Topological Defects in Anisotropic Multicomponent Superconductors

Ginzburg-Landau (GL) theory provides a phenomenological description of superconductors. We study one and two-dimensional topological solitons in unconventional superconductors that can be described by anisotropic multicomponent GL theory. The conventional ansatz, used for isotropic superconductors, fixes the direction of the (internal) magnetic field. However, anisotropy breaks rotational symmetry thus this ansatz is inconsistent with the three-dimensional GL equations. We consider a consistent ansatz that allows the direction of the magnetic field to freely change throughout the superconductor. This introduces novel magnetic phenomena such as magnetic field twisting which we study in p+ip, s+is and s+id superconductors. For domain walls, anisotropy means that changing the orientation of this one-dimensional topological soliton (within a three-dimensional sample) affects its physical properties. Spontaneous magnetic fields occur that can vanish and even change direction (or twist) away from the domain wall for some orientations, providing a way to distinguish between types of superconductors. For s+is and s+id superconductors we find novel types of domain walls that are not degenerate in energy. By linearising the GL equations we are able to predict and observe the oscillatory decay of solutions of the full nonlinear theory. Additionally, we are able to predict magnetic field twisting from the linearisation. This also occurs in the Meissner state but now, due to anisotropy, depends on the direction of the applied magnetic field. Using the consistent ansatz we study vortices in anisotropic superconductors. We consider the orientation dependence of field configurations which we classify. Magnetic field twisting also occurs for some orientations. Finally, we study vortex lattices in an external magnetic field, allowing us to determine the upper and lower critical fields as well as finding the unit cell shape that minimises energy for a given value of the external magnetic field.