Stiffnessometer: A magnetic-field-free superconducting stiffness meter and its application

We provide a detailed account for a method to measure superconducting stiffness ρs, critical current density jc, and coherence length ζ, in one apparatus, without subjecting the sample to magnetic field or attaching leads. The method is based on the London equation j=-ρsA, where j is the current density and A is the vector potential. Using a rotor free A and a measurement of j via the magnetic moment of a superconducting ring, we determine ρs. By increasing A until the London equation fails we determine jc and ζ. The method is sensitive to very small stiffness, which translates to penetration depth λ≲ 1 mm. It is also sensitive to low critical current density jc∼103Amm-2 or long coherence length ζ∼1μm. 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 La2-xSrxCuO4 with x=0.17.