Fractal vortices in disordered superconductors

Fluctuation conductivity and microscopic granularity in Bi-based high-temperature superconductors

“…The analysis of the Gaussian regimes indicates that T c (r) fluctuates in scales of approximately 10 to 25 nm, which are one order of magnitude larger than the intrinsic coherence length, but are much smaller than the size of crystallites. This situation meets the most important requirement to characterize a microscopically granular state, 3 where critical behavior is equivalent to that of classical granular systems.…”

“…For granular superconductors, it has been demonstrated that Х 4 3 . 3,5 For dϭ3 and assuming that Х0, the value cr Х3.0 would correspond to an anomalous relaxation with exponent zХ3.2. This value is intermediate between the homogeneous mean field zϭ2 and the value expected for a spin glass or a dirty ferromagnet system, where zХ4.…”

“…Recently, Rosenblatt et al 3,4 have introduced the concept of microscopic intragrain granularity to explain the scalinglike behavior of the field of first flux penetration into polycrystalline samples of fluorine-doped YBa 2 Cu 3 O 7Ϫ␦ . These authors argue that in the superconducting cuprates, due to the smallness of the coherence length, an unavoidable coupling is produced between microscopic defects ͑e.g., deviations of the stoichiometry͒ and spatial fluctuations of the critical temperature, T c (r).…”

“…5 In most of the measurements, the effects of microscopic granularity could be clearly separated from those resulting from ''classical'' mesoscopic granularity. 3 , and CaCO 3 . The preparation of these compounds proceeds in three stages.…”

“…According to the model in Ref. 3, there are two related conditions for a supercurrent to freely circulate between positions r and rЈ of a microscopically disordered superconductor: ͑i͒ r and rЈ must belong to the same single connected region, or cluster, defined by T c (r)ϾT, where T is the temperature, and ͑ii͒ the order-parameter correlation function ͗ (r) (rЈ)͘ should be nonzero within the cluster, that is ͉rϪrЈ͉р (T). Condition ͑i͒ defines a temperature-dependent percolation parameter such that for p(T c )ϭp c an infinite cluster spans the sample and infinite conductivity should be obtained.…”