Modelling the Effects of Surface Roughness on Superconductors

It is well known that within the London model, the magnetic field near the surface of a superconductor in the Meissner state decays exponentially as a function of depth. However, direct measurements of the magnetic field profile using low energy μSR find that the decayis non-exponential on a length scale much smaller than λ. It has been suggested this is due to surface roughness. In this paper we examine the effect of surface roughness theoretically. Through asymptotic and numerical analysis, we model the effects of surface roughness on the magnetic field profile for a superconductor with a two-dimensional sinusoidal variation in the surface boundary. The calculated field profiles are indeed non-exponential and with some unexpected behaviour. The model results show consistency with experimental results, indicating that surface roughness could explain the experimental anomalies.