The existing mean-field-like calculations of the different direct and indirect order parameter fluctuation (OPF) contributions to the in-plane paraconductivity Δ${\mathrm{\sigma }}_{\mathit{ab}}$ and fluctuation-induced magnetoconductivity Δσ̃${\mathrm{̃}\mathrm{̃}}_{\mathit{ab}}$ are extended here to layered superconductors with two different interlayer distances and different strengths of the tunneling couplings between adjacent layers (the so-called bilayered, or biperiodic layered, superconductors). The calculations are performed for magnetic fields H in the weak limit, applied perpendicular to the superconducting layers, and at temperatures near but above the H=0 mean-field transition temperature, ${\mathit{T}}_{\mathit{c}0}$. We obtain final explicit expressions and find that the effects of the layer biperiodicity may be summarized through an effective number ${\mathit{N}}_{\mathit{e}}$ of independent fluctuating superconducting layers per unit cell length, already encountered also in our recent calculations of the fluctuation-induced diamagnetism Δ${\mathrm{\chi }}_{\mathit{ab}}$ in biperiodic layered superconductors. Our study includes some limiting cases of the indirect contributions associated with the density of states (DOS) fluctuations, which have been recently proposed for Δ${\mathrm{\sigma }}_{\mathit{ab}}$ and Δσ̃${\mathrm{̃}\mathrm{̃}}_{\mathit{ab}}$ for single periodic layered superconductors. As an application, we use then our theoretical results to analyze the paraconductivity and the fluctuation-induced magnetoconductivity recently measured in the a direction (nonaffected by the presence of CuO chains) of untwinned ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ crystals. This analysis shows that the approaches based on the conventional Lawrence-Doniach (i.e., single layered) model cannot explain simultaneously and quantitatively the intrinsic Δ${\mathrm{\sigma }}_{\mathit{a}}$, Δσ̃${\mathrm{̃}\mathrm{̃}}_{\mathit{a}}$, and Δ${\mathrm{\chi }}_{\mathit{ab}}$ in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ crystals, even when the DOS contributions are considered. In contrast, when the double periodicity of this layered superconductor is taken into account, it is possible to explain consistently and at a quantitative level all such experimental data in the reduced temperature region above ${\mathit{T}}_{\mathit{c}0}$ bounded by, approximately, 2×${10}^{\mathrm{-}2}$ and ${10}^{\mathrm{-}1}$, which is expected to correspond to the mean-field region without high temperature and nonlocal effects. In the resulting biperiodic scenario, the indirect (i.e., Maki-Thompson and DOS) contributions to the in-plane Δ${\mathrm{\sigma }}_{\mathit{a}}$ and Δσ̃${\mathrm{̃}\mathrm{̃}}_{\mathit{a}}$ are negligible, confirming our earlier findings which suggested unconventional, pair-breaking, wave pairing. Moreover, the direct OPF effects have a dimensionality (two-dimensional–three-dimensional) crossover in the mean-field region. Our results strongly suggest also that to understand at a quantitative level the OPF effects on any in-plane or bulk physical observable in layered superconductors with various superconducting layers per unit cell length, it is crucial to take into account the influence of such a multiperiodicity. © 1996 The American Physical Society.

• Received 25 September 1995

DOI:https://doi.org/10.1103/PhysRevB.54.4341