Abstract

To answer the question of the main title, which concerns central aspects of the vortex behavior in multi-layered high- temperature copper-oxide superconductors (HTSC), in this paper we review some of our recent measurements of the thermal fluctuation effects on the magnetization around the superconducting transition of high-quality single-crystals of different HTSC families, with a different number, N, of superconducting CuO<SUB>2</SUB> layers per layering periodicity length, s. These results suggest that in highly-anisotropic multilayered HTSC the N successive pancakes in the closest N layers in s are strongly magnetically coupled but they are uncorrelated at longer distances. Therefore, they may be seen as an unique 'magnetic mille-feuilles' of N pancakes, with an effective thickness of the order of (N-1)-times the interlayer distance between the closest CuO<SUB>2</SUB> layers in s. In contrast, in these highly-anisotropic HTSC the Josephson coupling between the CuO<SUB>2</SUB> superconducting layers is very weak and the fluctuations of the Cooper pairs above T<SUB>c</SUB> are strongly located in each CuO<SUB>2</SUB> superconducting layer.

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