Magnetization dynamics and Majorana fermions in ferromagnetic Josephson junctions along the quantum spin Hall edge

We investigate the interplay between ferromagnetic and superconducting order at the edge of a quantum spin Hall insulator. Using complementary analytical and self-consistent numerical approaches, we study a ferromagnetic Josephson junction and show how the direct coupling between magnetism and the superconducting U(1) phase gives rise to several unusual phenomena which distinguishes the present system from its nontopological equivalent. In particular, we demonstrate how the anomalous current-phase relation triggers supercurrent-induced magnetization dynamics and also study the spatial localization of the Majorana fermions appearing in the junction.