The negative iron isotope effect is also reproduced. In addition, the magnitude of the SC gap on hole-pockets is predicted to be rather insensitive to the corresponding d-orbital (xz/yz- or z^2-orbital), which is consistent with the recent bulk-sensitive angle-resolved photoemission spectroscopy (ARPES) measurement for (Ba,K)Fe$_2$As$_2$ and BaFe$_2$(As,P)$_2$. These obtained results indicate that the orbital-fluctuation-mediated s_{++}-wave state is a plausible candidate for iron pnictides.