Isotope effect and the role of phonons in the iron-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 ($\ifmmode\pm\else\textpm\fi{}s$-wave) state. Within this mean-field model, we showed that the large isotope effect is not inconsistent with the $\ifmmode\pm\else\textpm\fi{}s$-wave pairing state and its high transition temperature. In principle, a large phonon isotope coefficient $\ensuremath{\alpha}$ implies a large phonon coupling constant. However, the asymmetric density of states between two bands substantially enhances the value of $\ensuremath{\alpha}$, so that a moderate value of the phonon coupling constant $({\ensuremath{\lambda}}_{\text{ph}}\ensuremath{\approx}0.4)$ can produce a very large value of $\ensuremath{\alpha}(\ensuremath{\approx}0.4)$ as well as a high transition temperature together with an antiferromagnet-induced interaction.