The two critical temperatures conundrum in La$_{1.83}$Sr$_{0.17}$CuO$_4$ - Abhisek Samanta, Itay Mangel, Amit Keren, Daniel P. Arovas, Assa Auerbach (SciPost Physics, 2024)
The in-plane and out-of-plane superconducting stiffness of ${\rm La}^{\vphantom{\dagger}}_{1.83}{\rm Sr}^{\vphantom{\dagger}}_{0.17}{\rm CuO}^{\vphantom{\dagger}}_4$ 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 ${T_{\rm c}}$, and the out-of-plane stiffness appears to vanish below ${T_{\rm c}}$ by a temperature shift of order $α L_a/{ξ^{\parallel}}$, where $L_a/{ξ^{\parallel}}$ 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 ${T_{\rm c}}$, which is significantly lower than its previously measured value near zero temperature.