Anomalous isotope effect in BCS superconductors with two boson modes

Gan Sun,Qiang-Hua Wang,Sheng-Qiang Lai,Da Wang,Pan-Xiao Lou

doi:10.1088/1367-2630/abfb8a

Abstract

The isotope effect in the superconducting transition temperature is anomalous if the isotope coefficient α < 0 or α > 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 α ⩽ 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 α > 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.

Highlights

Isotope effect [1, 2] is a cornerstone of the Bardeen-Cooper-Schrieffer (BCS) theory [3] for phonon mediated superconductors
Has been observed in many experiments
Low energy boson modes have been widely observed in many different experiments in cuprates, including mainly two candidates: phonon and magnetic modes. [43, 29, 30] We have listed several candidate boson modes in the appendix

Summary

Introduction

Isotope effect [1, 2] is a cornerstone of the Bardeen-Cooper-Schrieffer (BCS) theory [3] for phonon mediated superconductors. This issue has been explored rather extensively in the literature Among these studies, for cuprates in particular, some material dependent properties such as Van Hove singularity [14, 18], pseudogap [19], anharmonic phonon effect [16, 22], or bipolaron [13, 26, 27] are proposed to be responsible for the anomalous isotope effect. A universal understanding of the anomalous isotope effect is still lacking Motivated by these experimental and theoretical progresses, we ask a somewhat very simple question: what happens in the BCS framework ( with s-wave pairing) including two kinds of single-frequency bosons Ω1,2 with the electron-boson couplings λ1,2?

BCS theory with two boson modes

Summary and discussions