Critical current density and third-harmonic voltage in superconducting films

When a sinusoidal drive current I0 cos ωt flows in a small coil close to the surface of a superconducting film, third-harmonic voltage V3 cos(3ωt+θ3) is induced in the coil if the film causes a nonlinear response. We have developed an approximate theoretical method yielding the relationships among I0, V3, and θ3, thus providing the scientific basis for a widely used inductive method for measuring the critical current density Jc in large-area superconducting films. Our results show that V3 is near zero when I0 is smaller than a threshold value Ic0∝Jcd, where d is the film thickness. When I0>Ic0, on the other hand, the third-harmonic voltage is expressed as V3 exp(−iθ3)=ωIc0G(I0/Ic0), where G(x) is a scaling function determined by the configuration of the coil. We demonstrate the scaling law of V3/Ic0 vs I0/Ic0 in a YBa2Cu3O7−δ film.