On the dilemma between percolation processes and fluctuating pairs as the origin of the enhanced conductivity above the superconducting transition in cuprates

Abstract

The confrontation between percolation processes and superconducting fluctuations to account for the observed enhanced in-plane electrical conductivity above but near $T_c$ in cuprates is revisited. The cuprates studied here, La$_{1.85}$Sr$_{0.15}$CuO$_4$, Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$, and Tl$_2$Ba$_2$Ca$_2$Cu$_3$O$_{10}$, have a different number of superconducting CuO$_2$ layers per unit-cell length and different Josephson coupling between them, and are optimally-doped to minimize $T_c$-inhomogeneities. The excellent chemical and structural quality of these samples also contribute to minimize the effect of extrinsic $T_c$-inhomogeneities, a crucial aspect when analyzing the possible presence of intrinsic percolative processes. Our analyses also cover the so-called high reduced-temperature region, up to the resistivity rounding onset $\varepsilon_{onset}$. By using the simplest form of the effective-medium theory, we show that possible emergent percolation processes alone cannot account for the measured enhanced conductivity. In contrast, these measurements can be quantitatively explained using the Gaussian-Ginzburg-Landau (GGL) approach for the effect of superconducting fluctuations in layered superconductors, extended to $\varepsilon_{onset}$ by including a total energy cutoff, which takes into account the limits imposed by the Heisenberg uncertainty principle to the shrinkage of the superconducting wavefunction. Our analysis confirms the adequacy of this cutoff, and that the effective periodicity length is controlled by the relative Josephson coupling between superconducting layers. These conclusions are reinforced by analyzing one of the recent works that allegedly discards the superconducting fluctuations scenario while supporting a percolative scenario for the enhanced conductivity above $T_c$ in cuprates.