The Isotope Effect in d-Wave Superconductors

TL;DR

This paper investigates the isotope effect in high-temperature cuprate superconductors, showing that anharmonic lattice modes, rather than harmonic phonons, can explain experimental observations, suggesting a breakdown of conventional theory.

Contribution

It demonstrates that anharmonic lattice tunneling modes, not harmonic phonons, are responsible for the isotope effect, indicating a need to reconsider electron-phonon interactions in cuprates.

Findings

Harmonic phonons cannot explain the isotope effect.

Anharmonic lattice modes can account for the isotope effect.

Potential breakdown of Migdal-Eliashberg theory in cuprates.

Abstract

Based on recently proposed anti-ferromagnetic spin fluctuation exchange models for $d_{x^2-y^2}$-superconductors, we show that coupling to harmonic phonons {\it{cannot}} account for the observed isotope effect in the cuprate high-$T_c$ materials, whereas coupling to strongly anharmonic multiple-well lattice tunneling modes {\it{can}}. Our results thus point towards a strongly enhanced {\it{effective}} electron-phonon coupling and a possible break-down of Migdal-Eliashberg theory in the cuprates.