Mesoscopic thin film superconductors - A computational framework

Motivated by experiments on superconductors in the microscopic regime and the realization of small superconducting devices such as qubits, we initiate a computational project in the form of a numerical simulation package to model and predict the behavior of these type of systems. It is a multidisciplinary endeavor in that it employs theory, computational science, software design, and to some extent new visualization techniques. Our intention is to create a flexible and modular code library which is capable of simulating a wide variety of superconducting systems, while significantly shortening the startup time for computational projects. We base the numerical model in quasiclassical theory with the Eilenberger transport equation, and execute the highly parallel computations on a contemporary graphics card (GPU). In this thesis we touch on the theoretical background, describe the discretization of the theory, and present a thorough overview on how to solve the equations in practice for a general 2-dimensional geometry, as well as review the design principles behind the developed software. Moreover, a few selected results are presented to show that the output is sound, and to highlight some new findings. In paper I we examine a new low temperature phase in which spontaneous edge currents emerge in a d-wave superconducting square grain, breaking time-reversal symmetry. The modeling of such a system is made possible by our development of a simulation domain description which allows for specular boundary conditions in an arbitrarily shaped geometry.