Model for the inverse isotope effect of FeAs-based superconductors in the $\pi$-phase-shifted pairing state

TL;DR

This paper models the inverse isotope effect in FeAs-based superconductors using two-band Eliashberg theory, showing that magnetic fluctuations and phonon interactions can explain observed isotope effects.

Contribution

It introduces a theoretical framework combining phonon and magnetic fluctuations to explain inverse and positive isotope effects in Fe-based superconductors.

Findings

Inverse isotope effect explained by interband phonon interactions.

Positive isotope effect attributed to intraband phonon interactions.

The model aligns with experimental isotope effect measurements.

Abstract

The isotope effects for Fe based superconductors are considered by including the phonon and magnetic fluctuations within the two band Eliashberg theory. We show that the recently observed inverse isotope effects of Fe, $\alpha_{Fe} \approx -0.18 \pm 0.03 $,\cite{Shirage0903.3515} as well as the large positive isotope exponent ($\alpha\approx 0.35$) can naturally arise for the magnetically induced sign revered s-wave pairing state within reasonable parameter range. Either experimental report can not be discarded from the present analysis based on the parameter values they require. The inverse and positive isotope effects mean, respectively, the interband and intraband dominant eletron-phonon interaction. We first make our points based on the analytic result from the square well potential model and present explicit numerical calculations of the two band Eliashberg theory.