Quantitative Predictions of Dead Layers Induced by Surface Roughness in Isotropic Type II Superconductors

In type II superconductors where the coherence length ξ is small compared to the London penetration depth λ, the London equation is valid and it predicts that magnetic fields decay exponentially in magnitude with the depth into the superconductor with a length scale λ, provided the interface is flat. Various direct measurements of λ using low energy μSR on superconductors such as Yttrium-Barium-Copper-Oxide measure field profiles that differ from the anticipated exponential decay. There seems to be a dead layer, a distance δ over which the magnetic field magnitude does not decay, and some speculation has been made that this dead layer may be due to a suppression of the order parameter that causes the decay of a magnetic field, or surface roughness. 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 dead layer 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 Yttrium-Barium-Copper-Oxide crystals, we predict the field profiles the crystals could produce 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 λ and δ. Our work suggests that roughness within an isotropic model cannot produce the dead layers found in experiments on YBCO and that perhaps roughness must be combined with an anisotropy to yield the experimental dead layers; that the measurement of λ may be influenced by the presence of roughness; and that the local field orientation does change slightly with respect to the direction of the applied field.