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 LSCO 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 $\alpha$ of interplane over intraplane superconducting stiffnesses. 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 $T_{\mathrm{c}}$, and the out of-plane stiffness appears to vanish below $T_{\mathrm{c}}$ by a temperature shift of order $\alpha L_a/{\xi }^{\parallel }$, where $L_a/{\xi }^{\parallel }$ is the sample's width over coherence length. Including the effects of layer-correlated disorder, the measured temperature shifts can be fit by $\alpha =4.1\times 10^{-5}$ near $T_{\mathrm{c}}$, which is significantly lower than its previously measured value near zero temperature.

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