Novel Majorana mode and magnetoresistance in ferromagnetic superconducting topological insulator

Among the potential applications of topological insulators, we investigate theoretically the effect of coexistence of proximity-induced ferromagnetism and superconductivity on the surface states of 3-dimensional topological insulator, where the superconducting electron-hole excitations can be significantly affected by the magnetization of ferromagnetic order. We find that, Majorana mode energy, as a verified feature of TI F/S structure, along the interface sensitively depends on the magnitude of magnetization mzfs in FS region, while its slope in perpendicular incidence presents steep and no change. Since the superconducting gap is renormalized by a factor η(mzfs), hence Andreev reflection is more or less suppressed, and, in particular, resulting subgap tunneling conductance is more sensitive to the magnitude of magnetizations in FS and F regions. Furthermore, an interesting scenario happens at the antiparallel configuration of magnetizations mzf and mzfs resulting in magnetoresistance in N/F/FS junction, which can be controlled and decreased by tuning the magnetization magnitude in FS region.