We report detailed experimental results on the fluctuation-induced in-plane conductivity Δ${\mathrm{\sigma }}_{\mathit{ab}}$, magnetoconductivity Δσ${\mathrm{̃}}_{\mathit{ab}}$, and diamagnetism Δ${\mathrm{\chi }}_{\mathit{ab}}$, of high-quality ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_8$ crystals. The data were obtained with magnetic fields H applied perpendicularly to the superconducting (${\mathrm{CuO}}_2$) planes and up to ${\mathrm{\mu }}_0$H=5 T, which not too close to the transition [for reduced temperatures ɛ≡(T-${\mathit{T}}_{\mathit{C}0}$)/${\mathit{T}}_{\mathit{C}0}$≳${10}^{\mathrm{-}2}$] may be considered in the weak magnetic field limit. In the mean field region (MFR) above the transition, these data are analyzed in terms of thermal fluctuations of the superconducting order parameter amplitude (OPF), on the grounds of the existing theoretical approaches for layered superconductors that take into account the presence of two superconducting layers in the layer periodicity length, s, which for these compounds is equal to one-half the crystallographic unit-cell length in the c direction. These results show that, due to its strong ɛ dependence, Δσ${\mathrm{̃}}_{\mathit{ab}}$ is dramatically affected by the presence of small ${\mathit{T}}_{\mathit{C}}$ inhomogeneities, associated with small oxygen content inhomogeneities uniformly distributed in the crystals. These inhomogeneity effects are taken into account, consistently with our Δ${\mathrm{\sigma }}_{\mathit{ab}}$ and Δ${\mathrm{\chi }}_{\mathit{ab}}$ results, by using an effective medium approach proposed by Maza and Vidal. In this way, the amplitude and the ɛ behavior of the three observables studied here are explained in terms of the direct OPF effects, at a quantitative level, confirming then the absence of appreciable indirect contributions [as, for instance, the Maki-Thompson and the density-of-states (DOS) terms]. These last results may suggest unconventional (non ${}_{}{}^1{}_{}{}^{}$${\mathit{s}}_0$), pair breaking, wave pairing in these compounds, as first proposed from OPF analyses by Veira and Vidal. The resulting values of the in-plane and out-of-plane coherence length amplitudes are, respectively, ${\xi }_{\mathit{ab}}$(0)=(0.9±0.1) nm and ${\xi }_{\mathit{c}}$(0)≲0.05 nm. These coherence length amplitudes are consistent with the values that we have obtained before for other Bi-based crystals by analyzing the effects of the vortex position fluctuations on the magnetization below the transition. These results also confirm at a quantitative level that in Bi-2212 compounds the effective number of fluctuating ${\mathrm{CuO}}_2$ planes per periodicity length above the superconducting transition is ${\mathit{N}}_{\mathit{e}}$≊2 and that the OPF’s are essentially two dimensional over the entire MFR. © 1996 The American Physical Society.

• Received 26 March 1996

DOI:https://doi.org/10.1103/PhysRevB.54.7470