| dc.description.abstract | The finite element method is used to solve the quasiclassical Usadel equation, valid for diffusive superconducting hybrid systems, in higher dimensions than one. A detailed derivation of the method is given, and it is verified that the results generated are correct by comparing with known solutions. In addition, the numerical routine is applied to several case studies which explore novel phenomena that are intrinsically higher dimensional. Specifically, an analysis of a two dimensional Josephson junction with external flux reveals that vortices present in the system are influenced by the width of the junction and the phase difference between the superconductors, altering both the number of vortices and their positions. Spin-orbit coupling is investigated, where it is found that the symmetries in the induced magnetization and the spincurrents can be predicted. In addition, it is found that spincurrents flow in the system even without any charge current present. Finally, a three dimension model is considered, where superconducting islands are placed on a ferromagnetic substrate with different exchange field distributions. It is found that charge current flowing between the superconductors selects the easiest route, rather than the shortest, avoiding regions of highest magnetization. | |
