Studies of a Ginzburg-Landau model for d-wave superconductors

In this paper, we study a recently proposed Ginzburg-Landau-type model for some high-T-c superconductors with d-wave pairing symmetry. The scalar comp lex order parameter used in the conventional Ginzburg-Landau models for low -T-c superconductors is replaced by a multicomponent complex order paramete r, and the free energy functional is modified accordingly to account for th e symmetry properties in the setting of the d-wave pairing. A brief introdu ction to the physical and mathematical background of the d-wave models is p rovided first. We then present some rigorous mathematical analysis and disc uss the relation between the new model and the conventional Ginzburg{Landau models. Various limiting cases such as the high-kappa, high-field regime a re examined. Numerical methods for the approximations of the new model are also considered along with results from numerical simulations that illustra te the complex structures for isolated vortices, vortex lattices and vortex motion driven by the applied current in the context of d-wave models.