The two critical temperatures conundrum in La_1.83Sr_0.17CuO₄

The in-plane and out-of-plane superconducting stiffness of La_1.83Sr_0.17CuO₄ rings appear to vanish at different transition temperatures, which contradicts thermodynamical expectation. In addition, we observe a surprisingly strong dependence of the out-of-plane stiffness transition on sample width. With evidence from Monte Carlo simulations, this effect is explained by very small ratio α of inter-plane over intra-plane Josephson couplings. For three dimensional rings of millimeter dimensions, a crossover from layered three dimensional to quasi one dimensional behavior occurs at temperatures near the thermodynamic transition temperature T_c, and the out-of-plane stiffness appears to vanish below T_c by a temperature shift of order αL_a/ξ^∥, where L_a/ξ^∥ is the sample’s width over coherence length. Including the effects of layer-correlated disorder, the measured temperature shifts can be fit by a value of α = 4.1 × 10^-5, near T_c, which is significantly lower than its previously measured value near zero temperature.