Flux Pinning and Flux-Lattice Melting in Anisotropic High-T c Superconductors
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FLUX PINNING AND FLUX-LATTICE MELTING IN ANISOTROPIC HIGH-T, SUPERCONDUCTORS R.S. MARKIEWICZ Physics Department and Barnett Institute, Northeastern University, Boston, Mass. 02115 PINNING CENTER DENSITY AND THE NATURE OF COLLECTIVE PINNING The flux lattice in the new high-T, copper oxide superconductors, particularly in the layered compounds based on Bi and TI, displays behavior which is distinctly different from that observed in previous superconductors. In particular, the flux pinning weakens to the point of vanishing in a magnetic field significantly below H, 2 [1-31. This behavior has been interpreted both in terms of flux lattice melting[1,38] and in terms of conventional, thermally-activated flux creep[9,10]. Disentangling these two processes will require a close examination of certain underlying, but usually unstated assumptions. This paper will discuss some of these fundamental issues. One essential question has to do with the density of pinning centers. The conventional theory of collective flux pinning[Il] assumes that the pinning density is so large that most pinning centers are not occupied by vortices, because of the high energy cost in locally distorting the lattice. While this assumption may hold for conventional superconductors, it seems to be at odds with a number of experimental observations in the new materials. In particular, it is found that pinning may be so weak in some single crystals of Bi 2 Sr 2 CaCu 2 0 (Bi-2212) that the resistivity is better described as flux flow (i.e., negligible pinning) than flux creep. Furthermore, pinning can be enhanced up to one hundred-fold by introduction of radiation damage[12J. Hence, the opposite assumption of an intrinsically low pinning density may be more appropriate for these new materials. Indeed, it is only in this limit that a melting transition can be unambiguously defined: in the strong pinning limit, the concept of long range order becomes moot. The assumption of a low pinning density is intrinsic to, e.g., Tinkham's model of flux creep[10]. In the low pinning limit, only a small fraction of the vortices are directly pinned. The others are held in place by the rigidity of the flux lattice, so that the effective pinning force is actually the energy required to shear one group of vortices past another. Hence, the pinning force is directly proportional to the flux lattice shear modulus, Ce66. In contrast, in the conventional collective pinning theory, lattice rigidity limits the ability of vortices to distort and overlap pinning centers. The bulk pinning force (which defines the critical current) is not simply proportional to the elementary pinning force, but must be found by an appropriate statistical summation. Since any lattice softening will lead to an increase in this average pinning, the bulk pinning force is inversely proportional to the elastic moduli. In these circumstances, there may actually be an enhancement of the bulk pinning force ('peak effe..ct') near a melting transition, where the elastic moduli soften. The absence of this effect i
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