Anomalous isotope effect in BCS superconductors with two boson modes

TL;DR

This paper demonstrates that in BCS superconductors with both phonon and non-phonon modes, the isotope effect can be anomalous, with the isotope coefficient exceeding 1/2 or becoming negative, depending on the modes involved.

Contribution

It introduces a theoretical framework showing how coexistence of phonon and non-phonon modes can produce anomalous isotope effects in superconductors.

Findings

The isotope coefficient can take arbitrary values with phonon and non-phonon modes.

A pair-breaking phonon can cause a large isotope coefficient > 1/2.

Implications discussed for various superconductor families.

Abstract

The isotope effect in the superconducting transition temperature is anomalous if the isotope coefficient $\alpha<0$ or $\alpha>1/2$. In this work, we show that such anomalous behaviors can naturally arise within the Bardeen-Cooper-Schrieffer framework if both phonon and non-phonon modes coexist. Different from the case of the standard Eliashberg theory (with only phonon) in which $\alpha\le1/2$, the isotope coefficient can now take arbitrary values in the simultaneous presence of phonon and the other non-phonon mode. In particular, most strikingly, a pair-breaking phonon can give rise to large isotope coefficient $\alpha>1/2$ if the unconventional superconductivity is mediated by the lower frequency non-phonon boson mode. Based on our studies, implications on several families of superconductors are discussed.