On the Relation Between the Nonlinear Surface Impedance and the Superfluid Current Density in High-Temperature Superconductors

The nonlinear surface impedance is related to a local description of the nonlinear superfluid current density that depends on the condensate velocity, by use of the definition of surface impedance as the ratio between the electric field and magnetic field at the conductor surface. To obtain this relation, we follow a rigorous approach based on the time-domain nonlinear London equations and the two-fluid model. The formulation is compared with harmonic balance simulations of an equivalent transmission line circuit that models a plane wave propagating across a vacuum-superconductor boundary, and shows very good agreement for the resulting surface impedance as a function of current density at the surface.