Isotope Effect for the Penetration Depth in Superconductors

TL;DR

This paper explores how isotope effects influence the penetration depth in superconductors, considering factors like non-adiabaticity, impurities, and proximity effects, with implications for both conventional and high-temperature superconductors.

Contribution

It presents a general equation linking isotope coefficients of $T_c$ and penetration depth, and predicts isotope effects in various superconducting systems.

Findings

Isotope dependence of penetration depth can arise from non-adiabaticity, impurities, and proximity effects.

A general relation between isotope coefficients of $T_c$ and penetration depth is derived.

Predictions are made for isotope effects in both conventional and high-temperature superconductors.

Abstract

We show that various factors can lead to an isotopic dependence of the penetration depth $\delta$. Non-adiabaticity (Jahn-Teller crossing) leads to the isotope effect of the charge carrier concentration $n$ and, consequently, of $\delta$ in doped superconductors such as the cuprates. A general equation relating the isotope coefficients of $T_c$ and of $\delta$ is presented for London superconductors. We further show that the presence of magnetic impurities or a proximity contact also lead to an isotopic dependence of $\delta$; the isotope coefficient turns out to be temperature dependent, $\beta(T)$, in these cases. The existence of the isotope effect for the penetration depth is predicted for conventional as well as for high-temperature superconductors. Various experiments are proposed and/or discussed.