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

Abstract

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 $α$ implies a large phonon coupling constant. However, the asymmetric density of states (DOS) between two bands substantially enhances the value of $α$, so that a moderate value of the phonon coupling constant ($λ_{\rm ph} \approx 0.4$) can produce a very large value of $α$ ($\approx 0.4$) as well as a high transition temperature together with an antiferromagnet (AFM)-induced interaction.