Length-scale-dependent vortex-antivortex unbinding in epitaxialBi2Sr2CaCu2O8+δfilms

Abstract

The supercurrent transport properties of epitaxial ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\mathrm{\ensuremath{\delta}}}$ films in zero applied magnetic field were investigated in a temperature interval of \ensuremath{\approx}20 K below the mean-field critical temperature ${T}_{c0}.$ The modification of the shape of the $I\ensuremath{-}V$ curves observed by varying the temperature was explained in terms of vortex-fluctuation-induced layer decoupling and vortex-antivortex unbinding, revealing a strong probing-length dependence. The change of the effective dimensionality of thermally excited vortices involved in the dissipation process leads to the appearance of a few characteristic regions in the current-temperature diagram. Above a temperature value ${T}^{*}<{T}_{c0},$ the superconducting layers are decoupled, as predicted by Monte Carlo simulations and renormalization-group analyses. In this region, the resistivity exhibits two-dimensional (2D) behavior corresponding to the superconducting ${(\mathrm{C}\mathrm{u}\mathrm{O}}_{2}{)}_{2}$ layers (2D-layer behavior). However, the resistive transition seems to be mainly related to the 2D behavior at the film level. In the sensitivity window of our measurements, finite resistance in the limit of small transport currents was detected to occur above a temperature value ${T}_{c}<{T}^{*},$ through the dissociation of vortex-string--antivortex-string pairs. By decreasing the temperature and/or by increasing the transport current, the $I\ensuremath{-}V$ curves in the double logarithmic plot show a clear downward curvature. This can be described in terms of current-induced quasi-2D vortex pair unbinding, with a nonzero critical-current density resulting from the interlayer Josephson coupling. At even lower temperatures and/or higher transport currents, the $I\ensuremath{-}V$ curves exhibit a crossover from quasi-2D to 2D-layer behavior, due to the decrease of the probing length below the Josephson length, where the interlayer Josephson coupling becomes irrelevant. The temperature dependence of the 2D $I\ensuremath{-}V$ exponent is in good agreement with recent Langevin simulations of the Coulomb gas model, revealing an anomalous diffusion of vortex fluctuations.