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

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.Comment: 13 pages, 7 figure

Comment on "High Field Studies of Superconducting Fluctuations in High-Tc Cuprates. Evidence for a Small Gap distinct from the Large Pseudogap"

By using high magnetic field data to estimate the background conductivity, Rullier-Albenque and coworkers have recently published [Phys.Rev.B 84, 014522 (2011)] experimental evidence that the in-plane paraconductivity in cuprates is almost independent of doping. In this Comment we also show that, in contrast with their claims, these useful data may be explained at a quantitative level in terms of the Gaussian-Ginzburg-Landau approach for layered superconductors, extended by Carballeira and coworkers to high reduced-temperatures by introducing a total-energy cutoff [Phys.Rev.B 63, 144515 (2001)]. When combined, these two conclusions further suggest that the paraconductivity in cuprates is conventional, i.e., associated with fluctuating superconducting pairs above the mean-field critical temperature.Comment: 9 pages, 1 figur

An efficient MP algorithm for structural shape optimization problems

6th International Conference on Computer Aided Optimun Design of Structures, 2001, Bologna[Abstract] Integral methods -such as the Finite Element Method (FEM) and the Boundary Element Method (BEM)- are frequently used in structural optimization problems to solve systems of partial differential equations. Therefore, one must take into account the large computational requirements of these sophisticated techniques at the time of choosing a suitable Mathematical Programming (MP) algorithm for this kind of problems. Among the currently avaliable MP algorithms, Sequential Linear Programming (SLP) seems to be one of the most adequate to structural optimization. Basically, SLP consist in constructing succesive linear approximations to the original non linear optimization problem within each step. However, the application of SLP may involve important malfunctions. Thus, the solution to the approximated linear problems can fail to exist, or may lead to the highly unfeasible point of the original non linear problem; also, large oscillations often occurs near the optimum, precluding the algorithm to converge. In this paper, we present an improved SLP algorithm with line-search, specially designed for structural optimization problems. In each iteration, an approximated linear problem with aditional side constraints is solved by Linear Programming. The solution to the linear problem defines a search direction. Then, the objetive function and the non linear constraints are quadratically approximated in the search direction, and a line-search in perfomed. The algorithm includes strategies to avoid stalling in the boundary of the feasible region, and to obtain alternate search directions in the case of incompatible linearized constraints. Techniques developed by the authors for efficient high-order shape sensitivity analysis are referenced.Ministerio de Economía y Competitividad; TIC-98-0290Xunta de Galicia; PGIDT99MAR1180

Efficient structural shape optimization: using directional high order sensitivity analysis to improve MP algorithms

6th US National Congress on Computational Mechanics, Dearborn, US