Isotope effect on the superfluid density in conventional and high-temperature superconductors

TL;DR

This paper explores how isotope substitution affects the superfluid density in superconductors, showing a significant effect when the energy gap is comparable to phonon energy, especially relevant for high-temperature superconductors.

Contribution

It demonstrates, through a simplified model, that isotope effects can influence superfluid density even in non-phonon-mediated superconductors, highlighting a fundamental aspect of superconductivity.

Findings

Isotope effect on superfluid density is significant when the gap is comparable to phonon energy.

The model predicts the isotope effect can have different signs than observed in experiments.

The approach provides a proof of principle for isotope effects beyond phonon-mediated pairing.

Abstract

We investigate the isotope effect on the London penetration depth of a superconductor which measures $n_S/m^*$, the ratio of superfluid density to effective mass. We use a simplified model of electrons weakly coupled to a single phonon frequency $\omega_E$, but assume that the energy gap $\Delta$ does not have any isotope effect. Nevertheless we find an isotope effect for $n_S/m^*$ which is significant if $\Delta$ is sufficiently large that it becomes comparable to $\omega_E$, a regime of interest to high $T_c$ cuprate superconductors and possibly other families of unconventional superconductors with relatively high $T_c$. Our model is too simple to describe the cuprates and it gives the wrong sign of the isotope effect when compared with experiment, but it is a proof of principle that the isotope effect exists for $n_S/m^*$ in materials where the pairing gap and $T_c$ is not of phonon origin and has no isotope effect.