Anomalous isotope effects of fulleride superconductors

TL;DR

This paper demonstrates through numerical calculations that anharmonic lattice vibrations can cause anomalously high isotope effects in fulleride superconductors, explaining the variability in isotope coefficients observed experimentally.

Contribution

It introduces a formula for isotope effect that accounts for anharmonic vibrations, providing a theoretical explanation for anomalous isotope effects in fulleride superconductors.

Findings

Anharmonic vibrations enhance isotope effect coefficient $eta>1/2$.

Intra-molecule radial modes significantly influence superconductivity.

Calculated isotope effects match experimental variations in $^{12}$C/$^{13}$C substitutions.

Abstract

The numerical calculations of the standard Eliashberg-Nambu strong coupling theory and a formula of isotope effect derived in this paper provide direct evidences that an-harmonic vibrations of lattice enhance isotope effect with anomalous coefficient $\alpha>1/2$. The results in this paper explain very well the wide distributed $\alpha$ values for the samples with different ratios of substitutions of $^{12}$C by $^{13}$C of fulleride superconductor Rb$_{3}$C$_{60}$. The calculations of isotope effects indicate that the intra-molecule radial modes have more important contributions to superconductivity than the intra-molecule tangential modes with higher phonon frequencies