An investigation of granular behavior in the DC and microwave electronic transport properties of both a conventional and a high-temperature superconductor

Microwave surface resistance, R{dollar}rmsb{lcub}s{rcub}{dollar}(T,B), and dc resistivity and measurements, were used to compare NbN, a conventional superconductor, with {dollar}rm Smsb{lcub}2-x{rcub}Cesb{lcub}x{rcub}CuOsb{lcub}4-y{rcub},{dollar} a high-temperature superconductor, as a function of temperature (T) and magnetic field (B). A novel granular model for R{dollar}rmsb{lcub}s{rcub}{dollar}(T,B) is used both to confirm the granular make-up and to quantify the electrodynamic properties for both superconductors. Unlike {dollar}rm Smsb{lcub}2-x{rcub}Cesb{lcub}x{rcub}CuOsb{lcub}4-y{rcub}{dollar} (T{dollar}rmsb{lcub}c{rcub}{dollar} = 27.5 K) which exhibits a resistive transition which is field-broadened, NbN (T{dollar}rmsb{lcub}c{rcub}{dollar} = 16.1K) exhibits a resistive transition which is primarily field-shifted. In order to describe this feature, an extension to the Coffey-Clem theory of surface resistance which incorporates a critical temperature that is field-dependent is employed. Fitting the R{dollar}rmsb{lcub}s{rcub}{dollar}(T,B) data determined, among other parameters, the zero-temperature upper critical field parallel to the plane {dollar}(Bsbsp{lcub}c20{rcub}{lcub}a-b{rcub}){dollar} to be 84 T and 45 T for {dollar}rm Smsb{lcub}1.85{rcub}CeOsb{lcub}0.15{rcub}CuOsb{lcub}4-y{rcub}{dollar} and NbN respectively.; The complex conductivity ({dollar}sigma=sigmasb1+isigmasb2){dollar} of both NbN and {dollar}rm Smsb{lcub}1.85{rcub}Cesb{lcub}0.15{rcub}CuOsb{lcub}4-y{rcub}{dollar} were determined from a fit of the complex penetration depths given by the extended Coffey-Clem theory. These results indicated that the field-shifting behavior seen in {dollar}Rsb{lcub}s{rcub}{dollar} for NbN and the field-broadening behavior seen in {dollar}Rsb{lcub}s{rcub}{dollar} for {dollar}rm Smsb{lcub}1.85{rcub}Cesb{lcub}0.15{rcub}CuOsb{lcub}4-y{rcub}{dollar} are also manifested in the conductivities. These conductivities are plotted as a function of both T and B and reveal the anisotropy and Lorentz-force dependance of both superconductors.; That a single granular model for surface resistance, appropriately modified to account for the polycrystalline character of the {dollar}rm Smsb{lcub}2-x{rcub}Cesb{lcub}x{rcub}CuOsb{lcub}4-y{rcub}{dollar} samples and the film thickness the depression of T{dollar}rmsb{lcub}c{rcub}{dollar} with field in the NbN samples, could describe the behavior of such disparate superconductors as {dollar}rm Smsb{lcub}1-x{rcub}Cesb{lcub}x{rcub}CuOsb{lcub}4-y{rcub}{dollar} and NbN--and in addition to previous successful fits of BSCCO and YBCO--is further evidence for a granular nanostructure in superconductivity.