Nonlinear surface impedance in superconductors

Treatments available in the literature of RF nonlinear responses in superconductors have suffered from several deficiencies. First, there is lacking a unified treatment that can be used to both design passive RF devices and analyze the measured responses from them. Second, the figures of merit commonly used to discuss nonlinearities frequently blur the lines between directly measured and inferred quantities. Worse still, these parameters often are misconstrued as being generally meaningful when in fact they are specific to a particular experimental setup. For example, the familiar "surface resistance" is well defined only for a superconducting half space.; This thesis introduces a new and general framework for discussion of nonlinear RF responses as well as a method for extracting true bulk material parameters from measured data. The use of bulk quantities lends itself well to design work and clearly distinguishes between measured and inferred quantities. The method uses complex insertion loss data from a superconducting resonator and compensates for both experimental artifacts and RF current crowding effects.; This method is used to examine measurements performed on several materials using a modified parallel plate resonator technique. The first of these, niobium nitride, serves as a reference study to validate the whole procedure. Next, nonlinear responses in the more technologically interesting high T{dollar}sb{lcub}rm c{rcub}{dollar} materials YBCO and TBCCO are measured and analyzed to uncover the explicit local current dependence of the bulk RF resistivity {dollar}rho{dollar} and inductivity {dollar}{lcub}cal L{rcub}{dollar} with an eye to shedding light on which of a number of possible physical mechanisms underlies the nonlinear response.; Data from YBCO films indicate a slight J{dollar}sp1{dollar} dependence of both {dollar}{lcub}cal L{rcub}{dollar} and {dollar}rho{dollar} at low current densities. By contrast, data from TBCCO films show extremely large J{dollar}sp1{dollar} nonlinearities in these channels. In addition, the data from YBCO indicate that the nonlinearities, whatever their precise origins, are close to the fundamental lower limit due to depairing while the same is not true of these effects in TBCCO, which are most likely due to vortex motion. The results of the reference study of NbN films showed J{dollar}sp2{dollar} dependencies of {dollar}{lcub}cal L{rcub}{dollar} and {dollar}rho{dollar} consistent with Ginzburg-Landau theory.