Continuum theory of the mixed-state and surface Joule effects in type-II superconductors

Abstract

A phenomenological theory of vortex motion, where the mixed state is regarded as a continuum, has been proposed by two of the authors in a short previous letter. Its outlines are recalled in this paper with further comments and arguments; in particular the basic equations and their implications are discussed at some length. This theory leads to a model of pinning, from which we argue that critical currents Ic, in soft type-II samples of standard bulk homogeneity, should be governed essentially by surface defects. Ic is interpreted as a physically well-defined part of the total transport current I, which is flowing over a small depth close to the surface. Thus, on the scale of an ordinary sample, this part of the transport current is superficial, the remaining part I-Ic being uniformly distributed over the cross section. Coherently, an analysis of the dissipation in such samples predicts that the part VIc of the total Joule effect VI must arise as surface heat sources, while the Joule effect V(I-Ic), usually associated with the steady viscous flow of vortices, is uniformly distributed in the bulk. As a proof, we present a method, using second-sound acoustics, to detect and separate surface and volume heat sources. Experimental results give clear evidence of a surface Joule effect, and support the validity of our model of surface pinning in soft materials.

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