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 ${\mathit{I}}_{\mathit{c}}$, in soft type-II samples of standard bulk homogeneity, should be governed essentially by surface defects. ${\mathit{I}}_{\mathit{c}}$ 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-${\mathit{I}}_{\mathit{c}}$ being uniformly distributed over the cross section. Coherently, an analysis of the dissipation in such samples predicts that the part ${\mathit{VI}}_{\mathit{c}}$ of the total Joule effect VI must arise as surface heat sources, while the Joule effect V(I-${\mathit{I}}_{\mathit{c}}$), 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.