Anomalous isotope effect in BCS superconductors with two boson modes

Abstract

The isotope effect in the superconducting transition temperature is anomalous if the isotope coefficient $\hat{I}\pm <0$ or $\hat{I}\pm >1/2$. 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 $\hat{I}\pm \le 1/2$, 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 $\hat{I}\pm >1/2$ 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.

9 pages, 4 figures