Vortex dynamics in two-dimensional Josephson junction arrays

In this D.Sc. thesis we have studied the dynamical phenomena of the topological excitations, vortices and antivortices, in two-dimensional (2D) Josephson junction arrays (JJAs) by numerical calculation, analytical analysis and Monte Carlo simulation of XY model. We have restricted our calculations to the case of thermally excited vortices and antivortices in the array of superconducting islands. Both regular and disordered arrays where the particles (vortex and antivortex) move randomly due to the influences of temperature and Coulomb interactions between the charges of the particles have been considered. Our central quantity is the charge density correlator which is related to the charge response function. We have also explained the time evolution of the probability density function which is related to the charge density correlator. In this thesis the dynamics of vortices are explained considering (a) vortices and antivortices to be paired and (b) vortices and antivortices to be free. Both types of dynamics are explained above Berezinskii-Kosterlitz-Thouless (BKT) transition temperature in a 2D JJA. The pair dynamics are explained considering two types of models namely (i) consider in the JJAs there is a distribution of lengths of vortex-antivortex pairs and (ii) consider in the JJAs there is a distribution of pair life times of vortex-antivortex pairs. The free vortex dynamics is explained using a multiple trapping model in a disordered JJA where there are some superconducting sites missing. In both pair and free vortex dynamics we have calculated the mobility of vortices in the JJAs and using this mobility we have calculated several important parameters like dielectric function, flux noise, conductance of the array etc. At the beginning of this project we aimed at understanding the dynamics of thermally created vortices in Josephson junction arrays. We have developped here several approaches. Most of the time we tried to compare our theoretical results with experimental observations available but due to the lack of experimental data for all the details we sometimes had to restrict on only theoretical explanations. We also opened some questions to be solved in coming time. When more and more experimental data will be available our theoretical methodologies can be extended towards more understanding of the dynamics of Josephson junction arrays.

Thèse de doctorat : Université de Neuchâtel : 2004 ; 1764