A study of proximity-induced and magnon-mediated superconductivity on the surface of topological insulators

This thesis presents a study of superconducting phases in different effectively two-dimensional (2D) systems with spin-orbit coupling, with particular emphasis on systems consisting topological insulators (TIs) in proximity to superconductors (S) and magnetic insulators. The research has led to five papers. The first paper examines the possible superconducting phases in a 2D repulsive Hubbard model with Zeeman splitting and Rashba spin-orbit coupling, showing that the Kohn-Luttinger mechanism is responsible for the effective attractive pairing. The spin-orbit coupling, however, indirectly affects the symmetry of the order parameter, leading to a chiral p ± ip or p state depending on the orientation of the Zeeman field. Two papers consider the proximity effect between a superconductor and topological insulator, and the interplay with exchange fields. When a spin valve is placed on top of a TI Josephson junction, we find that vortices can be induced on the surface of the TI depending on the spin valve configuration. We also study the possibility of a strong inverse proximity effect — a significant reduction in the superconducting gap — in an S-TI bilayer, finding that this is unlikely for a conventional s-wave superconductor, but might occur in unconventional superconductors with low Fermi energies. The final two papers examine superconductivity mediated by magnons on the surface of a TI coupled to a magnetic insulator. When neglecting the frequency dependence of the magnons we find that, depending on the coupling between the magnons, both BCS type and Amperean p-wave pairing is possible. Including the magnon frequency dependence, we also find the possibility of odd-frequency s-wave Amperean pairing.