Andreev bound states and current-phase relations in three-dimensional topological insulators

To guide the search for the Majorana fermion, we theoretically study superconductor/topological-insulator/superconductor (S/TI/S) junctions in an experimentally relevant regime. We find that the striking features present in these systems, including the doubled periodicity of the Andreev bound states (ABSs) due to tunneling via Majorana states, can still be present at high electron densities. We show that via the inclusion of magnetic layers, this 4π periodic ABS can still be observed in three-dimensional (3D) topological insulators, where finite angle incidence usually results in the opening of a gap at zero energy and hence results in a 2π periodic ABS. Furthermore, we study the Josephson-junction characteristics and find that the gap size can be controlled and decreased by tuning the magnetization direction and amplitude. These findings pave the way for designing experiments on S/3DTI/S junctions.