Comment to the paper : Collapse of the vortex-lattice inductance and shear modulus at the melting transition in untwinned YBa2_2Cu3_3O7_7, by Matl \QTR{em}{et al.}

In a recent paper, Matl et al present a high-frequency study of the complex resistivity of a pinned vortex lattice in YBaCuO . They focus on the inductive-to-resistive transition which is investigated as a function of temperature at a constant field $B_0=2$ T, so that the transition is associated with the vanishing of vortex pinning strength. To our view, their conclusions rely on a rather brittle experimental body and the collapse of C66 results from an involved analysis of the finite frequency corrections to $\rho (\omega)$. These corrections are not necessary since the complex frequency spectrum has been previously interpreted by the two modes model, first proposed for low Tc materials. We think that it is more adequate to interpret the present data and should be at least considered.Comment: 4pages tex. submitted to PR

rf-studies of vortex dynamics in isotropic type-II superconductors

We have measured the surface impedance of thick superconductors in the mixed state over a broad 2 kHz - 20 MHz frequency range. The depinning cross-over is observed; but it is much broader than expected from classical theories of pinning. A striking result is the existence of size effects which invalidate the common interpretation of the low-frequency surface inductance in terms of a single penetration depth. Instead, a two-mode description of vortex dynamics, assuming free vortex flow in the bulk and surface pinning, accounts quantitatively for the spectrum of the complex apparent penetration depth.Comment: 20 pages, 6 figures, 28 reference

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.Comment: 4 pages, 4 figures, 14 reference

Phase-Sensitive Impurity Effects in Vortex Core of Moderately Clean Chiral Superconductors

We study impurity effects in vortex core of two-dimensional moderately clean su perconductors within the quasiclassical theory. The impurity scattering rate \G amma(E) of the Andreev bound states in vortex core with +1 vorticity of p-wav e superconductors with {\mib d}=\hat{\mib z}(p_x+\iu p_y) is suppre ssed, compared to the normal state scattering rate $\Gamma_{\rm n}$ in the energ y region \Gamma_{\rm n}^3/E_\delta^2\ll E\ll E_\delta\equiv |\delta_0|\Delta_\i nfty with scattering phase shift $\delta_0$ $(|\delta_0|\ll 1)$ and the pair-po tential in bulk $\Delta_\infty$. Further we find that $\Gamma(E)/\Gamma_{\rm n}$ for p-wave superconductors with {\mib d}=\hat{\mib z}(p_x-\iu p_y) is at most {\cal O}(E/\Delta_\i nfty). These results are in marked contrast to the even-parity case (s,d-wave), where $\Gamma(E)/\Gamma_{\rm n}$ is known to be proportional to \ln(\Delta_\i nfty/E) . Parity- and chirality-dependences of impurity effects are attributed to the Andr eev reflections involved in the impurity-induced scattering between bound states . Implications for the flux flow conductivity is also discussed. Novel enhanceme nt of flux flow conductivity is expected to occur at $T\ll E_\delta$ for {\mib d}=\hat{\mib z}(p_x+\iu p_y) and at $T\ll \Delta_\infty$ for {\mib d}=\hat{\mib z}(p_x-\iu p_y).Comment: 9 pages, No figures, To appear in JPSJ Vol. 69, No. 10 (2000

Ancrage des vortex dans les supraconducteurs.

Ce travail porte sur l'étude de l'ancrage des vortex par la réponse linéaire haute fréquence. Nous présentons une série de mesures de la profondeur de pénétration complexe dans l'état mixte sur une variété d'échantillons qui va des supraconducteurs classiques (Nb, V, PbIn), aux composés de fermions lourds non-conventionnels (UPt3), en passant par les cuprates à haute température critique (YBaCuO). La large gamme des fréquences explorées (1 kHz–10 MHz) permet de couvrir le changement de régime entre la réponse quasistatique dominée par l'interaction élastique des vortex avec les défauts, et la réponse haute fréquence amortie par la friction visqueuse du réseau de vortex au cristal ionique.
Pour décrire quantitativement le spectre de fréquence, nous nous appuyons sur une théorie phénoménologique qui fait une distinction explicite et rigoureuse entre lignes de vortex, décrites par un champ omega, et lignes de champ magnétique B. On prédit ainsi l'existence d'un second mode électrodynamique, évanescent et de courte portée, lié à la tension de ligne des vortex. On montre que la réponse aux petits mouvements, amplitude et phase, est réglée par une condition limite supplémentaire sur le réseau de vortex à la surface ; elle prend la forme d'une condition de glissement avec une longueur phénoménologique contrôlée par la rugosité de l'échantillon. Le spectre de fréquence associé à ce mécanisme se distingue nettement du spectre de Campbell, générique des modèles d'ancrage en volume.
Nos mesures sur des échantillons PbIn, Nb, V et YBaCuO confirment entièrement notre modèle, y compris des effets de taille peu intuitifs qui se produisent à basse fréquence quand l'échantillon devient transparent au mode flux flow. En revanche, l'étude des vortex dans les phases B et C d'UPt3 montre une contribution importante du volume à l'ancrage des vortex

Peak effect and surface crystal-glass transition for surface-pinned vortex array

We present a theoretical and experimental study of the peak effect in the surface pinning of vortices. It is associated with a sharp transition in the vortex slippage length which we relate to a crossover from a weakly disordered crystal to a surface glass state. Experiments are performed on ion-beam–etched \chem{Nb} crystals. The slippage length is deduced from 1\un{kHz}–1\un{MHz} linear AC penetration depth measurements