Theoretical Analysis of Josephson Junction Systems and Superconducting Superlattices.

Superconducting superlattices and Josephson junction networks provide a context for investigation of various problems related to superconductivity. Aspects of the layered nature of high-T_{c} materials, the statistical mechanics of Josephson junction systems, and the response of granular systems in the presence of a magnetic field are explored. Experiments on superlattices with a structure of alternating layers of superconducting { rm YBa_2Cu_3O}_{7-x } and insulating {rm PrBa _2Cu_3O}_{7-x} exhibit a suppression of the resistive transition temperature T_{c}, depending on layer thicknesses. This behavior can be explained by reduction of the bulk T_{c} through charge redistribution into insulating layers, and a further reduction through the Kosterlitz-Thouless nature of the transition, taking place in the effectively two-dimensional superconducting layers. The statistical mechanics of Josephson junction systems must account for their macroscopic quantum nature, and the "unusual constraints" arising from knowledge of superconducting wave function magnitudes in a steady state. Working with the maximum entropy formulation of statistical mechanics, the equivalence of state-probability level and density matrix quantum information entropy maximization is demonstrated; a state-level approach is then used to enforce the unusual constraint, providing an extension of the standard formalism. A novel physical result is predicted, where in equilibrium, the temperature dependence becomes modified from the usual 1/kT factor. Magnetically Modulated Resistance (MMR) techniques are effective in experimentally determining the quality of superconducting samples, in particular when weak links are present in granular materials. The weak link component of the MMR response can be explained using numerical studies of a disordered network of non-ideal Josephson junctions, where the non-linear oscillations in the macroscopic grain phases is simulated, in order to obtain the voltage across the network in the presence of an external magnetic field and applied current. Mesoscopic networks exhibit complex I-V characteristics with multiple branches, and finite size effects, while the typical experimental weak link signal, and its observed shifting behavior with different field strengths, is reproduced with large enough networks.