Isotope effect and the role of phonon in the Fe-based superconductors

We studied the isotope effect of phonon in the Fe-based superconductors using a phenomenological two band model for the sign-changing s-wave ($\pm$s-wave) state. Within this mean-field model, we showed that the large isotope effect is not inconsistent with the $\pm$s-wave pairing state and its high transition temperature. In principle, a large phonon isotope coefficient $\alpha$ implies a large phonon coupling constant. However, the asymmetric density of states (DOS) between two bands substantially enhances the value of $\alpha$, so that a moderate value of the phonon coupling constant (${\lambda }_{\mathrm{p}\mathrm{h}}\approx 0.4$) can produce a very large value of $\alpha$ ($\approx 0.4$) as well as a high transition temperature together with an antiferromagnet (AFM)-induced interaction.