Effect of Surface Roughness on the Magnetic Field Profile in the Meissner State of a Superconductor

摘要

It is well known that the London model (valid for a hard type II superconductor) predicts an externally applied magnetic field decays exponentially as a function of depth into the superconductor on a length scale lambda. Direct measurements of the field profile using low energy mu SR on high-Tc superconductors, such as YBa2Cu3 O (x) measure deviations from a simple exponential decay. In particular, there is a short length scale delta close to the surface where the magnetic field does not decay. It has been proposed that this is due to surface roughness, which leads to a suppression of the order parameter near the surface. A model of surface roughness has been studied for the case of a sinusoidally modulated surface roughness on an isotropic superconductor showing that in some cases the profiles resulting from surface roughness may be qualitatively similar to the dead layer phenomena in that the field magnitude decay rate may be slowed near the surface relative to a flat interface but that for modest roughness, the quantitative value of the length over which the field decay is slowed is much smaller than the experiments measure. In this paper, we extend this work in two directions: firstly, by using atomic force microscopy data of YBa2Cu3 O (x) crystals, we predict the expected field profiles within the context of the Isotropic London model of superconductivity given their actual surface geometry; and secondly, we consider how surface roughness could affect experimental values for lambda and delta. The main finding is that roughness within an isotropic model does not produce the dead layers found in experiments on YBa2Cu3 O (x) . However, we suggest that roughness in a highly anisotropic superconductor could account for the observed dead layer.