ABSTRACT
The pinning force per unit volume, FP, is connected to the measurable critical current by the following equation: FP = JCB. However, this equation does not give information on the pinning mechanisms or on the way to increase the critical current value. It also does not join JC to the pinning force, fP, of an individual vortex. Let us consider as an example a homogeneous defects distribution in a superconducting material. These defects, which constitute real traps for the vortices, can be described in terms of potentials of interaction with the flux lines. They can attract or repulse the vortices, in other words, they can favor or oppose the electrons condensation in the Cooper pairs. The problem which arises is to know how these interactions between the vortices and the defects contribute to the determination of the pinning force density FP. Right from the beginning, one is tempted to write:
FP = N fP (6.1)
where N is the number of these interactions. This is generally false because a rigid vortex lattice and a random distribution of defects lead in fact to no pinning phenomenon. Indeed, the sum of the individual pinning forces, of random orientations, is statistically zero. In other words, the interaction energy of an infinite surrounding is independent of the relative position of the rigid vortex lattice and the random defects present in this surrounding. But, the trapping of vortices exists in the superconductors and can be measured by different methods. The solution to this dilemma is that a process of pinning cannot take place except if the vortex lattice distorts itself. In this case, the total energy of the system is reduced by the distortion of the lattice, and the pinning occurs to prevent the growth of
energy that would be provoked by the vortices movement. In the opposite limit or for a liquid vortex lattice, JC is zero because in this case, it is necessary to prevent the movement of each vortex. The description of the rigidity of the vortices lattice is therefore essential to the understanding of the pinning phenomena which are the result of several types of interactions such as the vortex-defect interaction, the vortex-spin interaction and the vortex-vortex interaction. This last interaction can be studied by using the elastic constants of the vortices lattice.
