Irreversible effects and pinning

2014 In this paper we review the theoretical problems due to the pinning of vortices. We emphasize the difficulty of making a link between the elementary pinning force between an isolated vortex and a pinning center with the measured pinning force. We show how to define experimentally the pinning force which permit a theoretical study and we calculate it. Far from Hc2, we get Webb’s results. Finally, we briefly review calculations of the elementary pinning force. LE JOURNAL DE PHYSIQUE TOME 33, AOUT-SEPTEMBRE 1972, Classification Physics abstructs : 17.24 if a is the radius of the wire. For type II superconductors, if H is lower than H,,, the situation is stable. When H is higher than H,,, vortex lines begin to appear : they are bent in circles following the lines of force. Once created at the surface with radius a, they tend to shrink to decrease their line energy and finally annihilate near the axis of the specimen. This process dissipates energy. Thus, we have zero resistance only if Unhappily this corresponds to a low density of current. If we want to carry a higher density, we have to prevent vortex motion and achieve a non equilibrium situation. In this article, we first discuss the concept of vortex motion and the dissipation which results from this motion. Then we introduce the concept of pinning. We distinguish between the measured pinning force density P and the individual pinning force fp which prevents one vortex from moving. We first describe situations where these two quantities are simply related by P = nf,, where n is the number of vortices per unit volume. Then we show why the two quantities are not simply related in the general case and how to calculate one knowing the other. Finally we discuss various means to pin vortices and make very elementary calculations of the individual pinning force. II. Vortex motion and dissipation. If the concept of vortices is now well established both from a theoretical and experimental point of view, the motion of vortex lines and the dissipation which results, is not so firmly understood. This point stems from the fact that the concept of individuel vortex line is clearer when the distance between them is large i. e. at low temperature and low field. Unhappily, the theory is much easier near H,2 when the vortices are very close together and the concept of vortices looses its importance. This is the reason why we will review the thêory of vortex motion in these two limits and will try to explain the physical origin of dissipation. A) MOTION OF AN INDIVIDUAL VORTEX LINE H k Hcl. The concept of a vortex was introduced by Abrikosov [1]. Figure 1 represents a vortex line. In the core the order parameter drops to zero. The caracteristic length for the core is the coherence length. Outside the core is an electromagnetic region which spread over a distance of the penetration depth. As vortices are always within a distance Â, the concept Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01972003308-9080300