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

Abstract

We investigate the isotope effect on the London penetration depth of a superconductor which measures nS/m* [n subscript s / m superscript asterisk], the ratio of superfluid density to effective mass. We use a simplified model of electrons weakly coupled to a single phonon frequency ωE [omega subscript E], but assume that the energy gap Δ [delta] does not have any isotope effect. Nevertheless, we find an isotope effect for nS/m* [n subscript s / m superscript asterisk] which is significant if Δ [delta] is sufficiently large that it becomes comparable to ωE [omega subscript E], a regime of interest to high-Tc [high-T subscript c] cuprate superconductors and possibly other families of unconventional superconductors with relatively high Tc [T subscript 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 nS/m* [n subscript s / m superscript asterisk] in materials where the pairing gap and Tc [T subscript c] are not of phonon origin and have no isotope effect.