The stiffnessometer: a magnetic-field-free superconducting stiffness meter, and its application to the cuprates

We developed a new method to measure the stiffness $\rho_{s} $ of a superconductor without applying magnetic field. The method is based on the London equation ${\rm {\bf J}}=-\rho_{s} {\rm {\bf A}}$, where ${\rm {\bf J}}$ is the current density and ${\rm {\bf A}}$ is the vector potential. Using a rotor free ${\rm {\bf A}}$ and a ${\rm {\bf J}}$ measurement we determine $\rho_{s} $. We apply the method to La$_{\mathrm{2-x}}$Sr$_{\mathrm{x}}$CuO$_{\mathrm{4}}$ and find some surprising results.