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

Based on the analogy of the Bekarevich-Khalatnikov theory of He 11, a continuum description of vortex motion in the mixed state is presented. The possibility of critical surface currents and associated surface Joule effects is inferred, in agreement with experiment.

The surface impedance Z(f ) of conventional isotropic materials has been carefully measured for frequencies f ranging from 1 kHz to 3 MHz, allowing a detailed investigation of the depinning transition. Our results exhibit the irrelevance of classical ideas on the dynamics of vortex pinning. We propose a new picture, where the linear ac response is entirely governed by disordered boundary conditions of a rough surface, whereas in the bulk vortices respond freely. The universal law for Z(f ) thus predicted is in remarkable agreement with experiment, and tentatively applies to microwave data in YBaCuO films.PACS numbers: 74.60. Ge, 74.25.Nf. A perfect sample of a type-II superconductor in the vortex (or mixed) state would be transparent to an electromagnetic wave at very low frequencies. But defects are always present and strongly alter the quasistatic and low-frequency response; low frequencies here means Ω = 2πf ≪ Ω d , a so-called "depinning frequency" [1] depending on the material and vortex density. It is important for applications to know what kind of defects can pin vortices, how they hinder small vortex oscillations and thereby restrain the penetration of an ac ripple. In this respect, a study at low levels of excitation of both the resistive and inductive part of the surface impedance Z(Ω) = R − iX as a function of the frequency provides much information about the dynamics of pinning. It is generally accepted that bulk pinning centers limit the quasistatic skin effect to a pinning (or Campbell's) length λ C ∼ 1 − 100 µm, while dissipation is vanishingly small, as observed [1,2]. No model however has been able to account for variations of Z at higher frequencies. In particular, as the first increasing of R(f ) is stronger than expected, the understanding of dissipation remains a puzzling problem, including in high T c materials [3].Experiments are performed on a series of slabs of coldrolled polycrystalline PbIn and pure single-crystralline Nb. The slabs (xy) are immersed in a normal magnetic field B; unless specified their thickness 2d is much larger than the flux-flow penetration depth δ f (see below). At equilibrium, up to the upper critical field B c2 , a regular lattice of vortex lines parallel to z is formed, with the density n = B/ϕ 0 , where ϕ 0 is the flux quantum. Both faces of the slab, z = ±d, are then subjected to an ac magnetic field b 0 e −iΩt parallel to the length (xdirection) of the sample. Under such conditions, induced currents and electric fields, J(z) and e(z)e −iΩt , are along the y-direction, while vortices oscillate in the xz-planes. For low exciting fields (b 0 ∼ 1 µT), vortex displacements u(z) ∼ 1Å are very small compared with the vortex spacing a ≃ n − 1 2 (∼ 1000Å, for B ∼ 0.1 T) (Fig. 1a). The electric field e 0 at the surface z = d, e 0 = e(d) = −e(−d), is measured by means of a pick-up wound coil. The main experimental difficulty in such measurements is to ensure a precise calibration of the phase ϕ of e 0 (within better than 0.5 • at 100 kHz). Thus we get the surface impe...

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