Observation of non-exponential magnetic penetration profiles in the Meissner state - A manifestation of non-local effects in superconductors

TL;DR

This study used polarized muons to measure magnetic field profiles in superconductors, revealing non-exponential decay due to non-local effects, and providing insights into the superfluid density and coherence length.

Contribution

It provides direct experimental evidence of non-local magnetic penetration profiles in superconductors using muon implantation, and compares results with theoretical models.

Findings

Deviations from exponential B(z) profiles in all samples

Extraction of London penetration depth and coherence length

Temperature dependence of penetration depth follows two-fluid model

Abstract

Implanting fully polarized low energy muons on the nanometer scale beneath the surface of a superconductor in the Meissner state enabled us to probe the evanescent magnetic field profile B(z)(0<z<=200nm measured from the surface). All the investigated samples [Nb: kappa \simeq 0.7(2), Pb: kappa \simeq 0.6(1), Ta: kappa \simeq 0.5(2)] show clear deviations from the simple exponential B(z) expected in the London limit, thus revealing the non-local response of these superconductors. From a quantitative analysis within the Pippard and BCS models the London penetration depth lambda_L is extracted. In the case of Pb also the clean limit coherence length xi0 is obtained. Furthermore we find that the temperature dependence of the magnetic penetration depth follows closely the two-fluid expectation 1/lambda^2 \propto 1-(T/T_c)^4. While B(z) for Nb and Pb are rather well described within the Pippard and BCS models, for Ta this is only true to a lesser degree. We attribute this discrepancy to the fact that the superfluid density is decreased by approaching the surface on a length scale xi0. This effect, which is not taken self-consistently into account in the mentioned models, should be more pronounced in the lowest kappa regime consistently with our findings.