Y. Simon

Phenomenological Theory of Vortex Motion in Type-II Superconductors

Based on the analogy of the Bekarevich-Khalatnikov theory of He II, 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.

Quantitative analysis of the critical current due to vortex pinning by surface corrugation

The transport critical current of a Niobium (Nb) thick film has been measured for a large range of magnetic field. Its value and variation are quantitatively described in the framework of the pinning of vortices due to boundary conditions at the rough surface, with a contact angle well explained by the spectral analysis of the surface roughness. Increasing the surface roughness using a Focused Ion Beam results also in an increase of the superficial critical current.

The ε-algorithm allows to detect Dirac delta functions

The e-algorithm is well known as a numerical tool for accelerating the convergence of sequences. It is shown empirically that this property holds for convergent series in the general sense of distributions. This means that, at singular points, the e-algorithm also accelerates the divergence, and clearly reveals the presence of delta functions as well as other singularities such as 1/x, step functions .... As an example, the solution of an integral equation in a problem of electrostatics, developed as a series of Legendre polynomials, has been analyzed by the e-algorithm.

DEPINNING TRANSITION IN TYPE-II SUPERCONDUCTORS

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 to 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.

Small angle neutron scattering and vortex lattice dynamical phase diagram

We report a detailed neutron diffraction study of both pinned and moving magnetic Flux Line Lattice (FLL) in NbTa and PbIn samples. In NbTa, the FLL presents a hexagonal lattice even in the absence of current, meanwhile PbIn presents a strongly dislocated phase. In PbIn, dislocations are eliminated by the application of transport current in agreement with theoretical predictions. On the other hand, the absence of curvature of the flux lines for subcritical currents confirm the presence of surface pinning of the FLL.

Evidence for vortex pinning by surface irregularities in untwinned YBaCuO crystals

Abstract A direct method of induction in a small pick up coil shows that in untwinned YBaCuO crystals, the subcritical current flows close to the surfaces of the sample. By studying the frequency dependence of the ac penetration depth, we have also shown that the two-modes through Mathieu–Simon (MS) model of pinning by surface irregularities is able to account for the observed spectrum. The Campbell model of weak bulk pinning can be completely ruled out. Above the first order transition line, the critical current is zero and the ac response is that of an ohmic system. This can be interpreted by the curvature of the vortices close to the surface. This shows the irrelevance of weak bulk pinning models for clean untwinned YBaCuO crystals that were often proposed as model systems for this case.

La réponse à un échelon de champ d'un supraconducteur de type II: un moyen simple de tester l'ancrage des vortex en volume The magnetic-field step response of a type II superconductor as a simple test of the vortex bulk pinning

A slab in parallel field is submitted to a step-like magnetic-field excitation, of amplitude 1--10 G, in the same direction as the applied field. The slab has been rolled or spark cut, without special care, from a conventional superconductor ingot (lead-indium alloy), and its critical currents have standard values. The transitory electric field, induced on a face of the slab, has been measured. Thus, we obtain information about the magnetic flux penetrating and vortices entering the sample through this face. The only observed deviation from the ideal response is that magnetic-field diffusion being limited by surface screening, associated with a superficial critical-current density. Otherwise, the vortex array inside the slab responds exactly as if bulk pinning were ineffective.

Observation of the ideal low-frequency response of the mixed state and the diamagnetism of a type II superconductor

Abstract When driven by an overcritical DC current, a slab is submitted to a small AC ripple in the frequency range 1–100 kHz. The frequency and angular dependencies of its surface impedance accurately exhibit all features of the ideal linear AC response, such as calculated in the complete absence of pinning. The expected effects of the effective permeability μ at low fields, i.e. surface screening by diamagnetic currents and the μ-dependence of the flux-flow penetration depth δ f , are clearly observed. Thus we obtain a reliable method for investigating the ideal reversible magnetization curve. Furthermore, we give a consistent interpretation of the diamagnetism and a proper definition of μ relying on the Mathieu-Simon phenonenological theory published previously. As discussed in the conclusion, the conceptual difference between our approach and the classical view of local diamagnetism may be decisive in improving our understanding of pinning.

Critical currents in soft type II superconductors

Abstract A continuum description of the mixed state suggests that the critical state of soft superconductors is completely determined by the surface roughness. The disorder associated with surface irregularities gives rise to many non-dissipative states, including subcritical transport currents. The field and temperature dependence of critical currents is related to that of a local thermodynamic parameter, denoted as e, which in turn is simply related to the ideal magnetization curve. This interpretation of critical currents and pinning is strongly supported by currently available experimental data.

Vortex pinning in untwinned YBCO

Three different AC and DC experiments have been performed in untwinned YBCO to clarify the mechanism of vortex pinning. Pinning by surface irregularities is the only mechanism consistent with all experiments. This questions usual interpretation in terms of bulk collective pinning theories. In particular, the irreversibility line appears as the dissapearance of superficial critical current.