Crossover effects and finite-size scaling on the temperature dependence of paraconductivity in YBa2Cu3O6.9 and Bi2Sr2CaCu30x compounds

An investigation into the superconducting order parameter thermodynamic fluctuations and their manifestations on paraconductivity in cuprate superconductors is done using a renormalized Gaussian approach based on the Ginzburg–Landau theory. The temperature dependence of paraconductivity is affected by repulsive interactions between Cooper pairs and does not follow the universal power laws predicted by the conventional Aslamazov–Larkin theory. In addition to the well known Lawrence–Doniach crossover from three to two dimensions, we also highlight the crossover from one-dimensional to two-dimensional behavior and the crossover from weak two-dimensional to strong two-dimensional critical behavior in the vicinity of the critical temperature. These dimensional crossovers result from the resistance between Cooper pairs due to critical and thermal fluctuations which cause a transition from a metastable state to one with a smaller current. Two illustrative examples (the cases of ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.9}$ and ${\mathrm{Bi}}_2{\mathrm{Sr}}_2\mathrm{Ca}{\mathrm{Cu}}_3{\mathrm{0}}_x$ compounds) are provided in support of the analysis, so as to demonstrate the usefulness of the approach.