We provide a detailed account for a method to measure superconducting stiffness ${\rho }_s$, critical current density $j_c$, and coherence length $\xi$, in one apparatus, without subjecting the sample to magnetic field or attaching leads. The method is based on the London equation $\mathbf{j}=-{\rho }_s\mathbf{A}$, where $\mathbf{j}$ is the current density and $\mathbf{A}$ is the vector potential. Using a rotor free $\mathbf{A}$ and a measurement of $\mathbf{j}$ via the magnetic moment of a superconducting ring, we determine ${\rho }_s$. By increasing $\mathbf{A}$ until the London equation fails we determine $j_c$ and $\xi$. The method is sensitive to very small stiffness, which translates to penetration depth $\lambda \lesssim 1$ mm. It is also sensitive to low critical current density $j_c\sim {10}^3{\mathrm{A}\mathrm{mm}}^{-2}$ or long coherence length $\xi \sim 1\mu \mathrm{m}$. Naturally the method does not suffer from demagnetization factor complications, the presence of vortices, or out-of-equilibrium conditions. Therefore, the absolute values of the different parameters can be determined. We demonstrate the application of this method to ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ with $x=0.17$.

中文翻译：

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刚度计：一种无磁场的超导刚度计及其应用

我们详细介绍了一种测量超导刚度的方法 ${\rho }_s$，临界电流密度 ${Ĵ}_C$和相干长度 $\xi$在一台设备中，无需将样品置于磁场或连接导线的情况下。该方法基于伦敦方程$\mathbf{Ĵ}=-{\rho }_s\mathbf{一种}$，在哪里 $\mathbf{Ĵ}$ 是电流密度， $\mathbf{一种}$是矢量势。免费使用转子$\mathbf{一种}$ 和测量 $\mathbf{Ĵ}$ 通过超导环的磁矩，我们确定 ${\rho }_s$。通过增加$\mathbf{一种}$ 直到伦敦方程式失败，我们才能确定 ${Ĵ}_C$ 和 $\xi$。该方法对很小的刚度敏感，这会转化为穿透深度$\lambda \lesssim \mathrm{1个}$ 毫米 它也对低临界电流密度敏感${Ĵ}_C〜{10}^3{\mathrm{一种}\mathrm{毫米}}^{-2}$ 或长相干长度 $\xi 〜\mathrm{1个}\mu \mathrm{米}$。自然，该方法不会受到退磁因子并发症，涡流的存在或不平衡条件的影响。因此，可以确定不同参数的绝对值。我们演示了此方法在${啦}_{2-X}{r}_X{\mathrm{氧化铜}}_4$ 与 $X=0.17$。