The two critical temperatures conundrum in La$_{1.83}$Sr$_{0.17}$CuO$_4$

Abstract

The in-plane and out-of-plane superconducting stiffness of La_{1.83}Sr_{0.17}CuO_4La1.83Sr0.17CuO4 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 \alphaα 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}}Tc, and the out-of-plane stiffness appears to vanish below {T_{c}}Tc by a temperature shift of order \alpha L_a/{\xi^{\parallel}}αLa/ξ∥, where L_a/{\xi^{\parallel}}La/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 \alpha=4.1× 10^{-5}α=4.1×10−5, near {T_{c}}Tc, which is significantly lower than its previously measured value near zero temperature.