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

TL;DR

This paper investigates the discrepancy between in-plane and out-of-plane superconducting stiffness transition temperatures in LSCO, explaining it through Monte Carlo simulations and a small interlayer coupling ratio, revealing a crossover from 3D to quasi-1D behavior.

Contribution

The study introduces a Monte Carlo simulation-based explanation for the critical temperature discrepancy in LSCO, highlighting the role of small interlayer coupling and sample width effects.

Findings

Out-of-plane stiffness vanishes below the thermodynamic transition temperature.

Sample width significantly influences the out-of-plane stiffness transition.

The interlayer coupling ratio $eta$ is extremely small, around 4.1×10^{-5}.

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 $T_{\rm c}$, and the out of-plane stiffness appears to vanish below $T_{\rm c}$ 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 $T_{\rm c}$, which is significantly lower than its previously measured value near zero temperature.