Stiffnessometer, a magnetic-field-free superconducting stiffness meter and its application.

We developed a new method to measure superconducting stiffness $\rho_{s}$, critical current density $J^c$, and coherence length $\xi$ 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 ${\bf J}$ is the current density and ${\bf A}$ is the vector potential. Using a rotor free ${\bf A}$ and a measurement of ${\bf J}$ via the magnetic moment of a superconducting ring, we determine $\rho_{s}$. By increasing $\mathbf{A}$ until the London equation does not hold anymore we determine $J^c$ and $\xi$. The method is sensitive to very small stiffness, which translates to penetration depth $\lambda \lesssim 3$ mm. It is also sensitive to extremely low critical current density $J^c \sim 1$ Acm$^{-2}$ or long coherence length $\xi \sim 1\mu m$. 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 La$_{2-x}$Sr$_{x}$CuO$_{4}$.