The nature of the phase transition in the cuprates as revealed by a magnetic field free stiffness meter

Abstract

A new method to measure the superconducting stiffness tensor ${\overline{\rho }}_s$, without subjecting the sample to magnetic field, is applied to La${}_{1.875}$Sr${}_{0.125}$CuO${}_4$ (LSCO). The method is based on the London equation $\mathbf{J}=-{\overline{\rho }}_{\mathbf{s}}\mathbf{A}$, where $\mathbf{J}$ is the current density and $\mathbf{A}$ is the vector potential. Using rotor free $\mathbf{A}$ and measuring $\mathbf{J}$ via the magnetic moment of superconducting rings, we extract ${\overline{\rho }}_s$ at $T\to T_c$. The technique, named Stiffnessometer, is sensitive to very small stiffness, which translates to penetration depth on the order of a few millimeters. We apply this method to two different LSCO rings: one with the current running only in the CuO${}_2$ planes, and another where the current must cross planes. We find different transition temperatures for the two rings, namely, there is a temperature range with two dimensional stiffness. The Stiffnessometer results are accompanied by Low Energy $\mu$SR measurements on the same sample to determine the stiffness anisotropy at $T<T_c$.